Equivalent resistance in Series Combination


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1 Combination of Resistances There are two methods of joining the resistors together. SERIES CONNECTION An electric circuit in which three resistors having resistances R1, R2 and R3, respectively, are joined end to end. the resistors are said to be connected in series. PARALLEL CONNECTION An electric circuit in which a combination of three resistors are connected together between two common (points X and Y), the resistors are said to be connected in parallel. Equivalent resistance in Series Combination In a series combination of resistors the current is the same in every part of the circuit or the same current passes through each resistor.
2 The potential difference V is equal to the sum of potential differences V1, V2, and V3. That is the total potential difference across a combination of resistors in series is equal to the sum of potential difference across the individual resistors. That is, V = V1 + V2 + V3 let I be the current through the circuit. The current through each resistor is also I. Applying the Ohm s law to the entire circuit, we have V = I R On applying Ohm s law to the three resistors separately, V1 = I R1 V2 = I R2 V3 = I R3 I R = I R1 + I R2 + I R3 or Rs = R1 +R2 + R3 When several resistors are joined in series, the resistance of the combination Rs equals the sum of their individual resistances, R1, R2, R3, and is thus greater than any individual resistance. Equivalent resistance in Parallel Combination In a parallel combination of resistors the potential difference is the same in every individual resistor because they are connected between two common points in the circuit. The total current I, is equal to the sum of the separate currents through each branch of the combination. I = I1 + I2 + I3
3 Let Rp be the equivalent resistance of the parallel combination of resistors. By applying Ohm s law to the parallel combination of resistors, we have I = V/Rp On applying Ohm s law to each resistor, we have I1 = V /R1; I2 = V /R2; and I3 = V /R3 From Eqs. we have V/Rp = V/R1 + V/R2 + V/R3 or 1/Rp = 1/R1 + 1/R2 + 1/R3 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. Disadvantages of SERIES connection It is impracticable to connect electrical appliances in series, because 1) Different appliances need currents of widely different values to operate properly 2) when one component fails the circuit is broken and none of the components works. Eg;_ fairy lights difficult to locate dead bulb Advantages of PARALLEL connection 1) a parallel circuit divides the current through the electrical appliances 2) The total resistance in a parallel circuit is decreased This is helpful when each gadget has different resistance and requires different current to operate properly. HEATING EFFECT OF ELECTRIC CURRENT If an electric circuit is purely resistive, (only resistors are connected to a battery); the source energy continually gets dissipated entirely in the form of heat. This is known as the heating effect of electric current. Use Heating effect of electric current is utilised in devices such as electric heater, electric iron etc. P = V x I : H = VIt Consider a current I flowing through a resistor of resistance R. Let the potential difference across it be V
4 Let t be the time during which a charge Q flows across. The work done in moving the charge Q through a potential difference V is VQ. Therefore, the source must supply energy equal to VQ in time t. Hence the power input to the circuit by the source is P = V x Q/t = VI Or the energy supplied to the circuit by the source in time t is P t, that is, VIt. The energy gets dissipated in the resistor as heat. Thus for a steady current I, the amount of heat H produced in time t is H = VIt Apply ohm s law ( R = V/I, V = IR) Then H = I x R x I x t H = I 2 Rt Joule s Law of Heating Joule s law states that heat produced in a resistor is (i) directly proportional to the square of current for a given resistance, (ii) directly proportional to resistance for a given current, and (iii) directly proportional to the time for which the current flows through the resistor If I is the current, R is the resistance and t is the time for which current is flowing, the heat energy produced H = I 2 Rt This is known as Joule s law of heating Practical Applications of Heating Effect of Electric Current/ Uses of Joules Law of Heating 1. Electric heating devices (the electric laundry iron, electric toaster, electric oven, electric kettle and electric heater ) work based on Joule s heating. 2. The electric heating is used to produce light in an electric bulb
5 3. the fuse used in electric circuits is an application of Joule s heating. Working of an Electric Bulb: The filament of the bulb must retain much of the heat generated and gets very hot and emits light. It must not melt at such high temperature. The filament are thermally isolated, using insulating support, etc. The bulbs are usually filled with chemically inactive nitrogen and argon gases to prolong the life of filament. Most of the power consumed by the filament appears as heat, but a small part of it is in the form of light radiated Property of material used for making filament: / Reason for using Tungsten as filament Tungsten is a strong metal with high melting point (melting point 3380 C) is used for making bulb filaments. It does not get oxidized at high temperature. Tungsten has high resistivity among other metals.
6 Fuse: Fuse is a safety device used in electric circuits. I The fuse is an application of Joule s heating.it protects circuits and appliances by stopping the flow of any unduly high electric current. The fuse is placed in series with the device. Fuse Material: It consists of a piece of wire made of a metal or an alloy of appropriate melting point, for example aluminium, copper, iron, lead etc. Working of Fuse: If a current larger than the specified value flows through the circuit, the temperature of the fuse wire increases. This melts the fuse wire and breaks the circuit. The fuse wire is usually encased in a cartridge of porcelain or similar material with metal ends. Types of Fuses: The fuses used for domestic purposes are rated as 1 A, 2 A, 3 A, 5 A, 10 A, etc. Calculating the range of fuse: Eg For an electric iron which consumes 1 kw electric power when operated at 220 V, a current of (1000/220) A, that is, 4.54 A will flow in the circuit. a 5 A fuse must be used. ( P= VI I = P / V) Electric Power: the rate at which electric energy is dissipated or consumed in an electric circuit is termed as electric power. The power P is given by P = VI Or P = I 2 R ( V= IR) P = I x I x R = P = I 2 R P = VI ( I = V/R) P = V x V/R = V 2 /R
7 The SI unit of electric power is watt (W). watt ( W) is the power consumed by a device that carries 1 A of current when operated at a potential difference of 1 V. Thus, 1 W = 1 volt 1 ampere = 1 V A Higher Unit of Power: kilowatt. It is equal to 1000 watts. Smaller unit of Electical energy;_ the unit of electric energy is watt hour (W h). One watt hour is the energy consumed when 1 watt of power is used for 1 hour. The commercial unit of electric energy is kilowatt hour (kw h), commonly known as unit. 1 kw h = 1000 watt 3600 second 1 kw h = watt second 1 kw h = joule (J)
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