Question

A uniform wire of resistance $R$ is cut into two equal pieces, and these pieces are joined in parallel. What is the equivalent resistance of the combination?

• A. $R/2$
• B. $R/4$
• C. $2R$
• D. $4R$

Answer 1

The correct option is B $R/4$

Given, resistance of the wire $=R$

We know that, resistance,
$R=\rho \frac{l}{A}$

For same wire, $R\propto l$

So, if wire length is halved, then its resistance is also halved.

Hence, the resistance of each half of the wire will be $R/2$.

The circuit diagram, when these two equal pieces of the wire are joined in parallel, is shown in the figure.

Therefore, equivalent resistance of the combination,

$R_{\text{eq}}=\frac{R_1{R}_2}{R_1+R_2}=\frac{R/2\times R/2}{R/2+R/2}=R/4$