A piece of wire of resistance $R$ is cut into five equal parts. These parts are then connected in parallel. If the equiv

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 $R'$, then the ratio $R/R'$ is:

Accepted Answer

When a wire of resistance $R$ is cut into five equal parts, the resistance of each part becomes $R/5$. When these five parts are connected in parallel, the equivalent resistance $R'$ is given by $\frac{1}{R'} = \frac{5}{R/5} + \frac{5}{R/5} + \frac{5}{R/5} + \frac{5}{R/5} + \frac{5}{R/5} = \frac{25}{R}$, which means $R' = \frac{R}{25}$. Therefore, the ratio $R/R'$ is equal to 25.

Electricity

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