Question

You are given n identical wires, each of resistance R When these are connected in parallel, the equivalent resistance is X. When these will be connected in series, then the equivalent resistance will be

• A. $X/n^2$
• B. $n^{2}X$
• C. X/n
• D. nx

Answer 1

Answer: (B)

$n^{2}X$

We know
1.When n identical wires, each of resistance R are connected in parallel, the equivalent resistance is $\frac{R}{n}$.
Let this be called$R_{Parallel}.$
2.When n identical wires, each of resistance R are connected in series, the equivalent resistance is $n\times R$.
Let this be called$R_{Series}$.
Therefore,
$\frac{R_{Parallel}}{R_{Series}}=\frac{\frac{R}{n}}{n\times R}=\frac{1}{n^2}$
$R_{Series}=X{n}^2$