Question

A piece of wire of resistance $R$ is cut into five parts of equal length. These parts are then connected in parallel. If the equivalent resistance of the parallel combination is $R^{{}^{\prime }}$, then the ratio $\frac{R}{R^{{}^{\prime }}}$ is:

• A. (1/25)
• B. (1/5)
• C. 5
• D. 25

Answer 1

The correct option is D

25

The resistance of the wire = R.
The wire is cut into 5 parts of equal length.
If the length of the wire is L, then the length of each part = $\frac{L}{5}$
Since $R\propto L$,
Resistance of each one of the five parts = $\left(\frac{R}{5}\right)$
Resistance of five parts connected in parallel is given by
$\frac{1}{R^{\prime }}=\frac{1}{R/5}+\frac{1}{R/5}+\frac{1}{R/5}+\frac{1}{R/5}+\frac{1}{R/5}{R}^{\prime }=\frac{R}{25}$

$\frac{R}{R^{\prime }}=25$