If $n$ equal resistors are first connected in series and then parallel, what will be the ratio of the maximum to minimum resistance?

n

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1 / n^{2}

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n^{2}

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1 / n

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Solution

The correct option is C $n^{2}$
Let the resistance of each resistor be $R$ .
Series connection :
Equivalent resistance (maximum) $R_{s} = R + R + . . . . + n$ terms
$⟹$ $R_{s} = n R$
Parallel connection :
Equivalent resistance (minimum) $\frac{1}{R_{p}} = \frac{1}{R} +$ $\frac{1}{R} + . . . + n$ terms
We get $\frac{1}{R_{p}} = \frac{n}{R}$
$⟹$ $R_{p} = \frac{R}{n}$
Thus ration of maximum to minimum resistance $\frac{R_{s}}{R_{p}} = \frac{n R}{R / n}$
$⟹$ $\frac{R_{s}}{R_{p}} = n^{2}$

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If n equal resistors are first connected in series and then parallel, what will be the ratio of the maximum to minimum resistance?

If $n$ equal resistors are first connected in series and then parallel, what will be the ratio of the maximum to minimum resistance?