Question

a wire resistance R is cut into n equal parts .these parts are then connect in parallel .the equivalent resistance of the combination will be .?

Answer 1

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Answer 2

Answer:

The equivalent resistance of the combination will be $\frac{R}{n^2}$.

Explanation:

The resistance of each segment =$\frac{R}{n}$

As per question "n" segments are connected in parallel.

And for parallel combination equivalent resistance($R_p$) is calculated as,

$\frac{1}{R_p} =\frac{1}{R_n} +\frac{1}{R_n}+......+\frac{1}{R_n}$

$\frac{1}{R_p}= \frac{n}{R}\times n$

$R_p=\frac{R}{n^2}$   (1)

Hence, the equivalent resistance of the combination will be $\frac{R}{n^2}$.

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