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Classification of Circuits

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We have seen a simple circuit in which source, fuse, switch & lamps are connected in series with the help of wires. In this circuit only one lamp was connected. However, you will often find that a circuit has more than one load. It may have 2, 3, 4 or a number of lamps or resistance. They may be connected in series or parallel.

Series circuit Whenever you connect resistances end to end they are said to be series connected. If all the resistances around a circuit are connected in end to end so that there is only one path for current flow. They form a series circuit. In series circuit total resistance equals, the sum of the individual resistances. There total resistance of series circuit we can calculate by following equation- RT = R1 + R2 + R3 where, R1, R2, R3 = Individual Resistance; in ohms RT= Sum of individual resistances; in ohms.

Ex 1. The resistors of 10 ohm’s, 15 ohm’s, and 30 ohm’s are connected in series across a battery, what is the total resistance? Ans- Given, R1 = 10 ohms R2 = 15 ohm R3 = 30 ohm RT = R1 + R2 + R3 RT = 10 + 15 + 30 RT = 55 Ohm ...Ans. In a series circuit there is only one path for current flow, this means that all the current must flow through each resistance in the circuit. Ans- IT = I1 + I2 + I3 where, IT = Total current, in ampere I1 + I2 + I3 = Individual current of each resistance in ampere. Ex 2. A series circuit consists of 3 resistors having values of 20 ohms, 30 ohms and 50 ohms respectively calculte the current flowing through the circuit and current flowing through each resistance if it is connected 200 volts supply? Ans- Given, R1 = 20 ohms R2 = 30 ohms R3 = 50 ohms E = 200 Volt First we calculate RT RT = R1 + R2 + R3 = 20 + 30 + 50 = 100 ohms. Now we calculate current ( total)

…Ans.

The resistance are connected in series so current flowing through R1, R2, R3 is = 2A therefore, I1 = 2A, I2 = 2A, I3 = 2A In series circuit the sum of the resistance voltage drop must equal to source voltage.

Example - 2. A series circuit consist of 3 resistors having values of 20, 30 & 50 ohms respectively. Find the applied voltage, if the current through circuit is 2 ampere? Ans- Given, R1 = 20 ohms, R2 = 30 ohms, R3 = 50 ohms, I = 2A Let us calculate voltage drop across each resistance. Vr1= I x R1 = 2 x 20 = 40 V Vr2= I x R2 = 2 x 30 = 60 V Vr3= I x R3 = 2 x 50 = 100 V therefore, Vr1 = 40 V, Vr2 = 60 V, Vr3 = 100 V Once individual voltage drops are known they can be added to find total or applied voltage. therefore, E1 = Vr1 + Vr2 + Vr3 = 40 + 60+ 100 = 200 V E1 = 200 V ...Ans. The total voltage drop across a resistor in a circuit is proportional to the ohmic value of the resistors.

Open Circuit in Series

You already know that a current to pass through a circuit, a closed path is required, so any break in the series circuit causes an open circuit, & stops current flow. There is no power wastage in circuit. If more than 2 lamps are connected in series and if one of them is fused then there is no current flowing through the circuit and so one lamp will light.

Short Circuit in Series

If the short circuit created in series circuit the total resistance will be reduces & a large current will flow through the circuit. Uses of series circuit: 1. Decorative 2. Fan regulator which is connected in series with fan can reduce the speed. 3. To measure circuit current with the help of ammeter. 4. The fuse used for protection of electrical installation. 5. To control the speed of DC Motors. 6. To increase the battery voltages.

Example - 2. A series circuit consist of 3 resistors having values of 20, 30 & 50 ohms respectively. Find the applied voltage, if the current through circuit is 2 ampere? Ans- Given, R1 = 20 ohms, R2 = 30 ohms, R3 = 50 ohms, I = 2A Let us calculate voltage drop across each resistance. Vr1= I x R1 = 2 x 20 = 40 V Vr2= I x R2 = 2 x 30 = 60 V Vr3= I x R3 = 2 x 50 = 100 V therefore, Vr1 = 40 V, Vr2 = 60 V, Vr3 = 100 V Once individual voltage drops are known they can be added to find total or applied voltage. therefore, E1 = Vr1 + Vr2 + Vr3 = 40 + 60+ 100 = 200 V E1 = 200 V ...Ans. The total voltage drop across a resistor in a circuit is proportional to the ohmic value of the resistors. Open Circuit in Series You already know that a current to pass through a circuit, a closed path is required, so any break in the series circuit causes an open circuit, & stops current flow. There is no power wastage in circuit. If more than 2 lamps are connected in series and if one of them is fused then there is no current flowing through the circuit and so one lamp will light.

Short Circuit in Series

If the short circuit created in series circuit the total resistance will be reduces & a large current will flow through the circuit. Uses of series circuit: 1. Decorative 2. Fan regulator which is connected in series with fan can reduce the speed. 3. To measure circuit current with the help of ammeter. 4. The fuse used for protection of electrical installation. 5. To control the speed of DC Motors. 6. To increase the battery voltages.

Parallel Circuit

When you connect resistances side by side with the ends connected, they are parallel connected. A parallel circuit is one in which there are one or more points where current divided & flows different paths. When circuit connected in such a way that they provide different current paths it is to be said that connected in parallel. In parallel circuit, total resistance is not the sum of individual resistances. More resistances there are the lower is the total resistance & total resistance is smaller than any of the individual resistance. The total resistance can be find out by a or product over the Sum method to use this method you first multiplied the values of two resistances to get their product then added the values of two resistances to get there sum. Finally you divide the , & the result is total resistance following equation may be used.


This method can be used only for two parallel resistances. This method is not suitable for more than two resistances which are connected in parallel. Combinations of 3 or more unequal resistances in parallel are sometimes used. To find the resistance of such combinations, you first find the total resistance of any two of the resistances. Combine this total in the same way with another of the resistance values & you have total for 3 resistances. Continue to combine the total with additional resistances until all of the resistances has been combine to give the total resistance of all parallel resistances. You can apply another method also, to find out the effective resistance of the parallel circuit. therefore,

The reciprocal of the resistance is known as the conductance of a circuit. Using this term, you can state that the combined conductance of a number of conductors in parallel is equal to sum of their separate conductance. e.g. 1. 4 ohms, 2 ohms & 6 ohms respectively 3 resistors are connected in parallel. Calculate the combined resistance ( Reff.) of the circuit. Ans- Given, R1 = 4 ohms R2 = 2 ohms R3 = 6 ohms




Reff = 1.1 ohms therefore, Reff = 1.1 ohms

Parallel circuit voltages

In this type of circuit the voltages across each branch resistance is equal to that across the other. In other words, in a parallel circuit, the same voltage is present across the resistors of a parallel group. This voltage is equal to the applied voltage. therefore, VT = Vr1 = Vr2 = Vr3 e.g. 1. 3 resistors of 4ohms, 2 ohms , & 6ohms respectively are connected in parallel. If current flowing through 4 ohms resistance is 2.5 A, current flowing through 2 ohms resistance is 5 A & current flowing through 6 ohms resistance 1.68 A, calculate voltage across each resistance & supply voltage? Ans: Given- R1 = 4 ohms R2 = 2 ohms R3 = 6 ohms Vr1 = I x R1 = 2.5 x 4 = 10 V Vr2 = I x R2 = 5 x 2 = 10 V

Vr3 = I x R3 = 1.68 x 6 = 10 V VT = Vr1 = Vr2 = Vr3 1 = 10 = 10 = 10 = 10V therefore, VT = 10 V

Current in Parallel Circuit:

Current divides among the various branches of a parallel circuit in a manner depending on the resistance of each branch. However source current in a parallel circuit divides among the available paths in relation to the value of resistors in the circuit for a given voltage current varies inversely with resistance. e.g.1. Three resistances of 10 ohms, 20 ohms & 30 ohms respectively are connected in parallel across 50 volts DC supply calculate the current flowing through each circuit & total current of the circuit? Ans- Given R1 = 10 ohms R2 = 20 ohms R3 = 30 ohms E = 50 V Ir1 = = = 5 A Ir2 = = = 2.5 A Ir3 = = = 1.67 A R3 30 therefore, Ir1 = 5 A, Ir2 = 2.5 A, Ir3 = 1.67 A Let us calculate circuit current: IrT = Ir1 + Ir2 + Ir3

= 5 + 2.5 + 1.67 IrT = 9.17 A

Short in Parallel Circuit

The equivalent resistance of the straight wire & the resistors, all connected in parallel, will be less than the resistance of the straight wire. This follows from the fact that the total resistance of a parallel circuit is always less than the smallest resistance in the branch. Since a complete path still exists to permit current flow, & the equivalent resistnce is effectively zero, the current will rise rapidly until the current capacity of the fuse is reached. The fuse will then open the circuit causing the current to stop flowing. A short usually causes components to fail in a circuit which is not properly used or otherwise protected. The failure may take the form of burned out resistor, damaged source or a fire in the circuit components & wiring. Uses of parallel circuit 1. In general lighting ( house, shops, offices) 2. Ammeter shunt.

Series - Parallel Circuit

Circuits consisting of three or more resistors may be connected in, partly series, & partly parallel one in which a resistance is connected in series with a parallel combinations & the other in which one or more branches of a parallel circuit consist of resistances in series. While solving circuit first solve parallel circuit first solve parallel circuit & then series circuit by applying parallel circuit & series circuit laws respectively.

What You Have LearnT

In this unit you have learnt about circuits & ohms law. We also learn the simple circuit i.e. electric circuit. Close circuit, open circuit, short circuit are the types of circuit. Ohms law founded by George S.Ohm. This is the Formula of to find out the voltage, current resistance. We studied: the Laws of resistance and Classification of circuit. 5.7 Terminal Questions 1. Which factors consist by an electrical circuit? 2. What do you mean by close circuit? 3. What are the examples of open circuit?

4. What is the meaning of short circuit? 5. State the ohm’s law? 6. State ohms law with equations? 7. What is simple circuit? Explain with neat diagram 8. Write a short note on series circuit 9. Write a short note on parallel circuit 10. State the uses of series circuit parallel circuit & series parallel circuit?

Answer to intext questions

(A) 5.1 1. Safety 2. Electrical, light energy 3. Safety, controlling 4. Closed (B) True or False: 1) True 2) True 3) True 4) False 5) True (C) (a) - 1 (b) - 2 (c) - 4 (d) - 1 (e) - 3

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