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The minimum resistance which can be obtained using five resistors each of $\frac{1}{5} Ω$ will be?

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\frac{1}{5} ohm

25 ohm

\frac{1}{25} ohm

\frac{1}{10} ohm

answer is C.

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Detailed Solution

The minimum resistance which can be obtained using five resistors each of

\frac{1}{5} Ω

, will be

\frac{1}{25} ohm .

It is known that “in a parallel combination of resistance, the reciprocal of the equivalent resistance is minimum because the equivalent resistance is given by the sum of reciprocals of the resistances.” Mathematically,

\frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + \frac{1}{R_{4}} + \frac{1}{R_{5}}

On substituting the given resistance value of

\frac{1}{5} Ω

0.2 Ω

, we get

\Rightarrow \frac{1}{R} = \frac{1}{0.2} + \frac{1}{0.2} + \frac{1}{0.2} + \frac{1}{0.2} + \frac{1}{0.2}

\Rightarrow \frac{1}{R} = 25

\Rightarrow R = \frac{1}{25} Ω

Hence, the minimum resistance is

\frac{1}{25} Ω

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