Physics Class 12 NCERT Solutions: Chapter 3 Current Electricity Part 9

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Series and parallel resistors

Series and Parallel Resistors

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Q: 20. [A] Given n resistors each of resistance R, how will you combine them to get the (i) maximum (ii) minimum effective resistance? What is the ratio of the maximum to minimum resistance?

[B] Given the resistances of how will be combine them to get an equivalent resistance of

(i) (ii) (iii) (iv)?

[C]Determine the equivalent resistance of networks shown in fig.3.31.

Q 20 C a Image of the Equivalent Resistance of Networks

Q 20 C a Image of the Equivalent Resistance of Networks

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Q 20 C b Image of the Equivalent Resistance of Networks

Q 20 C B Image of the Equivalent Resistance of Networks

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Answer:

(a) Total number of resistors

Resistance of each resistor

(i) When resistors are connected in series, effective resistance is the maximum, given by the product.

Hence, maximum resistance of the combination,

(ii) When n resistors are connected in parallel, the effective resistance is the minimum, given by the ration.

Hence, minimum resistance of the combination,

(iii) The ration of the maximum to the minimum resistance is,

(B) The resistance of the given resistors is,

i. Equivalent resistance,

Consider the following combination of the resistors.

Q 20 B i Combination of the Resistors

Q 20 B I Combination of the Resistors

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Equivalent resistance of the circuit is given by,

ii. Equivalent resistance,

Consider the following combination of the resistors.

Q 20 B ii Combination of the Resistors

Q 20 B II Combination of the Resistors

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Equivalent resistance of the circuit is given by,

(iii) Equivalent resistance,

Consider the following combination of the resistors, as shown in the given circuit.

Q 20 B iii Combination of the Resistors

Q 20 B III Combination of the Resistors

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Equivalent resistance of the circuit is given by the sum,

(iv)Equivalent resistance,

Consider the following combination of the resistors, as shown in the given circuit.

Q 20 B iv Combination of the Resistors

Q 20 B IV Combination of the Resistors

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Equivalent resistance of the circuit is given by the sum,

(C) (a) It can be observed form the given circuit that in the first small loop, two resistors of resistance each are connected in series.

Hence, their equivalent resistance

It can also be observed that two resistors of resistanceeach are connected in series.

Hence, their equivalent resistance

Therefore, the circuit can be redrawn as

Q 20 C a The Circuit of Redrawn

Q 20 C a the Circuit of Redrawn

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It can be observed that and resistors are connected in parallel in all the four loops. Hence, equivalent resistance of each loop is given by,

The circuit reduces to,

Q 20 C A 1 All the Four Resistors are Connected in Series.

Q 20 C a 1 All the Four Resistors Are Connected in Series

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All the four resistors are connected in series.

Hence, equivalent resistance of the given circuit is

(b) It can be observed from the given circuit that five resistors of resistance each are connected in series.

Hence, equivalent resistance of the circuit