Physics Unit 4: Static and Current Electricity PDF

Unit 4 Static and Current Electricity Introduction Physical phenomenon associated with the presence and flow of electric charge is known as electricity. In Ethiopia and elsewhere around the world, people depend on electricity to provide power for most appliances in the home, at work and out in the world in general. For example, lights, electric heating and electric stoves that you use in your home all depend on elec- Brain storm- tricity to work. To realize just how big impact electricity has on our daily ing question lives, just think about what happens when there is a power failure. Thus, What constitutes electricity has an important place in modern society. It is a controllable electricity? and convenient form of energy for a variety of uses in homes, schools, industries and so on. In this unit, you will learn topics related to electricity. By the end of this unit, you should be able to: understand the basic properties of electric charge; explain the charging and discharging processes; have a conceptual understanding of an electrical force; understand the concept of an electric field; understand the relationship among voltage, current and resistance; describe arrangement of resistors in a circuit; apply the concept of electricity in solving real life problems. 91 92 Unit 4 Static and Current Electricity 4.1 Charges in Nature By the end of this section, you should be able to: distinguish between the two types of electric charges; show that the total electric charge in an isolated system is conserved; use conservation of charge to calculate quantities of charge trans- ferred between objects. Objects surrounding us (including people) contain large amounts of elec- tric charge. There are two types of electric charge: positive charge and negative charge. Protons have a positive charge, and electrons have a negative charge. If the same amounts of negative and positive charge are brought together, they neutralize each other and there is no net charge. Positive and negative charges are present in neutral objects, but their num- bers are equal. However, if there is a little bit more of one type of charge than the other, then the object is said to be electrically charged. Exercise 4.1 When do you Unit of Charge say that a body The SI unit of electric charge is Coulomb (C). One coulomb (1 C) of charge is charged posi- is carried by 6.25 × 1018 electrons. An electron possesses a negative charge tively? of 1.6 × 10−19 C. In electrostatics, you often work with charge in micro Coulombs (1µC = 1 × 10−6 C) and nano coulombs (1nC = 1 × 10−9 C). Key Concept Conservation of Charge If an object gains electrons, During electrification, electric charges are neither created nor destroyed, it becomes nega- but are transferred from one material to another. This is called the law tively charged; if of conservation of charge. There are some practical examples of charge it loses electrons, transfer from one material to another. For example, have you ever seen it becomes posi- the old comb and hair trick where your hair rises and sticks to the comb? tively charged. This arises because of the simple conservation of charge, i.e., the transfer of charge either from the comb to the hair or vice versa. Thus, the total 4.1 Charges in Nature 93 charge in an isolated system never changes. By isolated, you mean that no particles are allowed to cross the boundary of the system. Exercise 4.2 Quantization of charge A conductor possesses a pos- The smallest charge that is possible to obtain is that of an electron or itive charge of proton. The magnitude of this charge is denoted by e. Charge is said to 3.2 × 10−19 C. be quantized when it occurs as the integral multiples of e. This is true for How many elec- both negative and positive charges and is expressed as; trons does it have in excess q = ne where n is positive or negative integer. (4.1) or deficit (use: e = 1.60 × 10−19 Section summary C)? There are two types of electric charges: positive and negative. Neutral objects have equal number of positive and negative charges. The total electric charge in an isolated system, that is, the algebraic sum of the positive and negative charges present at any time, does not change. Electric charges are quantized, occurring only in discrete amounts. Review questions 1. What are the different types of charges that exist in nature? 2. When do you say that a body is negatively charged? 3. What does the law of conservation of charges say? 4. What does it mean by quantization of a charge? 5. Write the properties of electric charges. 94 Unit 4 Static and Current Electricity 4.2 Methods of Charging a Body By the end of this section, you should be able to: demonstrate different charging processes; explain the results of different charging processes. In the previous section, you discussed that charges are transferred from one body to another by a process known as charging. Charging is the process of electrifying bodies, by removing or adding charges. Activity 4.1 The following are the different methods of charging a body: In groups, try i Charging by rubbing to think of the different ways of ii Charging by conduction charging a body? iii Charging by induction Charging by rubbing Charging by rubbing occurs when two different neutral materials are rubbed together and electric charges are transferred from one object to the other. Some materials, such as silk are more likely to attract extra electrons and become negatively charged, where as others, such as glass and ebonite rod, are more likely to give electrons and become positively charged. This is because some kinds of atoms are more strongly attracted Figure 4.1 (a) The comb and to electrons than others. For example, in Figure 4.1 (a), the hair and the the hair are both neutral. (b) Af- comb are both neutral. When they are rubbed together, the atoms in the ter being rubbed together, the comb gain electrons and the atoms in the hair lose electrons (Figure 4.1 comb is negatively charged and the hair is positively charged. (b)). Due to this, the comb attracts tiny pieces of paper. 4.2 Methods of Charging a Body 95 Activity 4.2 Exercise 4.3 Tear a piece of paper into several small pieces. Charge a plastic pen Charge an object and two other objects by rubbing them on your hair or on some by friction and fabric. Bring each charged object near the pieces of paper. bring it near a (a) Describe what you observe, listing the three materials you stream of smoke charged. rising from a (b) Why are the pieces of paper attracted to the charged object? wooden splint. (c) Why do some pieces of paper fall off your charged objects after a What do you see? short while? Explain why it happens. (d) When using a conducting sphere with a large charge, the paper "jumps" off instead of falling. Explain why this happens. Key Concept Charging by Charging by Conduction rubbing leaves the two bodies with Charging by conduction occurs when a charged object make contact with a an opposite sign neutral object. Figure 4.2 depicts the use of a positively charged aluminum of charges. plate being touched by a neutral metal sphere. A positively charged alu- minum plate has an excess of protons. When looked at from an electron perspective, a positively charged aluminum plate has a shortage of elec- trons. So when the positively charged aluminum plate is touched to the neutral metal sphere (Figure 4.2 (b)), countless electrons on the metal sphere migrate towards the aluminum plate. There is a mass migration of Key Concept electrons until the positive charge on the aluminum plate-metal sphere system becomes redistributed. Having lost electrons to the positively Charging by conduction charged aluminum plate, there is a shortage of electrons on the sphere leaves the charged body and the uncharged body with the same sign of charge but a weaker strength than the original object. Figure 4.2 Charging by conduction. 96 Unit 4 Static and Current Electricity and an overall positive charge as shown in Figure 4.2 (c). The aluminum plate is still charged positively; only it now has less excess positive charge than it had before the charging process began. This process is called charging by conduction, or "by contact" and the two rods end up with the same sign on charge. Charging by Induction Charging by induction is a process where the charged object is held near to an uncharged conductive material that is grounded on a neutrally charged material. When a charge flows between two objects and the uncharged conductive material develops a charge with the opposite polarity. Figure 4.3 Charging by induction. In Figure 4.3, a negatively charged ebonite rod is brought close to, but does not touch a neutral metal sphere. In the sphere, the free electrons closest to the rod move to the other side, as part (a) of the drawing indicates. Key Concept As a result, the part of the sphere closer to the rod becomes positively Charging by in- charged and the opposite part becomes negatively charged. If the rod were duction leaves the removed, the free electrons would return to their original places, and the charged body and charged regions would disappear. Under most conditions the earth is a the uncharged good electrical conductor. So when a metal wire is attached between the body with the sphere and the ground, as in Figure 4.3 (b), some of the free electrons leave opposite sign of the sphere and distribute themselves over the much larger earth. If the charge. grounding wire is then removed, followed by the ebonite rod, the sphere is left with a positive net charge, as part (c) of the picture shows. 4.3 The electroscope 97 Section summary Charging is the process of supplying the electric charge (elec- trons) to an object or losing the electric charge (electrons) from an object. An uncharged object can be charged in different ways: charg- ing by rubbing, conduction and induction. Review questions 1. State the three methods of charging a body. 2. Describe how uncharged objects can be charged by contact and rubbing. 4.3 The electroscope By the end of this section, you should be able to: Exercise 4.4 describe the function of an electroscope; What do you think about the use a simple electroscope to detect charges; purpose of an make a simple electroscope out of locally available materials. electroscope? The electroscope is a very sensitive instrument which can be used to de- Key Concept tect the type of electric charge, to identify whether an object is charged For detecting or not, to measure the quantity of charge and to know whether an object the presence of is conductor or insulator. It consists of a glass container with a metal rod a charge on the inside that has two thin pieces of gold foil attached. The other end of the body, you use metal rod has a metal plate attached to it outside the glass container. A the collapsing diagram of a gold leaf electroscope is shown in Figure 4.4. or diverging of the leaf of the When a charged object, like the positively charged rod in Figure 4.4 is electroscope. brought close to (but not touching), the neutral metal plate of the elec- 98 Unit 4 Static and Current Electricity Figure 4.4 Charging an electroscope. troscope, the negative charge in the gold foil, metal rod, and metal plate would be attracted to the positively charged rod. The charge can move freely from the foil up the metal rod and onto the metal plate because the metal (gold is a metal too) is a conductor. There is now more negative charge on the plate and more positive charge on the gold foil leaves. This is called inducing a charge on the metal plate. It is important to remember that the electroscope is still neutral; the charges have just been induced to move to different parts of the instrument. The induced positive charge on the gold leaves forces them apart since like charges repel. This is how you can tell that the rod is charged. When the rod is now moved away from the metal plate, the charge in the electroscope spreads out evenly again, and the leaves will fall down again because there is no longer an induced charge on them. 4.4 Electrical Discharge 99 Activity 4.3 Section summary Based on what An electroscope is a device that is used to detect the presence you have learnt of an electric charge on a body. here, try to design or construct a sim- Review questions ple electroscope in groups using 1. What is the function of an electroscope? easily available 2. How do you know that whether or not an electroscope is materials. charged? Exercise 4.5 Can a charged 4.4 Electrical Discharge object become neutral again? By the end of this section, you should be able to: explain the nature of electric discharge; describe how lightning happens; Key Concept list the importance of grounding. Once an ob- ject is charged, So far, you have learnt about the techniques of charging a material. There is the charges are also a technique for removing the excess electric charges from the charged trapped on it objects. This process of removing electric charges from a charged body until they are is called discharging. A charged body can be made to lose its charges given a path to by touching it with a conductor. When a body is discharged, it becomes escape. When neutral. electric charges are transferred Lightning very quickly, the process is called Lightning is a very large electrical discharge caused by induction. In a an electrical dis- thunderstorm, a charged area, usually negative, builds up at the base of a charge. Sparks cloud (Figure 4.5 (a)). The negative charge at the base of the cloud creates are an example a temporary positively charged area on the ground through the induc- of electrical dis- tion process (Figure 4.5 (b)). When enough charge has built up, a path of charge. charged particles is formed (Figure 4.5 (c)). The cloud then discharges its 100 Unit 4 Static and Current Electricity excess electrons along the temporary path to the ground, creating a huge spark (Figure 4.5 (d)). This discharge also causes a rapid expansion of the air around it, causing thunder. Activity 4.4 Air is normally an insulator. If it were not, lightning would occur every time that cloud formed. For lightning to happen, charges in the clouds Lightning are a must build up to the point where the air cannot keep them separated from common expe- the ground. Then, the air stops being an insulator and becomes a fair rience during rainy season. But, conductor, resulting in a lightning strike. how it is formed? Discuss in groups. One way to avoid the damage caused by electric discharges is to make the excess charges flow harmlessly into the Earth’s surface. The Earth is a donator or receiver of charge and is so large that, overall it is not affected by the electron transfer of huge lightning strikes. So, it can absorb an Activity 4.5 enormous quantity of excess charge. As a result, the ground is always considered neutral. In your commu- nity, what did The process of providing a pathway to drain excess charge into the earth people do when they encountered is called grounding. The pathway is usually a conductor such as a wire a person struck by or a pipe. You might have noticed lightning rods at the top of buildings lightning? Have and towers. A lightning conductor is often fitted to the top of a building you observed that they bury some parts of the person’s (usually below the neck) in the ground? Figure 4.5 Lightning is an atmospheric electrical discharge. 4.4 Electrical Discharge 101 to help discharge the clouds safely. These rods are made of metal and are connected to metal cables that conduct electric charge into the ground if the rod is struck by lightning. The idea is that it should get struck before Exercise 4.6 the building and conduct the surge of charge harmlessly into the Earth’s Have you ever surface. heard of someone being killed by Most lightning deaths and injuries occur outdoors. If you are outside and lightning? can see lightning or hear thunder, take shelter indoors immediately. If you cannot go indoors, you should take these precautions: avoid high places and open fields; stay away from tall objects such as trees, flag poles, or light towers; and avoid objects that conduct current such as bodies of water, metal fences, picnic shelters, and metal bleachers. It is very rare that people are struck by lightning, and certainly you will Exercise 4.7 not be struck while you are inside a car or in an airplane. The metal shell Would you please around you would divert charges away. add any other mechanisms that Section summary you know to make peoples safe from Lightning is a gigantic (very large) discharge between clouds lightning? and the earth, or between the charges in the atmosphere and the earth. Review questions 1. Describe the terms "charging" and "discharging". 2. Explain what causes the lightning that is associated with a thunderstorm. 3. What is grounding? 102 Unit 4 Static and Current Electricity Exercise 4.8 4.5 Coulomb’s law of electrostatics You might already By the end of this section, you should be able to: know that like charges repel state Coulomb’s laws of electrostatics; each other and find the magnitude of electric force between two charges using unlike charges Coulomb’s law. attract each other. But have you The magnitude of the forces between charged spheres was first investi- taken a minute gated quantitatively in 1785 by Charles Coulomb (1736-1806), a French to wonder how scientist. He observed that the electrostatic force between the two charges strong these is proportional to the product of the charges and is inversely proportional forces are? to the square of their distance apart. Coulomb’s law can be stated in mathematical terms as 1 F ∝ q 1 q 2 , F∝ (4.2) r2 q 1 q 2 F∝ r2 Figure 4.6 (a) Attractive and where F is the magnitude of the electric force between the two charges q 1 (b) repulsive electrostatic force and q 2 , and r is the distance between the two charges. between two charges. You can convert the above proportionality expression to an equation by Key Concept writing q 1 q 2 The electro- F =k (4.3) static force ex- r2 2 1 erted by a point where, k = 4π o ≈ 9 × 109 NCm2 is the electrostatic constant; 2 charge on a test o = 8.85 × 10−12 NCm 2 is called permittivity of free space. charge at a dis- tance r depends The SI unit of force is the Newton. The electrostatic force is directed along on the charge of the line joining the charges, and it is attractive if the charges have unlike both charges, as signs and repulsive if the charges have like signs. Figure 4.6 shows the well as the dis- attractive and repulsive electrostatic forces. tance between the two. 4.5 Coulomb’s law of electrostatics 103 Example 4.1 Charges q 1 = 5.0µC and q 2 = −12.0µC are separated by 30 cm on the x-axis. What is the magnitude of the force exerted by the two charges? Solution: You are given q 1 = 5.0µC , q 2 = −12.0µC and r = 30 cm. You want to find the magnitude of the force F. Using Coulomb’s law, 2 q 1 q 2 9 × 109 NCm2 (5 × 10−6 C )(−12 × 10−6 C ) F =k = = 6.0 N r2 (0.3m)2 Since the two charges are of opposite sign, the force between the charges is an attractive force. Section summary The force between two point charges is directly proportional to the magnitude of each charge. inversely proportional to square of the separation between their centers. directed along the line joining their centers. Review questions 1. Two charges 1 C and - 4 C exist in the air. What is the direction of the force between them? 2. Two charges q 1 = 2 × 10−6 C and q 1 = −4 × 10−3 C are placed 30 cm apart. Determine the magnitude and direction of the force that one charge exerts on the other. 104 Unit 4 Static and Current Electricity 4.6 The electric field By the end of this section, you should be able to: state the meaning of an electric field; distinguish the elements that determine the strength of the electric field at a given location; Exercise 4.9 What do you think show electric field lines diagrammatically; is the definition calculate the strength of an electric field. for an electric field? An electric field is a region where an electric charge experiences a force, just as a football field is an area where the game is played. Electric field lines are an excellent way of visualizing electric fields. They were first introduced by Michael Faraday. The space around a charge or an arrangement of charges differ from space in which no charges are present. You can test whether a space has an electric field by bringing a small, point positive charge q o into the space. If q o experiences an electric force, then there is an electric field. If no force is experienced, then there is no electric field. For this reason, the small charge is called a test charge: it tests for the existence of electric fields. It has to be small so that its presence does not disturb the electric field it is Key Concept trying to detect. Figure 4.7 shows the electric field lines of a positively and negatively charged body. A test charge is a positive electric charge whose charge is so small that it does not significantly dis- turb the charges that create the electric field. Figure 4.7 Electric field lines from positive and negative charges. 4.6 The electric field 105 Figure 4.8 Electric field lines between (a) similar charges (b) opposite charges. Properties of electric field lines The field lines never intersect or cross each other. The field lines are perpendicular to the surface of the charge. The magnitude of the charge and the number of field lines are pro- portional to each other. Field lines originate at a positive charge and terminate at a negative charge. The lines of force bend together when particles with unlike charges attract each other. The lines bend apart when particles with like Key Concept charges repel each other. This is clearly indicated in Figure 4.8 The magnitude is the force of E per unit charge Electric Field Strength and its direction (i.e., is that of F The strength of the electric field, E, at any point in space is equal to the the direction of force per unit charge exerted on a positive test charge. Mathematically, the force which F acts on a positive E= or F = Eq (4.4) charge). q 106 Unit 4 Static and Current Electricity is a vector. If q is positive, the electric field E Thus, E has the same direction as the force acting on the charge. If q is negative, the direction of E is . On the other hand, the SI unit of electric opposite to that of the force F field is Newton per Coulomb ( N C ). Electric field strength due to a point charge In order to measure the electric field in a given region, you introduce a test charge and measure the force on it. However, you should realize that the test charge q o exerts forces on the charge that produce the field, so it may change the configuration of the charges. Since the electric field is force per unit charge, you divide the force by the charge q o to obtain the field due to q at the location of q o. That is q q F k ro2 q qo q E= = =k 2 where F = k (4.5) Figure 4.9 Electric field at a qo qo r r2 distance r from a charge. The above equation gives the field arising due to the charge q at any Exercise 4.10 location which is at a distance r from q. The direction of the field is taken as the direction of the force that is exerted on the positive charge. Thus, What is the the electric field extends radially from a positive charge and inwards from direction of the electric field due a negative point charge. to a positive pont charge? Example 4.2 Calculate the strength and direction of the electric field E due to a point charge of 2.0 nC at a distance of 5.0 mm from the charge. Solution: In this example q = 2.00 × 10−9 C and r = 5.00 × 10−3 m. You want to find the magnitude and direction of the electric field. You can find the electric field created by a point charge using the equation q E =k r2 4.7 Electric circuits 107 Substituting those values into the above equation gives 2 Nm 2.00 × 10−9C N E = 9 × 109 2 −3 2 ≈ 7.2 × 105 C (5.00 × 10 m) C This electric field strength is the same at any point 5.00 mm away from the charge q that creates the field. It is positive, meaning that it has a direction pointing away from the charge q. Section summary A test charge is a positive electric charge whose charge is so small that it does not significantly disturb the charges that create the electric field. Electric field lines are directed radially outward from a positive charge and directed radially inward towards a negative charge. Review questions 1. What is an electric field line? 2. What is the magnitude and direction of the force exerted on a 3.50µ C charge by a 250 N/C electric field that points due East? 3. Calculate the magnitude of the electric field 2.00 m from a point charge of 5.00 mC. 4.7 Electric circuits Activity 4.6 What do you think By the end of this section, you should be able to: are the differences define what an electric circuit is; between an open and closed cir- describe the components of a simple circuit; cuits? Discuss in sketch an electric circuit diagram. groups. 108 Unit 4 Static and Current Electricity When a wire connects the terminals of the battery to the light bulb, as shown in Figure 4.10, charges built up on one terminal of the battery have a path to follow to reach the opposite charges on the other terminal. The charge that flows around a circuit is carried by electrons. The charges moving through the wire cause the filament to heat up and then give off light. Together, the bulb, battery, switch, and wire form an electric circuit. Thus, an electric circuit is a path through which charges can flow. A schematic diagram for a circuit is sometimes called a circuit diagram. Any element or group of elements in a circuit that dissipates energy is called a load. A simple circuit consists of a source of potential difference and electrical energy, such as a battery, and a load like a bulb or group of Figure 4.10 Simple electric bulbs. Because the connecting wire and switch have negligible resistance, circuit. you will not consider these elements as part of the load. For the simple circuit shown in Figure 4.11 (a), a closed path is formed by wires connected to a light bulb and to a battery. As long as there is a closed path for electrons to follow, electrons can flow in a circuit. They move away from the negative battery terminal and toward the positive terminal. Thus, electric charge flows in the circuit as long as none of the wires, including the glowing filament wire in the light bulb, are disconnected or broken. Figure 4.11 (a) Closed circuit Such a circuit is called a closed circuit. (b) open circuit. If the circuit is broken anywhere (or the switch is turned off), the charge Key Concept stops flowing and the bulb does not glow. Thus, without a complete path, A physical cir- there is no charge flow and therefore no current. This situation is an open cuit is the electric circuit. If the switch in Figure 4.11 were open, as shown in Figure 4.11(b), circuit you create the circuit would be open, the current would be zero, and the bulb would with real compo- not light up. nents. It consists of a battery, wire, Electric circuits are incorporated into our lives in many different ways. switch, and load. They are used in nearly every type of item that uses electricity, from a 4.7 Electric circuits 109 phone to a lamp. Components of electrical circuits As you studied earlier, some common elements (components) that can be found in electrical circuits include light bulbs, batteries, connecting wires, switches, resistors, voltmeters, and ammeters. You will learn more about these items in later sections, but it is important to know what their symbols are and how to represent them in circuit diagrams. Table 4.1 summarizes the symbols of electrical components. Table 4.1 Names of electrical components and their circuit symbols Exercise 4.11 What would hap- pen to the lamp if Components Symbol Usage the circuit is bro- ken somewhere? Bulb or lump bulb glows when charge moves through it Battery provides energy for charge to move Switch allows a circuit to be open or closed Resistor resists the flow of charge Voltmeter measures potential difference Ammeter measures current in a circuit connecting lead connects circuit elements to- gether 110 Unit 4 Static and Current Electricity Section summary The simplest electric circuit contains a source of electrical energy (such as a battery), an electric conductor (such as a wire connected to the battery) and a load (like lamps). Charges flow through a circuit. A closed path, or closed circuit, is needed for making electric charge to flow through the circuit. Review questions 1. What does an electric circuit mean? 2. What is the name of the unbroken path that current follows? 3. What is the difference between an open electric circuit and a closed electric circuit? 4.8 Current, Voltage, and Ohm’s Law By the end of this section, you should be able to: define current, voltage, and resistance; state Ohm’s Law; calculate current, and solve problems involving Ohm’s Law. Exercise 4.12 Dear students, if the electric charge flows through a conductor (for exam- ple, through a metallic wire), you say that there is an electric current in the How would you explain what an conductor. In a torch, you know that the cells (or a battery, when placed in electric current is? proper order) provide flow of charges or an electric current that makes the torch bulb to glow. The flow of charge particles or the rate of flow of electric charge through a point in a conducting medium is called electric current. The charge 4.8 Current, Voltage, and Ohm’s Law 111 particles can be negative or positive. Since electrons were not known at the time when the phenomenon of electricity was first observed, electric current was assumed to be the flow of positively charged particles. The current produced due to the flow of positively charged particles is called conventional current (or simply current) and it flows out from the positive terminal of the battery into the negative terminal. This was the convention chosen during the discovery of electricity. But this assumption was found to be wrong once the electron was discovered. So, in practice, the electric current is the flow of electrons (negatively charged particles). Electron cur- rent is the flow of negatively charged particles from the negative terminal of the battery to the positive terminal, as shown in Figure 4.12. However, the direction of the current does not affect the properties of the circuit as long as you keep it consistent. Therefore, the conventional current is taken as the standard current direction. If a net charge ∆Q, flows across any cross-section of a conductor in time Key Concept ∆t , then the current I, through the cross-section is Electric cur- ∆Q rent is defined as I= (4.6) ∆t the rate at which electric charges The SI unit for electric current is the ampere (A), named after the French flow. scientist Andre-Marie Ampere (1775-1836). One ampere is constituted by the flow of one coulomb of charge per second, that is, 1 A = 1 C/s. Small quantities of current are expressed in milliampere (1m A = 10−3 A) or in Figure 4.12 Conventional current and electron current. 112 Unit 4 Static and Current Electricity microampere (1µA = 10−6 A). An instrument used to measure electric current is called the ammeter. Example 4.3 A current of 0.5 A is drawn by a filament of an electric bulb for 10 minutes. Find the amount of electric charge that flows through the circuit. Solution: You are given I = 0.5 A, and ∆t = 10 minutes = 600 s. You want to find the net charge, ∆Q. From the equation for current, you have ∆Q = I × ∆t = 0.5 A × 600 s = 300 C Potential Difference Exercise 4.13 Charges do not flow in a copper wire by themselves, just as water in a What makes elec- perfectly horizontal tube does not flow. If one end of the tube is connected tric charges to to a tank of water kept at a higher level, such that there is a pressure differ- flow? ence between the two ends of the tube, water flows out of the other end of the tube. Thus, in a water circuit, a pump increases the gravitational potential energy of the water by raising the water from a lower level to a higher level. For the flow of charges in a conducting metallic wire, the electrons move only if there is a difference of electric pressure called the potential differ- ence along the conductor. This difference of potential may be produced by a battery, consisting of one or more electric cells. A battery supplies energy to an electric circuit. When the positive and negative terminals of a battery are connected in a circuit, the electric potential energy of the electrons in the circuit is increased. As these electrons move toward the positive battery terminal, this electric potential energy is transformed into 4.8 Current, Voltage, and Ohm’s Law 113 other forms of energy, just as gravitational potential energy is converted into kinetic energy as water falls. A battery supplies energy to an electric circuit by converting chemical Key Concept energy to electric potential energy. The chemical action within a cell gen- The voltage or erates the potential difference across the terminals of the cell, even when potential differ- no current is drawn from it. When the cell is connected to a conducting ence in a circuit is circuit element, the potential difference sets the charges in motion in the a measure of the conductor and produces an electric current. In order to maintain the cur- electrical poten- rent in a given electric circuit, the cell has to expend its chemical energy tial energy of the stored in it. electrons in the circuit. A battery The electric potential difference (V ) between two points in an electric supplies energy circuit carrying some current is defined as the work done to move a unit to an electric cir- charge from one point to the other. cuit by increasing the electric po- Work done (W) W tential energy of V= = Charge (Q) Q electrons in the circuit. The SI unit of electric potential difference is the volt (V ), named after Alessandro Volta (1745-1827), an Italian physicist. One volt (1 V ) is the potential difference between two points in a current-carrying conductor when 1 Joule (1 J) of work is done to move a charge of 1 coulomb (1 C) from J one point to the other. Therefore, 1 V = 1 C.On the other hand, potential difference is measured by means of an instrument called the voltmeter. You might have seen birds sitting and even running along electric line Exercise 4.14 wires high in the air. There are times when these wires can be filled with How can birds dozens of birds. Since birds are not good conductors, that is one reason sit on those wires they don’t get shocked when they sit on electrical wires. The energy by- in Figure 4.13 and passes the birds and keeps flowing along the wire instead. not get an electric shock? There is another reason why birds can sit on a wire without getting shocked. There is no voltage difference on a single wire. There must be a difference 114 Unit 4 Static and Current Electricity Figure 4.13 Birds on an electric cable. in electrical potential for electrons to move. For example, energy flows from areas of high voltage to areas of low voltage. If it flows through a Activity 4.7 single power line at 35,000 volts, it will continue along the path of least resistance. That means it will bypass birds because there is no difference Would you be in electrical potential. harmed if you touch one of the It would be a different story if a bird is connected to the ground through wires of a high- voltage transmis- some means (like a tree) while sitting on the wire. That would cause it to sion line just like get shocked. This would also happen if a bird touched another wire with a birds without different voltage. In these cases, the bird’s body would become a path for having contact electricity. It would move through the bird to reach either the ground or with the ground? another place with a different voltage. This is why power lines tend to be If yes, then how high in the air with plenty of space between the wires. can birds not die when they sit on Example 4.4 such lines? How much work is done in moving a charge of 2 C across two points having a potential difference 12 V ? 4.8 Current, Voltage, and Ohm’s Law 115 Solution: In this example, you are given with V = 12 V and q = 2C. What you want to find is the work done. The amount of work W, done in moving the charge is W = V Q = 12 V × 2 C = 24 J Ohm’s Law In an electric circuit, charges do not flow freely. So the electrical current in Exercise 4.15 a wire can be reduced by many factors including impurities in the metal of Is there a rela- the wire that increases the resistance of the wire or collisions between the tionship between electrons and nuclei in the material. These factors create a resistance to the potential dif- the electrical current. Resistance is a description of how much a wire or ference across other electrical component opposes the flow of charge through it. a conductor and the current In the 19th century, the German physicist Georg Simon Ohm (1787-1854) through it? found experimentally that current through a conductor is proportional to the voltage drop across a current-carrying conductor. In other words, V αI In an equation form, Exercise 4.16 V = R or V = IR (4.7) Describe how I the current in a This relationship is called Ohm’s law. It can be viewed as a cause-and- circuit changes effect relationship, with voltage being the cause and the current being the if the resistance effect. Ohm’s law is an empirical law like that for friction, which means increases and the that it is an experimentally observed phenomenon. voltage remains constant. In the above expression, R is a constant for the given metallic wire at a 116 Unit 4 Static and Current Electricity given temperature and is called its resistance. It is the property of a conduc- tor to resist the flow of charges through it. Thus, the motion of electrons through a conductor is retarded by its resistance. The units of resistance V V are volts per ampere, or A. You call a A an "ohm", which is represented by V the uppercase Greek letter omega (Ω). Thus, 1 Ω = 1 A. In many practical cases, it is necessary to increase or decrease the current in an electric circuit. In an electric circuit, a device called a rheostat is Key Concept often used to change the resistance in the circuit. Resistance Ohm’s law is an empirical relationship valid only for certain materials. is a measure of Materials that obey Ohm’s law and hence have a constant resistance over how difficult it is for electrons to a wide range of voltage, are said to be ohmic materials. Ohmic materi- flow through a als include good conductors like copper, aluminum, and silver. Ohmic material. materials have a linear current-voltage relationship over a large range of applied voltages (Figure 4.14 (a)). Non-ohmic materials have a nonlinear current-voltage relationship (Figure 4.14 (b)). Exercise 4.17 Would you please Figure 4.14 The current-voltage characteristics of (a) ohmic materi- think of an anal- als and (b) non-ohmic materials. ogy for current, The magnitude of the electric current depends on the material of the voltage and resis- wire, length of the wire, area of cross section, and etc. The resistance of tance? an ohmic conductor increases with length, which makes sense because the electrons going through it must undergo more collisions in a longer conductor. A smaller cross-sectional area also increases the resistance of a conductor, just as a smaller pipe slows the fluid moving through it. The 4.8 Current, Voltage, and Ohm’s Law 117 resistance, then, is proportional to the conductor’s length, and is inversely proportional to its cross sectional area A. Thus, L Rα A L R =ρ (4.8) A Figure 4.15 A uniform conductor of length L, and cross-sectional area A. Exercise 4.18 where the constant of proportionality, ρ, is called the resistivity of the ma- For the same terial. Resistivity is the electrical resistance of a conducting material per crossection of unit length. In other words, it is the degree to which a conductor opposes a wire, describe the flow of electricity through itself, instead allowing the energy to flow how the electric out of the electrical circuit, most often as heat. The SI unit of resistivity is resistance of a Ωm. It is a characteristic property of the material. wire changes as the wire becomes On the other hand, conductivity is resistivity’s reciprocal. So a high resis- longer. How does tivity means a low conductivity, and a low resistivity means a high conduc- the resistance tivity. change as the wire becomes thicker for the Example 4.5 same length of a How much current will an electric bulb draw from a 220 V source, if the wire? resistance of the bulb filament is 1200 Ω? Solution: You are given V = 220 V and R = 1200 Ω. You want to find the value for the current, I. 118 Unit 4 Static and Current Electricity From Ohm’s law, current can be calculated by: V 220 V I= = = 0.18 A R 1200 Ω Example 4.6 The potential difference between the terminals of an electric heater is 60 V when it draws a current of 4 A from the source. What current will the heater draw if the potential difference is increased to 120 V ? Solution: You are given V = 60 V and I = 4 A. What you want to find is the resistance, R. According to Ohm’s law, V 60 V R= = = 15 Ω I 4A When the potential difference is increased to 120 V, the current is given by V 120 V I= = =8 A R 15 Ω The current through the heater becomes 8 A. Example 4.7 The resistance of a metal wire of length 1 m is 26 Ω at 20 o C. If the diam- eter of the wire is 0.3 mm, what will be the resistivity of the metal at that temperature? Solution: You are given the resistance R of the wire = 26 Ω, the diameter d = 0.3 mm = 3×10−4 m, and the length L of the wire = 1 m. You want to find the resistivity. 4.8 Current, Voltage, and Ohm’s Law 119 From the expression of the resistance, the resistivity of the given metallic wire is R A Rπd 2 ρ= = L 4l Substitution of values in the above expression gives ρ = 1.84 × 10−6 Ωm The resistivity of the metal at 20 o C is 1.84 × 10−6 Ωm. This is the resistivity of manganese. Section summary Resistance is a property that resists the flow of electrons in a conductor. It controls the magnitude of the current. The SI unit of resistance is ohm (Ω). The potential difference, also referred to as voltage difference between two given points is the work in joules required to move one coulomb of charge from one point to the other. According to Ohm’s law, the potential difference across the ends of a resistor is directly proportional to the current through it, provided its temperature remains the same. The resistance of a conductor depends directly on its length, inversely to its cross-sectional area, and also on the material of the conductor. Review questions 1. What is the term used to state the flow of an electric charge per unit time? 2. What is the relationship among voltage, current, and resis- tance in a circuit? 120 Unit 4 Static and Current Electricity 3. What is meant by the potential difference between two points is 1 V ? 4. What are the factors that determine the resistance of a con- ductor? 5. Will current flow more easily through a thick wire or a thin wire of the same material, when connected to the same source? Why ? 6. Let the resistance of an electrical component remains con- stant while the potential difference across the two ends of the component decreases to half of its former value. What change will occur in the current through it? Exercise 4.19 4.9 Combination of resistors in a circuit How many dif- By the end of this section, you should be able to: ferent paths can electric current draw a diagram that shows series and parallel connections of resis- follow in a series tors; circuit? describe what happens to the current and potential difference when the resistors are connected in series and in parallel; Exercise 4.20 If a series cir- calculate the equivalent resistance for a circuit of resistors in series cuit containing or in parallel; mini-light bulbs is opened and some calculate the current and potential difference across resistors con- of the light bulbs nected in series and parallel. are removed, In this section, you consider simple circuits containing only resistors and what happens when the circuit is batteries. Such circuits often contain a number of resistors connected in closed? series or in parallel. 4.9 Combination of resistors in a circuit 121 Resistors in Series Key Concept Students, what if you wanted to watch TV and had to turn on all the lights, A series dcir- a refrigerator, and every other electrical appliance in the house to do so? cuit describes two That is what it would be like if all the electrical appliances in your house or more compo- were connected in a series circuit. nents of a circuit that provide a A series circuit is a circuit that has only one path for the electric current to single path for follow, as shown in Figure 4.16. If this path is broken, then the current will current. no longer flow and all the devices in the circuit will stop working. As an example, if the entire string of lights went out when only one bulb burned out, then the lights in the string were wired as a series circuit. Exercise 4.21 What happens to the value of the current when a number of resistors are connected in series circuit? Figure 4.16 Series connection of three resistors. What would be Since charge is conserved, charges cannot build up or disappear at one their equivalent point. As there is only one path for a charge to flow, the amount of charge resistance? entering and exiting the first resistor must equal the amount of charge that enters and exits the second resistor in the same time interval. Because the Key Concept current is the amount of charge moving past a point per unit of time, the In a series current in the first resistor must equal the current in the second resistor. combination of This is true for any number of resistors arranged in series. When many resistors, the cur- resistors are connected in series, the current in each resistor is the same. rent is the same in every part of The potential difference across the battery, V , must equal the sum of the the circuit or the potential differences across the load, V1 + V2 + V3 , where V1 , V2 , and V3 same current are the potential differences across R 1 , R 2 , and R 3 respectively. That is, through each resistor. V = V1 + V2 + V3 (4.9) 122 Unit 4 Static and Current Electricity Let I be the current through the circuit. The current through each resistor is also I. It is possible to replace the three resistors joined in series by an equivalent single resistor of resistance R eq such that the potential differ- ence V across it, and the current I through the circuit remain the same. Applying Ohm’s law to the entire circuit, you have V = I R eq By making use of equation 4.9, I R eq = V1 + V2 + V3 Since V1 = I R 1 ,V2 = I R 2 ,V3 = I R 3 , Key Concept I R eq = I R 1 + I R 2 + I R 3 The equivalent resistance in a series circuit is ∴ R eq = R1 + R 2 + R 3 (4.10) the sum of the cir- cuit’s resistances. Thus, when several resistors are joined in series, the resistance of the combination R eq equals the sum of their individual resistances, R 1 , R 2 , R 3 , and is thus greater than any individual resistance. Resistors in Parallel Exercise 4.22 As discussed above, when a single bulb in a series light set burns out, the entire string of lights goes dark because the circuit is no longer closed. A Explain why build- ings are wired wiring arrangement that provides alternative pathways for the movement using parallel cir- of a charge is a parallel circuit. A parallel circuit is a circuit that has more cuits rather than than one path for the electric current to follow, as shown in Figure 4.17. series circuits. The figure shows the arrangement of three resistors joined in parallel with a combination of cells (or a battery). The current branches so that elec- trons flow through each of the paths. The bulbs of the decorative light set that you use in your home are arranged in parallel with each other. Thus, if one path is broken, electrons continue 4.9 Combination of resistors in a circuit 123 to flow through the other paths. Adding or removing additional devices in one branch does not break the current path in the other branches, so the devices on those branches continue to work normally. Houses, schools, and other buildings are wired using parallel circuits. Exercise 4.23 How does con- necting devices in parallel affect the electric current in Figure 4.17 Parallel connections of three resistors. a circuit? Because charge is conserved, the sum of the currents in each bulb equals the current I delivered by the battery. This is true for all resistors in parallel. I = I 1 + I 2 + I 3... (4.11) Key Concept Parallel de- Therefore, the total current I is equal to the sum of the separate currents scribes two or through each branch of the combination. more components of a circuit that Let R eq be the equivalent resistance of the parallel combination of resistors. provide sepa- By applying Ohm’s law to the parallel combination of resistors, you have rate conducting paths for cur- V rent because the I= R eq components are Since I = I 1 + I 2 + I 3 , applying Ohm’s law to each resistor gives you connected across common points V V1 V2 V3 = + + or junctions. A R eq R 1 R 2 R 3 parallel circuit V V V where I 1 = ,I R1 2 = R2 , and I 3 = R3 has more than Because the potential difference across each bulb in a parallel arrangement one path for the equals the terminal voltage V = V1 = V2 = V3 , you can divide each side of current to follow. the equation by V to get the following equation. 1 1 1 1 = + + R eq R 1 R 2 R 3 124 Unit 4 Static and Current Electricity Thus, the reciprocal of the equivalent resistance of a group of resistances joined in parallel is equal to the sum of the reciprocals of the individual resistances. An extension of this analysis shows that the equivalent re- sistance of two or more resistors connected in parallel can be calculated using the following equation. 1 1 1 1 1 = + +... + (4.12) R eq R 1 R 2 R 3 Rn Example 4.8 In the circuit shown in Figure 4.18, find: a) the equivalent resistance, b) the current through each resistor. Solution: You are given R 1 = 12 Ω, R 2 = 3.0 Ω, R 3 = 4.0 Ω, R 4 = 5.0 Ω and V = 12 V. The required quantities are R eq and I. a) Since all the four resistors are in series combination, R eq = R 1 + R 2 + R 3 + R 4 = 12 Ω + 3.0 Ω + 4.0 Ω + 4.0 Ω = 24 Ω. b) The current through all resistors in a series circuit is the same. Thus, Figure 4.18 Circuit diagram using Ohm’s law, for four resistors connected in series. V V 12V I= = = = 0.50 A R R 1 24 Ω Example 4.9 In the circuit shown in Figure 4.19, find: a) the equivalent resistance, Figure 4.19 Circuit diagram for b) the current through the battery and each resistor. three resistors connected in parallel. Solution: The given quantities are R 1 = 12 Ω, R 2 = 12 Ω, R 3 = 6.0 Ω and V = 12 V. 4.9 Combination of resistors in a circuit 125 The required quantities are R eq and I. a) The three resistors are in a parallel combination. So 1 1 1 1 1 1 1 1 = + + = + + = R eq R 1 R 2 R 3 12 Ω 12 Ω 6.0 Ω 3.0 Ω R eq = 3.0 Ω Therefore, the equivalent resistance should be less than the smallest resis- tance as expected. b) From Ohm’s law, V 12 V I= = = 4.0 A R eq 3.0 Ω Since the voltage is constant in a parallel connection, V 12 V I1 = = = 1.0 A R 1 12 Ω V 12 V I2 = = = 1.0 A R 2 12 Ω V 12 V I3 = = = 2.0 A R 3 6.0 Ω On the other hand, resistors in a circuit may be connected in a variety of series-parallel combinations. The general procedure for analyzing circuits with different series-parallel combinations of resistors is to find the voltage across and the current through the various resistors as follows: Start from the resistor combination farthest from the voltage source, find the equivalent series and parallel resistances. Reduce the current until there is a single loop with one total equiva- lent resistance. Find the total current delivered to the reduced circuit using Ohm’s law. 126 Unit 4 Static and Current Electricity Expand the reduced circuit in the reverse order of the above steps to find the currents and voltages for the resistors in each step. Example 4.10 Find the equivalent resistance and the current across the 4.0 Ω resistor shown in Figure 4.20. Solution: You are given R 1 = 4.0 Ω, R 2 = 5.0 Ω, R 3 = 9.0 Ω, and V = 6 V. V You want to find the value for R eq and I. Since the 5.0 Ω and 9.0 Ω resistors are connected in parallel, 1 1 1 1 1 14 = + = + = R par al l el R 2 R 3 5 Ω 9 Ω 45 Ω R par al l el = 3.21 Ω Now the 4.0 Ω and R par al l el resistors are connected in parallel. Therefore, Figure 4.20 Circuit diagram for R eq = 4.0 Ω + R par al l el = 4.0 Ω + 3.21 Ω = 7.21 Ω. series-parallel combination of resistors. The current through the circuit can be calculated by V V 6V I= = = = 0.830 A. R R eq 7.21 Ω This is equivalent to the value of the current across the 4.0 Ω resistor as the 4.0 Ω resistor is connected in parallel with R par al l el. Section summary The formulae made about both series and parallel circuits are summarized in Table 4.2. 4.9 Combination of resistors in a circuit 127 Table 4.2 Summary for a series and parallel circuits Resistors in Series Parallel Current I = I 1 = I 2 = I 3 =... = same I = I 1 + I 2 + I 3 +...= sum of for each resistor currents. Potential V = V1 + V2 + V3 +... = sum V = V1 = V2 = V3 =... = difference of potential differences same for each resistor. 1 1 1 1 Equivalent R eq = R 1 +R 2 +R 3 +... = sum R eq = R 1 + R 2 + R 3 +... = resistance of individual resistances reciprocal sum of resis- tances. Review questions 1. Which type of circuit has more than one path for electrons to follow? 2. A 4.0 Ω resistor, an 8.0 Ω resistor, and a 12.0 Ω resistor are connected in series with a 24.0 V battery. a. Calculate the equivalent resistance. b. Calculate the current in the circuit. c. What is the current in each resistors? 3. A length of wire is cut into five equal pieces. The five pieces are then connected in parallel, with the resulting resistance being 2.00 Ω. What was the resistance of the original length of wire before it was cut up? 4. How can you tell that the headlights of the car are wired in parallel rather than in series? How would the brightness of the bulbs differ if they were wired in series across the same 12 V battery instead of in parallel? 128 Unit 4 Static and Current Electricity 4.10 Voltmeter and ammeter connection in a cir- cuit By the end of this section, you should be able to: list the devices used for measuring current and voltage; use voltmeter and ammeter to measure the voltage and current in an electric circuit, respectively; explain why an ammeter is connected in series and voltmeter is connected in parallel. As you have seen in previous sections, an electric circuit is made up of a number of different components such as batteries, resistors and light bulbs. There are devices that are used to measure the properties of these components. These devices are called meters. Meters are of two types: analog and digital. Analog meters have a needle that swivels to point at numbers on a scale as opposed to digital meters, which have numerical readouts similar to a hand-held calculator. Figure 4.21 (a) Ammeter and voltmeter connection in a circuit. (b) Circuit diagram with ammeter and voltmeter. 4.10 Voltmeter and ammeter connection in a circuit 129 Voltmeter A voltmeter is a device that is used to measure potential differences across a resistor or any other component of a circuit that has a voltage drop. In Key Concept analogy with a water circuit, a voltmeter is like a meter designed to mea- Voltmeters sure pressure differences. are connected in parallel with To measure the potential difference between two points in a circuit, a whatever device’s voltmeter must be connected in parallel with the portion of the circuit on voltage is to be which the measurement is made. A parallel connection is used because measured. objects in parallel experience the same potential difference. Since the resistance of a voltmeter is high, it draws minimum current from the main circuit and, thus, the potential difference of the component that is going to be measured is not affected. If a voltmeter is connected in series, it would increase the equivalence resistance of the circuit and no current would flow through it. Hence, it should be connected in parallel. Figure Exercise 4.24 4.21 shows a voltmeter is connected in parallel with a resistor. One lead of How do we con- the voltmeter is connected to one end of the battery and the other lead is nect the ammeter connected to the opposite end. and voltmeter in an electrical circuit? Draw a circuit diagram in order to jus- tify your answer. What will be happening if the positions of these Figure 4.22 (a) Analog voltmeter (b) Digital voltmeter (c) Voltmeter instruments are symbol. interchanged? Specify the rea- Ammeter sons. An ammeter is a device that is used to measure the the flow of electric current in amperes. To measure the current of a circuit, the ammeter shown in Figure 4.23 is connected in series in the circuit so that the same current that is in the circuit flows through it and gets measured. Ammeter 130 Unit 4 Static and Current Electricity has low (nearly zero) resistance because you do not want to change the current that is flowing through the circuit. So its inclusion in series in the circuit does not change the resistance and hence the main current in the circuit. A series connection is used because objects in a series have the same current passing through them. All of the current in this circuit flows through the meter. Figure 4.23 (a) Analog ammeter (b) A digital ammeter (c) Ammeter symbol. If an ammeter is connected in parallel, it would draw most of the current and get damaged. Hence, it must be connected in series. Key Concept Table 4.3 summarizes the use of each measuring instrument that you discussed and the way it should be connected to a circuit component. Ammeters are connected in se- Table 4.3 Summary of the use and connection of an ammeter and a voltmeter ries with whatever device’s current is Instrument Measured Quantity Proper Connection to be measured. Voltmeter Voltage In Parallel Ammeter Current In Series On the other hand, multimeter is a measuring instrument that can mea- sure multiple electrical properties. Figure 4.24 shows a digital multimeter, a convenient device with a digital readout that can be used to measure voltage, current, or resistance. 4.10 Voltmeter and ammeter connection in a circuit 131 Figure 4.24 Multimeter used for measuring electrical properties. Section summary Voltmeters measure voltage and ammeters measures current. Voltmeter is connected in parallel with the voltage source to receive full voltage and must have a large resistance to limit its effect on the circuit. An ammeter is connected in series to get the full current flow- ing through a branch and must have a small resistance to limit its effect on the circuit. Review questions 1. Explain why a voltmeter is connected in parallel with a resis- tor. 2. Explain why an ammeter is connected in series with a resistor. 3. What will happen when you connect an ammeter in parallel and a voltmeter in a series circuit? 4. In Figure 4.25, there are four positions available for the place- ment of meters. Figure 4.25 Ammeter and volt- a)Which position(s) would be appropriate for placement of meter connection in a circuit. an ammeter? b) Which position(s) would be appropriate for placement of a voltmeter? 132 Unit 4 Static and Current Electricity c) Which position could hold an ammeter that would read the total current through the circuit? d) Which position could hold a voltmeter that would read the total voltage drop through the circuit? 5. Suppose you are using a multimeter to measure current in a circuit and you inadvertently leave it in voltmeter mode. What effect will the meter have on the circuit? What would happen if you were measuring voltage but accidentally put the meter in ammeter mode? Exercise 4.25 4.11 Electrical safety in general and local context Have you ever had By the end of this section, you should be able to: a mild electric shock? state the safety measures to be taken to protect us from electrical accidents or shocks. Key Concept You probably felt only a mild tingling sensation from the electric shock, The first pre- but electricity can have much more dangerous effects. In some ways your caution to take for body is like a piece of insulated wire. The fluids inside your body are good personal safety conductors of current. The electrical resistance of dry skin is much higher. is to avoid com- Skin insulates the body like the plastic insulation around a copper wire. ing into contact with an electrical conductor that Your skin helps keep electric current from entering your body. A current might cause a can enter your body when you accidentally become part of an electric voltage across a circuit. If direct body contact is made with an electrically energized part human body or while a similar contact is made simultaneously with another conductive part of it, thus surface that is maintained at a different electrical potential, a current will causing a current flow, entering the body at one contact point, traversing the body, and then through the body exiting at the other contact point, usually the ground. that could be dangerous. A person can be electrocuted by touching a live wire while in contact with 4.11 Electrical safety in general and local context 133 the ground. Such a hazard is ofte

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