A piece of wire of resistance R

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Solution

Q.
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 $\frac{R}{R'}$ is

1 1/25

2 1/5

3 5

4 25

Ans.
(4)

Given, a piece of wire with resistance R is cut into 5 equal parts

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

now, these pieces of wire are connected in parallel then the resistance is (R')

$\frac{1}{R'} = \frac{5}{R} + \frac{5}{R} + \frac{5}{R} + \frac{5}{R} + \frac{5}{R} S o, \frac{1}{R^{'}} = \frac{25 R}{R} R^{'} = \frac{R}{25} N o w, \frac{R}{R'} = \frac{\frac{R}{R}}{25} \frac{R}{R'} = \frac{25}{R} \frac{R}{R'} = 25$

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