Electricity PDF

ELECTRICITY Electric Charge – → A charge is a physical quantity which is defined by excess or deficiency of electrons on a body. → There are two types of electric charges : positive charge and negative charge. → A body...

ELECTRICITY Electric Charge – → A charge is a physical quantity which is defined by excess or deficiency of electrons on a body. → There are two types of electric charges : positive charge and negative charge. → A body is said to be -ve charged, if it gains electrons, e.g., an ebonite rod rubbed with fur acquires -ve charge. → A body is said to be +ve charge, if it loses electrons, e.g., a glass rod rubbed with a silk cloth acquires +ve charge. → Opposite charges or unlike charges attract each other. → Similar charges or like charges repel each other. → The SI unit of electric charge is coulomb (C). One coulomb is that quantity of electric charge which exerts a force of 9 × 109 N on an equal charge placed at a distance of 1 metre from it. → 1 Coulomb is equivalent to the charged contained in nearly 6 × 1018 electrons. 1 C = 6 × 1018 electrons → Positive charged particles are called protons and negative charged particles are called electrons. Magnitude of charge on 1 proton, p = 1.6 × 10-19 C. Magnitude of charge on 1 electron, e = -1.6 × 10-19 C. Quantisation of charge – The total charge acquired by a body is an integral multiple of magnitude of charge on a single electron. This principle is called quantisation of charge. Charge on n electrons, q = ne = n × 1.6 × 10-19 C. Electric Current The rate of flow of electric charge or electrons in a cross-section of a conductor in unit time. 𝐶ℎ𝑎𝑟𝑔𝑒(𝑞) 𝑞 𝑛𝑒 Electric Current (I) = 𝑇𝑖𝑚𝑒(𝑡) = 𝑡 = 𝑡 Here, n = number of electrons flowing through the conductor. The SI unit of electric current is Ampere (A), named in the honor of French scientist Andre-Marie Ampere (1775- 1836). It is a scalar quantity. When 1 coulomb of charge flows through any cross-section of a conductor in 1 second, the electric current flowing through it is said to be 1 ampere. 1 𝑐𝑜𝑢𝑙𝑜𝑚𝑏 1𝐶 i.e., 1 ampere = 1 𝑠𝑒𝑐𝑜𝑛𝑑 ⇒ 1𝐴 = 1𝑠 smaller units of current are milliampere (1 mA = 10-3 A) and microampere (1 µA = 10-6 A). Direction of electric current – The direction of electric current is taken as opposite to the direction of the flow of electrons (-ve charges). In an electric circuit the current flows from +ve terminal to the -ve terminal of the cell. Flow of Charges inside a wire / How the current flows in a wire? When electricity is supplied in a wire, the electron present in it move at random in all the directions. When a steady current flows in the wire, then the electrons start moving in certain speed from -ve end to the +ve end of the wire. This flow of electrons produces the electric current in the wire. ❖ The constant speed of the electron inside the conductor due the electric force is known as its average drift speed. The average drift speed of electron is 10-4 m/s. Electric Potential The amount of work done in moving a unit positive charge from infinity to a point is defined as electric potential. Potential is denoted by symbol V and its SI unit is ‘volt’. It is a scalar quantity.  ELECTRICITY It is named after Italian physicist Alessandro Volta. If work done in moving a positive charge q from infinity to a point is W, then electric potential V of that point is 𝑊 𝑉= 𝑞 Electric Potential Difference (V) – The potential difference between two points in an electrical circuit is defined as the work done in moving a unit positive charge from one point to other point. The potential difference between two points in a conductor is said to be 1 Volt, if 1 joule of work done in moving 1 coulomb of electric charge from one point to other point. 1 𝑗𝑜𝑢𝑙𝑒 Thus, 1 volt = 1 𝑐𝑜𝑢𝑙𝑜𝑚𝑏 1𝐽  1 V = 1𝐶  1 V = 1 J/C = 1 JC-1 Smaller units of electric potential, 1 mV = 10-3 V, 1µV = 10-6 V Larger units of electrical potential, 1 kV = 103 V, 1MV = 106 V Differentiate between Ammeter and Voltmeter Ammeter Voltmeter Electric current in a circuit is measured by device called Electric potential difference between two points in a ammeter. circuit is measured by device called voltmeter. It is a low resistance device. It is a high resistance device. Ammeter is always connected in series connection. Voltmeter is always connected in parallel connection. Electric Circuit A closed and continuous path through which electric current flows is known as electric circuit. It has various component including a cell or battery, a bulb or any appliance, a switch/key, a fuse, all connected by wires. When the key is closed, then the circuit is called closed circuit. This means that current would flow through the circuit. When the key is open, then the circuit is called open circuit. This means that current would not flow through the circuit. Circuit Diagram – A diagram which indicates how different components in a circuit have been connected by using the electrical symbols for the components, is called a circuit diagram. Circuit Symbols Circuit Symbols Circuit Symbols components components components An electric cell wires joint Rheostat or variable resistance Battery Wires crossing Ammeter without joining (or touching) Switch or Plug Electric bulb Voltmeter key (Open) Switch or Plug Resistor or Fuse key (Closed) resistance  ELECTRICITY OHM’s LAW – Ohm’s law gives a relationship between current (I), flowing in a wire and potential difference (V), across the terminal. According to Ohm’s law, the electric current flowing through a conductor is directly proportional to the potential difference applied across its ends at constant physical condition (such as temperature). 𝑉 ∝𝐼 Or 𝑉 = 𝐼𝑅 𝑉 Or 𝐼= 𝑅 Here, R is the constant of proportionality called resistance of the conductor. Its value depends upon nature, length, area of cross-section and temperature of the conductor. From Ohm’s law, we get that, (i) The current is directly proportional to potential difference, (ii) The current is inversely proportional to resistance. If the potential difference across the ends of conductor is doubled then the current flowing through it also gets doubled. If the potential difference across the ends of conductor is halved then the current flowing through it also gets halved. If the resistance is doubled then the current gets halved and if the resistance is halved then the current gets doubled. V-I Graph – The potential difference (V) and the corresponding current (I) is found to be a straight line passing through the origin for ohmic (metallic) conductors. ❖ The conductors which obey Ohm’s law are called ohmic conductors. The conductors which do not obey Ohm’s law are called non-ohmic conductors. Resistance – The property of a conductor due to which it opposes the flow of current through it is called resistance. Its SI unit is ‘ohm’ and is represented by the Greek letter Ω. 𝑃𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑉 Or, 𝑅= 𝐼 The resistance of a conductor depends on length, thickness, nature of material and temperature, of the conductor. 1 ohm is the resistance, if a potential difference of 1 volt across the ends of the conductor makes a current of 1 ampere to flow through it. 1 𝑣𝑜𝑙𝑡 1 𝑜ℎ𝑚 = 1 𝑎𝑚𝑝𝑒𝑟𝑒 1𝑉  1Ω= 1𝐴 = 1 𝑉𝐴−1 Some Important Terms Related to Resistance – Resistor – A component in an electric circuit which resists the flow of electric current is known as resistor. It has high electrical resistance. It reduces current in a circuit. Resistors are used to make those electrical devices where high resistance is required.  ELECTRICITY The alloys like nichrome, manganin and constantan have high resistance, so these are called resistors. Rheostat/Variable resistance – It is a variable resistor. It is used to control the flow of electric current by manually increasing or decreasing the resistance. Good Conductor – A material which has low electrical resistance is known as good conductor. A good conductor allows the electricity to flow through it easily. Silver, copper and aluminum are good conductors. Silver is the best conductor of electricity. Poor conductor – A material which has higher electrical resistance than conductors is known as poor conductors. A poor conductor does not allow the electricity to flow through it easily. Mercury, lead, stainless steel, alloys of iron and chromium are poor conductors. Insulators – A material which has infinitely high electrical resistance are called insulators. An insulator does not allow electricity to flow through it. Rubber, dry wood and plastic are insulators. Factors on which the Resistance of a conductor depends – The electrical resistance of a conductor depends – Length of the conductor Area of cross-section of the conductor (or thickness of the conductor) Nature of the material of the conductor Temperature of the conductor 1. Length of the conductor – → The resistance of a conductor ‘R’ is directly proportional to its length ‘l’. i.e., R∝l → When the length of a wire is doubled/halved, then its resistance also gets doubled/halved. → A long wire or conductor has more resistance and a short wire has less resistance. 2. Area of cross-section of the conductor – → The resistance of a conductor ‘R’ is inversely proportional to its area of cross-section ‘A’. 1 i.e., 𝑅 ∝ 𝐴 → When the area of cross-section of wire is doubled, then its resistance gets halved and if area of cross-section of wire is halved, then its resistance will get doubled. → A thick wire or conductor has less resistance and a thin wire or conductor has more resistance. NOTE – Short length of a thick wire is used for getting low resistance. Long length of a thin wire is used for getting high resistance. 3. Nature of the material of the conductor – → The resistance of a conductor depends on the nature of the material of which it is made. Some materials have low resistance, whereas others have high resistance. → Ex – the resistance of nichrome wire is about 60 times more than that of the copper wire. 4. Temperature of the conductor – → The resistance of metals increases on increase in the temperature and decreases on decrease in the temperature.  ELECTRICITY → The resistance of insulators like ebonite, glass and diamond is very high and does not change with temperature. → Resistance of alloys like manganin, constantan and nichrome is unaffected by temperature. Resistivity It is defined as the resistance of a conductor of unit length and unit area of cross-section. Resistivity is also known as specific resistance. Resistivity is denoted as 𝜌 (rho). The SI unit is ohm-metre (Ω 𝑚). The resistance of a given conductor is directly proportional to its length. That is : 𝑅 ∝ 𝑙...... (1) 1 The resistance of a given conductor is inversely proportional to its area of cross-section. That is : 𝑅 ∝ 𝐴..... (2) 𝑙 By combining the equn (1) and (2), we get : 𝑅 ∝ 𝐴 𝜌 ×𝑙 ⟹ 𝑅= 𝐴 𝑅 ×𝐴 ⇒ 𝜌= 𝑙 R = resistance of the conductor A = area of cross-section of the conductor l = length of the conductor Resistivity is numerical equal to the resistance of a rod of that substance which is 1 m long and 1 m2 in cross-section. A = 1, l = 1 then, 𝜌 = 𝑅 The resistivity of a material does not depend on its length or thickness. It depends on the nature of the material and temperature. (In other words, resistivity is a characteristic property of the material of the conductor and varies only, if its temperature changes.) Insulators such as glass, rubber, ebonite, etc., have a very high resistivity (1012 to 1017 Ω 𝑚). Conductors such as silver, copper, aluminum, etc., have a low resistivity (10-8 to 10-6 Ω 𝑚). Alloys have higher resistivity than the metals they are made of. Alloys – → The resistivity of alloys is much higher than those of the pure metals from which they are made of. → Ex –  Constantan is an alloy of copper and nickel. Resistivity of constantan is 30 times more than that of copper.  Manganin is an alloy of copper, manganese and nickel. Resistivity of manganin is 25 times more than that of copper.  Nichrome is an alloy of nickel, chromium and manganese and iron. Resistivity of nichrome is 60 times more than that of copper. → Alloys are used to make heating elements of devices such as electrical iron, heaters etc. because they have high resistivity and they do not oxidise (or burn) easily at high temperatures. → Nichrome is used for making the heating elements of electrical appliances such as electric iron, toaster, electric kettle, room heaters, water heaters and hair dryers etc. because : (i) Nichrome has very high resistivity. (ii) Nichrome does not undergo oxidation (or burn) easily at high temperature. ❖ The resistivity of semi-conductors like silicon and germanium is in between conductors and insulators. Their resistivity decreases on increasing temperature. ❖ Semi-conductors are used for making solar cells and transistors. Combination of Resistances or Resistors / Resistance of a system of Resistors There are two methods of connecting the resistors together. Series connection and Parallel connection. Resistors in Series connection – When two or more resistors are connected end to end each other, then they are said to be connected in series. The equivalent resistance of all resistors combined is equal to the sum of the all individual resistances.  ELECTRICITY The equivalent resistance is thus greater than the resistances of either resistor. This is also known as maximum effective resistance. The current through each resistor is same. The potential difference across each resistor is different. Resultant Resistance of Resistors connected in Series – An applied potential V produces current I in the resistors and R1, R2 and R3 causing a potential drop V1, V2 and V3 respectively, through each resistor. Total potential, V = V1 + V2 + V3 By Ohm’s law, V1 = IR1, V2 = IR2 and V3 = IR3 Thus, V = V1 + V2 + V3 = IR1 + IR2 + IR3 ⇒ V = I (R1 + R2 + R3) If R is the equivalent resistance and V = IR Hence, IR = I (R1 + R2 + R3) ⇒ R = R1 + R2 + R3 Disadvantages of Series Combination – ▪ In series combination, if any of the component fails to work, then the circuit will break and none of the components will works. ▪ It is not possible to connect a bulb and a heater in series simultaneously because they need different values of current to operate. ▪ In the series connection of electrical appliances, the overall resistance of the circuit increases too much due to which the current from the power supply is low. Resistors in Parallel connection – When two or more resistors are connected simultaneously between two points to each other, then they are said to be connected in parallel combination. The reciprocal of the combined resistance of resistors connected in parallel is equal to the sum of the reciprocal of all individual resistances. The equivalent resistance is less than the resistance of either resistor. This is also known as minimum effective resistance. The current from the source is greater than the current through either resistor. The potential difference across each resistor is same.  ELECTRICITY Resultant Resistance of Resistors connected in Parallel – An applied potential difference V produces current I1 in R1, I2 in R2 and I3 in R3. 𝑉 𝑉 𝑉 By Ohm’s law, 𝐼1 = 𝑅1 , 𝐼2 = 𝑅2 and 𝐼3 = 𝑅3 Total current, 𝐼 = 𝐼1 + 𝐼2 + 𝐼3 𝑉 𝑉 𝑉 𝑉 Thus, 𝑅 =𝑅 +𝑅 +𝑅 1 2 3 𝑉 𝑉 𝑉 𝑉 ⟹ 𝑅 = 𝑉 (𝑅 + 𝑅 + 𝑅 ) ! 2 3 1 1 1 1 ⟹ 𝑅 =𝑅 +𝑅 +𝑅 1 2 3 Advantages of parallel connection – ▪ Parallel combination divides the current among the components, so that they can have necessary amount of current to operate properly. This is the reason of connecting electrical appliances in parallel combination in household circuit. ▪ In parallel circuit, if one electrical appliance stops working due to some defect, then all other appliances keep working normally. ▪ In parallel circuit, each electrical appliance has its own switch due to which it can be turned on or turned off independently, without affecting other appliance. ▪ In parallel circuits, each electrical appliance gets the same voltage. ▪ In the parallel connection of electrical appliance, the overall resistance of the household circuit is reduced due to which the current from the power supply is high. ❖ The circuit in which some resistances connected in series combination and some in parallel combination is known as complex circuit. Heating of Effect of Electric Current – When an electric current is passed through a high resistance wire, like nichrome wire, the resistance wire becomes very hot and produces heat. This is called the heating effect of electric current. The heating of electric current is obtained by transformation of electrical energy into heat energy. Ex – electric heater, electric iron, etc. Calculation of Heat Generated in a Conductor – When the current I flows through a wire of resistance R. When electric charge q moves against a potential difference V. then, Amount of work, W = q × V - - - - - - - (i) 𝑞 Electric Current = 𝐼= 𝑡 So, 𝑞 =𝐼 ×𝑡 From Ohm’s law, 𝑉 = 𝐼𝑅  ELECTRICITY Putting the values of q and V in equn (i), we get 𝑊 = (𝐼 × 𝑡) × 𝐼𝑅 = 𝐼 2 𝑅𝑡 Assuming that all electrical work done or electrical energy consumed is converted into heat energy, i.e., heat produced. So heat produced is given by 𝐻 = 𝐼2 × 𝑅 × 𝑡 This formula gives us the heat produced in joules when a current of I amperes flows in a wire of resistance R ohms for time t seconds. This is known as Joule’s law of heating. According this law, the heat is produced in a resistor is (i) Directly proportional to the square of current for a given resistance. (ii) Directly proportionality to the resistance for a given current. (iii) Directly proportional to the time for which the current flows through the resistor. Application of Heating of Electric Current – Electric Bulb – → It has a filament made of tungsten because it has high resistivity and high melting point. → So, most of the power consumed by tungsten is dissipated in the form of heat some part is converted into light. → If air is present in an electric bulb, then the extremely hot tungsten filament would burn up quickly in the oxygen of air. → So, the bulb is filled with chemically unreactive gas nitrogen and argon gas to prolong the life of filament. Electric Fuse – → It is used as a safety device in household wiring and electrical appliances. → It protects the circuits, by stopping the flow of any high electric current. → It is connected in series with main supply. → It consists of an alloy of lead, tin or copper. → When the current in a household electric circuit exceeds the safe limit, the temperature of the fuse wire increases and the fuse wire melts and breaks the circuit. → Fuse helps to protect the other circuits from hazards caused by heavy current. → Fuses are always have current values such as 1A, 2A, 5A, 10A, 15A, etc. Electric Power – The amount of electric energy consumed in a circuit per unit time. If W be the amount of electric energy consumed in a circuit in t seconds, then the electric power is given by 𝑊𝑜𝑟𝑘𝑑𝑜𝑛𝑒 𝑃𝑜𝑤𝑒𝑟 = 𝑇𝑖𝑚𝑒 𝑊 𝑃= 𝑡 But W = electrical energy = 𝑉𝑞 = 𝑉𝐼𝑡 𝑉𝐼𝑡 So, 𝑃= 𝑡 ⇒ 𝑃 = 𝑉𝐼 According to Ohm’s law, 𝑉 = 𝐼𝑅 ⇒ 𝑃 = 𝐼𝑅 × 𝐼 = 𝐼 2 𝑅 𝑉2 𝑉 ⇒ 𝑃= 𝑅 [𝑝𝑢𝑡𝑡𝑖𝑛𝑔 𝐼 = 𝑅] The SI unit of electric power is watt (W). 1 watt of electric power means if 1 ampere current flows through circuit having 1 volt potential difference.  ELECTRICITY Bigger units of power are as given below: 1 kilowatt (kW) = 103 W 1 megawatt (MW) = 106 W 1 gigawatt (GW) = 109 W Practical unit of power is horse power. 1 HP = 746 W Commercial unit of electrical energy 1 kWh = 1000 Wh =1000 × 3600 Ws = 3.6 × 106 Ws = 3.6 × 106 J Number of units consumed by electric appliances is 𝑤𝑎𝑡𝑡 × ℎ𝑜𝑢𝑟𝑠 = 1000 Are electrons already consumed in an electric Circuit? → No, electrons are not consumed in an electric circuit. We pay the electricity board or electric company to provide energy to move electrons through all the electric gadgets like fan, bulb, refrigerator, etc. installed in our homes. We pay for the electrical energy that we use.