A piece of wire of resistance R is cut into five equal parts.
Question.
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 $R^{\prime}$, then the ratio $R / R^{\prime}$ is

(1) $\frac{1}{25}$

(2) $\frac{1}{5}$

(3) 5

(4) 25

solution:

Resistance of each one of the five parts $=\frac{\mathrm{R}}{5}$ Resistance of five parts connected in parallel is

given by

$\frac{1}{\mathrm{R}^{\prime}}=\frac{1}{\mathrm{R} / 5}+\frac{1}{\mathrm{R} / 5}+\frac{1}{\mathrm{R} / 5}+\frac{1}{\mathrm{R} / 5}+\frac{1}{\mathrm{R} / 5}$

or $\frac{1}{R^{\prime}}=\frac{5}{R}+\frac{5}{R}+\frac{5}{R}+\frac{5}{R}+\frac{5}{R}=\frac{25}{R}$

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

Thus, (4) is the correct answer.
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