Static and Current Electricity (Chapter 4) G10 2017 PDF

Unit 4 Static and Current Electricity Introduction  Physical phenomenon associated with the presence and flow of electric charge is known as electricity. 4.1 Charges in Nature  Objects surrounding us (including people) contain large amounts of electric charge.  In phys...

Unit 4 Static and Current Electricity Introduction  Physical phenomenon associated with the presence and flow of electric charge is known as electricity. 4.1 Charges in Nature  Objects surrounding us (including people) contain large amounts of electric charge.  In physics, charge refers to a fundamental property of matter that causes it to experience a force when placed in an electric and magnetic field.  There are two types of electric charge: positive charge and negative charge.  Protons have a positive charge, and electrons have a negative charge.  Charge is the fundamental property of matter associated with electrons and protons which are found in any atom.  When the number of electrons and protons in an object are equal that object is said to be electrically neutral.  Electric charge can be carried by subatomic particles such as protons (which carry a positive charge) and electrons (which carry a negative charge). The interaction between charges results in the fundamental forces known as electrostatic force. Unit of Charge  The standard unit of electric charge is the coulomb (C), but charges are often discussed in terms of elementary charge (e), which is the charge carried by a single proton or electron (approximately 1.602×10−19 c)  One coulomb (1 C) of charge is carried by 6.25×1018 electrons.  In electrostatics, you often work with charge in micro Coulombs (1µC = 1×10-6 C) and nano coulombs (1nC = 1×10-9 C). Conservation of Charge  Charge is conserved, meaning it cannot be created or destroyed, only transferred between objects. This concept underpins many electrical phenomena, such as the operation of circuits, capacitors, and batteries.  During electrification, electric charges are neither created nor destroyed, but are transferred from one material to another. This is called the law of conservation of charge.  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.  The net charge in an isolated system remains unchanged, even when electrical processes like the movement of electrons or chemical reactions occur.  Quantization of charge  Electric charges are quantized, occurring only in discrete amounts.  The smallest charge that is possible to obtain is that of an electron or proton.  The magnitude of this charge is denoted by e. Charge is said to be quantized when it occurs as the integral multiples of e.  The quantization of charge refers to the principle that electric charge can only exist in discrete amounts, and these amounts are integer multiples of a fundamental unit of charge, often denoted as e, which is the charge of a single electron (or proton). This means that the charge on any object is always a whole number multiple of this smallest unit of charge.  This is true for both negative and positive charges and is expressed as; q = ne- where n is positive or negative integer. Exercise 1. A conductor possesses a positive charge of 3.2 × 10−19 C. How many electrons does it have in excess or deficit (use: e = 1.60 × 10−19 C)? 2. How many electrons are required to make up a negative charge of one Coulomb? 3. How many electrons must be removed from an object so that it is left with a charge of 8 x10-10 C? [5 x 109 electrons] 4. An object has a total charge of -2 x10-6 C. How many excess electrons does the object have? 5. How many elementary charges are in 1 µC of charge? 6. What is the total charge of 20g of electrons? 4.2 Methods of Charging a Body Charging an object refers to the process of transferring electric charge to or from the object, resulting in the object gaining a net positive or negative charge. There are several mechanisms by which an object can be charged, with the most common methods being friction, conduction, and induction. These processes involve the movement of electrons, which are the primary carriers of electric charge. 1. Charging by rubbing- Charging by rubbing leaves the two bodies with an opposite sign of charges. Charging by rubbing occurs when two different neutral materials are rubbed together and electric charges are transferred from one object to the other. The material that has a greater affinity for electrons (like rubber) will acquire extra electrons and become negatively charged. The other material (like fur) loses electrons and becomes positively charged. Rubbing a balloon on your hair causes the balloon to become negatively charged (by gaining electrons), while your hair becomes positively charged (by losing electrons). 2. Charging by Conduction-Charging by conduction leaves the charged body and the uncharged body with the same sign of charge but a weaker strength than the original object. Charging by conduction occurs when a charged object comes into direct contact with a neutral object, transferring charge to or from the neutral object. If a charged object (say a negatively charged metal rod) touches a neutral conductor (like a metal sphere), the electrons in the charged object move into the neutral object (or vice versa) depending on the type of charge of the object. If the charged object is negatively charged, electrons flow from it to the neutral object, leaving the charged object with less negative charge and the neutral object with an excess of negative charge. If the charged object is positively charged, electrons flow from the neutral object to the charged object, making the neutral object positively charged. 3. Charging by Induction-Charging by induction leaves the charged body and the uncharged body with the opposite sign of charge. Induction is a method of charging an object without direct contact. It involves the redistribution of charge within a conductor when exposed to an electric field created by a nearby charged object. When a charged object (e.g., a negatively charged rod) is brought near a neutral object, the charges in the neutral object rearrange due to electrostatic induction. The total charge of the system is still conserved, but the charges on the neutral object redistribute themselves. If the rod is negatively charged, the electrons in the conductor will be repelled, pushing them to the far side of the conductor, leaving the near side with a positive charge. If a grounding path is provided (e.g., touching the conductor to the earth), the excess electrons on the far side of the conductor can flow into the ground, leaving the conductor with a net charge opposite to that of the nearby charged object. A charged object induces a redistribution of charge in a nearby neutral conductor without direct contact, and the conductor may become charged if grounded. 4.3 The electroscope  The electroscope is a very sensitive instrument which can be used to-  detect the type of electric charge,  to identify whether an object is charged or not,  to measure the quantity of charge and  to know whether an objects conductor or insulator.  4.4 Electrical Discharge  Discharging refers to the process by which a charged object loses its excess charge. This can occur through various mechanisms, depending on the nature of the charged object and its environment. The primary mechanisms for discharging are contact (conduction), grounding, and electrostatic discharge (ESD).  The process of removing electric charges from a charged body is called discharging.  A charged body can be made to lose its charges by touching it with a conductor.  When a body is discharged, it becomes neutral.  Sparks and lighting are an example of electrical discharge.  Lightning- is a very large electrical discharge caused by induction.  The process of providing a pathway to drain excess charge into the earth is called grounding. The pathway is usually a conductor such as a wire or a pipe. Discharging by Contact (Conduction): The charged object loses charge to a neutral or oppositely charged object by direct physical contact, equalizing the charge between the two objects. Discharging by Grounding (Earthing ): The charged object loses charge to the Earth (or receives charge from it), neutralizing its excess charge through direct or indirect connection. Electrostatic Discharge (ESD): A sudden flow of electrons occurs when the potential difference between the charged object and a nearby object becomes large enough to overcome the dielectric (insulating) properties of air, resulting in a spark or arc. Discharging in Capacitors: A capacitor releases its stored charge through a connected load (e.g., resistor or circuit), following an exponential discharge curve. 4.5 Coulomb’s law of electrostatics  The magnitude of the forces between charged spheres was first investigated quantitatively in 1785 by Charles Coulomb.  He observed that the electrostatic force between the two charges is proportional to the product of the charges and is inversely proportional to the square of their distance apart.  Coulomb’s law can be stated in mathematical terms as Where fig. (a) Attractive and (b) repulsive electrostatic force between two charges.  F is the magnitude of the electric force between the two charges q 1 and q2, and r is the distance between the two charges.  We can convert the above proportionality expression to an equation by writing-  The force between two point charges is directly proportional to the magnitude of each charge. And inversely proportional to square of the separation between their centers. directed along the line joining their centers. Comparison of Electrostatic and Gravitational Force 1. Identical Properties :  Both the forces are central forces, i.e., they act along the line joining the centers of two charged bodies.  Both the forces obey inverse square law, F  Both are conservative forces, i.e. the work done by them is independent of the path followed.  Both the forces are effective even in free space. 2. Non identical properties:  Gravitational forces are always attractive in nature while electrostatic forces may be attractive or repulsive.  Gravitational constant of proportionality does not depend upon medium; the electrical constant of proportionality depends upon medium.  Electrostatic forces are extremely large as compared to gravitational forces Example eg. Charges q1 = 5.0µC and q2 = -12.0µC are separated by 30 cm on the x-axis. What is the magnitude of the force exerted by the two charges? eg. Two charges q1 = 2×10-6 C and q1 = -4×10-3 C are placed 30 cm apart. Determine the magnitude and direction of the force that one charge exerts on the other. Why study electrostatics? Electrostatics is the basis of industrial processes such as electrostatic spray painting, and xerography, and of the unintentional build-up of electrostatic charge which can trigger explosions and fires in, for example, grain silos and operating theatres. The electrostatic force binds electrons and nuclei together to form atoms and the same force holds atoms and molecules together in bulk material.  4.6 The electric field  An electric field is a region where an electric charge experiences a force.  Electric field lines are an excellent way of visualizing electric fields.  They were first introduced by Michael Faraday.  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. and negative charges. Fig. 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 proportional 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 charges repel each other. Electric Field Strength  The strength of the electric field, E, at any point in space is equal to theforce per unit charge exerted on a positive test charge. Mathematically,  Thus, E is a vector. If q is positive, the electric field E has the same directionas the force acting on the charge.  If q is negative, the direction of E is opposite to that of the force F.  On the other hand, the SI unit of electric field is Newton per Coulomb ( N/C )  Electric field strength due to a point charge  The test charge qo exerts forces on the charge that produce the field, so it may change the configuration of the charges. Fig. Electric field at a distance r from a charge. Example 1. Calculate the strength and direction of the electric field E due to a point charge of 2nc at a distance of 5 mm from the charge. 2. What is the magnitude and direction of the force exerted on a3.50µ C charge by a250 N/C electric field that points due East? 4. Calculate the magnitude of the electric field 2.00 m from a point charge of 5.00 mC 4.7 Electric circuits  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.  Open circuits do not allow an electrical current to flow through the circuit. Closed circuits are complete and allow electricity to flow through them.  A physical circuit is the electric circuit you create with real components. It consists of a battery, wire, switch, and load. Components of electrical circuits  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.  Let us consider a conductor having length L, cross-sectional area A, containing ‘n’ no. of electron per unit volume, having charge e in each electron.   Volume of the given conductor =AL  Total no. of free electron in given conductor ( N)=nAL  Total no. of the charge in given conductor= nALe In n particle each having a charge q, pass through a given area in time t then If n particles each having a charge q pass per second per unit area, the current associated with cross sectional area A is i = nqA If there are n particle per unit volume each having a charge q and moving with velocity v, the current thorough, cross section A is i = nqvA , for electrons i= neavd Drift Velocity :When Electric Field is applied across a conductor, the free electrons experience a force in the direction opposite to field. Due to this force they start drifting in the direction of force. The Velocity of this drift is called drift velocity “Vd”. During the drift they maintain their thermal velocity. Drift velocity is the average uniform velocity acquired by free electrons inside a metal by the application of an electric field which is responsible for current through it. Eg. A beam of electrons moving at a speed of 106 m/s along a line produces a current of 1.6 x10–6 A. The number of electrons in the 1m of the beam is Eg. A conducting wire of cross-sectional area 1 cm2 has 3x1023 m–3 charge carriers. If wire carries a current of 24 mA, the drift speed of the carrier is [5mm/sec]  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.  Open circuits do not allow an electrical current to flow through the circuit. Closed circuits are complete and allow electricity to flow through them. 4.8 Current, Voltage, and Ohm’s Law  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 particles can be negative or positive.  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.  If a net charge ∆Q,, flows across any cross cross-section section of a conductor in time ∆t, then the current I,, through the cross cross-section is  The time rate of flow of charge through any cross cross-section section is called current  The SI unit for electric current is the ampere ((A).  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 mill ampere (1mA (1 -3 -6 =10 A) or in microampere (1 (1µA = 10 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. Potential Difference((V)  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.  The voltage or potential difference in a circuit is a measure of the electrical potential energy of the electrons in the circuit.  A battery supplies energy to an electric circuit by increasing the electric potential energy of electrons in the circuit.  The electric ectric potential difference ((V)) between two points in an electric circuit carrying some current is defined as  The SI unit of electric potential difference is the volt ((V), ), named after Alessandro Volta (1745-1827).  On the other hand, potential difference is measured by means of an instrument called the voltmeter. Exercise 1. How can birds sit on those wires in Figure 4.13 and not get an electrics hock? 2. How much work is done in moving a charge of 2 C across two points having a potential difference 12 V?  Ohm’s Law  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.  Ohm’s law is an empirical law like that for friction, which means that it is an experimentally observed phenomenon.  In the above expression, R is a constant for the given metallic wire at a given temperature and is called its resistance.  The units of resistance are volts per ampere, or  which is represented by the uppercase Greek letter omega (Ω). Thus, 1 Ω = 1V/A.  Resistance is a measure of how difficult it is for electrons to flow through a material.  Materials that obey Ohm’s law and hence have a constant resistance over a wide range of voltage, are said to be ohmic materials.  Ohmic materials include good conductors like copper, aluminum, and silver.  Ohmic materials have a linear current-voltage relationship over a large range of applied voltages.  The conductors which obey ohm’s law strictly are called Ohmic conductors.  The conductors which do not follow ohm’s law are called non – ohmic conductors.  Non-ohmic materials have a non linear current-voltage relationship a) ohmic materials and b) non-ohmic materials.   The resistance of the conductor depends on the following factors:  The temperature of the conductor  The cross-sectional area of the conductor  Length of the conductor  Nature of the material of the conductor.  Length - longer wires have greater resistance.  Thickness - smaller diameter wires have greater resistance.  Temperature - heating a wire increases its resistance  The resistance is proportional to the conductor’s length, and is inversely proportional to its cross sectional area A. Thus,  where the constant of proportionality, ρ, is called the resistivity of the material.  Resistivity is the electrical resistance of a conducting material per unit length.  The SI unit of resistivity is Ωm. It is a characteristic property of the material.  where ρ is the resistivity of the material (measured in Ωm, ohm meter)  Resistivity is a qualitative measurement of a material’s ability.material, eg copper, has lower resistance than steel.  On the other hand, conductivity is resistivity’s reciprocal.  So a high resistivity means a low conductivity, and a low resistivity means a high conductivity.  Example 1. How much current will an electric bulb draw from a 220V source, if the resistance of the bulb filament is 1200Ω? 2. The potential difference between the terminals of an electric heater is 60V when it draws a current of 4A from the source. What current will the heater draw if the potential difference is increased to 120V? 3.The resistance of a metal wire of length 1 m is 26 Ω at 20 oC. If the diameter of the wire is 0.3 mm, what will be the resistivity of the metal at that temperature? 4.What is the relationship among voltage, current, and resistance in a circuit?  4.9 Combination of resistors in a circuit Resistors in Series  A series circuit is a circuit that has only one path for the electric current to follow, as shown in Figure.  If this path is broken, then the current will no longer flow and all the devices in the circuit will stop working.  Fig- Series connection of three resistors.  The potential difference across the battery, V , must equal the sum of thepotential differences across the load,V = V1+ V2+ V3 ….  the current I through the circuit remain the same.I= I1=I2=I3….  Applying Ohm’s law to the entire circuit, you have V = IReq  Thus, when several resistors are joined in series, the resistance of the combination R eq equals the sum of their individual resistances, R1, R2, R3,and is thus greater than any individual resistance. Resistors in Parallel  Parallel describes two or more components of a circuit that provide separate conducting paths for current because the components are connected across common points or junctions.  A parallel circuit has more than one path for the current to follow.  Example In the circuit shown in Figure, find: a) the equivalent resistance the current through each resistor.e voltage through each resistor. 1. 2. 3. Find the equivalent resistance and the current across the 4.0 Ω resistor shown in Figure. 4. 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? 4.10 Voltmeter and ammeter connection in a circuit  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.  Volt meters are connected n parallel with whatever device’s voltage is to be measured.  Since the resistance of a voltmeter is high.  An ammeter is a device that is used to measure the flow of electric current in amperes.  Ammeters are connected in series.  Ammeter has low (nearly zero) resistance because you do not want to change the current that is flowing through the circuit. 4.11 Electrical safety in general and local context  Safety of an electrical installation could be ensured by proper insulation, good earthling system and adopting adequate protection and control systems.  Electrical hazards can cause burns, shocks and electrocution (death).  You should follow proper rules and regulations to avoid accident.  Qualified electricians are recommended to inspect electrical equipment’s.  In damp locations, inspect electric cords and equipment in order to ensure they are in good condition; use a ground-fault circuit interrupter (GFCI).