# A set of ‘n’ identical resistors, each of resistance ‘R’ when connected in series have an effective resistance ‘X’. When they are connected in parallel, their effective resistance becomes ‘Y’. Find out the product of X and Y.

When a set 'n' identical resistors each of resistance 'R' connected in series have an effective resistance 'x'.

Thus, X=nR _____(i)

and when they are connected in parallel, their effective resistance becomes 'Y'.

Thus, $Y=\frac{R}{n}$ _____(ii)

Hence, from the equation (i) and (ii), the product of X and Y

we get,

$X\times Y=nR\times \frac{R}{n}$

$XY=R^{2}$

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