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
$(a)$. 1/25
$(b)$. 1/5
$(c)$. 5
$(d)$. 25

The correct answer is $(c)$. 5

Explanation:

Given: 

A piece of wire of resistance $R$ is cut into five equal parts and these parts are then connected in parallel. The equivalent resistance of this combination is $R'$.

To do:

To find the ratio $R/R′$.

Solution:

If a piece of wire of resistance $R$ is cut into five equal parts the resistance$(R)$ of each part will be the same.

Then, $\frac{1}{R'}=\frac{1}{R}+\frac{1}{R}+\frac{1}{R}+\frac{1}{R}+\frac{1}{R}$ 

Or $\frac{1}{R'}=\frac{5}{R}$

Or $R'=\frac{R}{5}$

So, $\frac{R}{R'}=\frac{R}{\frac{R}{5}}$

Or $\frac{R}{R'}=5$

Therefore, the ratio $R/R′$ is $5$

So, option $(c)$ is correct.

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Updated on: 10-Oct-2022

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