You are given 'mn' wires of equal resistance, If m wires are in series and n such combinations are in parallel the resultant resistance is $R_{1}$ . If n wires are in series and m such combinations are in parallel, the resultant resistance is $R_{2}$ . Then $\frac{R_{1}}{R_{2}}$ is:

1 : 1

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m : n

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m^{2} : n^{2}

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n^{2} : m^{2}

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Solution

The correct option is D $m^{2} : n^{2}$

For N equal resistance of resistance R, the equivalent resistance when all are connected in
1. Series is $R_{e q} = N \times R$
2. Parallel is $R_{e q} = \frac{R}{N}$
Hence,
in first case the equivalent resistance is $R_{e q_{1}} = \frac{m \times R}{n} = \frac{m R}{n}$
whereas,in second case,the equivalent resistance is $R_{e q_{2}} = \frac{n \times R}{m} = \frac{n R}{m}$
So,
$\frac{R_{1}}{R_{2}} = \frac{m^{2}}{n^{2}}$

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You are given 'mn' wires of equal resistance, If m wires are in series and n such combinations are in parallel the resultant resistance is R1. If n wires are in series and m such combinations are in parallel, the resultant resistance is R2. Then R1R2 is:

You are given 'mn' wires of equal resistance, If m wires are in series and n such combinations are in parallel the resultant resistance is $R_{1}$ . If n wires are in series and m such combinations are in parallel, the resultant resistance is $R_{2}$ . Then $\frac{R_{1}}{R_{2}}$ is: