Question

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:

• A. R
• B. $\frac{R}{2}$
• C. $\frac{R}{4}$
• D. 2R

Answer 1

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, $R_{eff\left(APB\right)}$ = 2R
and $R_{eff\left(AQB\right)}$ = 2R
APB is in parallel with AQB, therefore the equivalent resistance across them $\Rightarrow \frac{1}{R^{\prime }}$ = $\frac{1}{2R}$ + $\frac{1}{2R}$
$\Rightarrow R^{\prime }=R$