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 $\dfrac{\text{R}}{\text{R}'}$ is ……………

1. $\dfrac{1}{25}$

2. $\dfrac{1}{5}$

3. 5

4. 25

25

Reason — Given,

Wire of resistance R is cut into five equal parts hence, resistance of each part is $\dfrac{\text{R}}{5}$

$\dfrac{1}{\text{R}'} = \dfrac{1}{\dfrac{\text{R}}{5}} + \dfrac{1}{\dfrac{\text{R}}{5}}+ \dfrac{1}{\dfrac{\text{R}}{5}} + \dfrac{1}{\dfrac{\text{R}}{5}} + \dfrac{1}{\dfrac{\text{R}}{5}} \\[1em] = \dfrac{5}{\text{R}} + \dfrac{5}{\text{R}} + \dfrac{5}{\text{R}} + \dfrac{5}{\text{R}} + \dfrac{5}{\text{R}} \\[1em] = \dfrac{25}{\text{R}} \\[1em] \Rightarrow \text{R}' = \dfrac{\text{R}}{25}$

Hence,

$\dfrac{\text{R}}{\text{R}'} = \dfrac{\text{R}}{\dfrac{\text{R}}{25}} \\[1em] \Rightarrow \dfrac{\text{R}}{\text{R}'} = 25$