Question

Question 1
A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R', then the ratio $\frac{R}{R^{\prime }}$ is:

(a) $\frac{1}{25}$
(b) $\frac{1}{5}$
(c) 5
(d) 25

Answer 1

(d) 25

The wire is cut into 5 equal parts, each resistance will be of $\frac{R}{5}$. All the 5 parts are connected in parallel.
Therefore, equivalent resistance (R') is given as
$\frac{1}{R^{\prime }}=\frac{5}{R}+\frac{5}{R}+\frac{5}{R}+\frac{5}{R}+\frac{5}{R}$ = $\frac{5+5+5+5+5}{R}$ = $\frac{25}{R}$
$\frac{R}{R^{\prime }}$ = 25