Four wires each of same length, diameter and material are connected to each other to form a square. If the resistance of each wire is R, then equivalent resistance across the opposite corners is:

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\frac{R}{2}

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\frac{R}{4}

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Solution

The correct option is A R
Given, resistance of each wire is $R$ .
We have to calculate the resistance from A to B,
Since wire AP and PB are in series, the equivalent resistance across the path APB is R + R = 2R;
also, wire AQ and QB are in series, therefore resistance across path AQB is R + R = 2R
therefore, $R_{e f f (A P B)}$ = 2R
and $R_{e f f (A Q B)}$ = 2R
APB is in parallel with AQB, therefore the equivalent resistance across them $\Rightarrow \frac{1}{R^{'}}$ = $\frac{1}{2 R}$ + $\frac{1}{2 R}$
$\Rightarrow R^{'} = R$

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