A piece of wire of resistance R is cut into five equal parts. These parts are th

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

\frac{R}{R^{^{'}}}

is:

Options:

A . 125

B . 15

C . 5

D . 25

Answer: Option D
:
D
Given the wire iscut into 5 equal parts.
Let the initial resistance of the wire be

R

where

R = ρ \frac{l}{A} \to R \propto l (l e n g t h o f t h e w i r e)

then, resistance of each one of the five parts

= (\frac{R}{5})

Equivalent resistance (R')of resistorsconnected in parallel is given by

\frac{1}{R^{'}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} . . \frac{1}{R_{n}}

Equivalent resistance (R') of five parts connected in parallel is given by:

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

Therefore,

\frac{R}{R^{^{'}}} = 25

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