The resistance of the series combination of two resistance is S. When they are joined in parallel the total resistance is P. If S = nP, then the minimum possible value of n is
Text Solution
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If two resistances are $R_1$ and $R_2$ then
$S = R_1 + R_2$ and $P = \frac{R_1 R_2}{(R_1 + R_2)}$
From given condition S = nP i.e. $\left(R_1 R_2\right) = n \left(\frac{R_1 R_2}{R_1 + R_2}\right)$
⇒ ⇒ $(R_1 + R_2)^2 = n \, R_1 R_2$ ⇒ ⇒ $(R_1 - R_2)^2 + 4R_1 R_2 = n R_1 R_2$
So $n=4+\frac{\left(R_{1}-R_{2}\right)^{2}}{R_{1} R_{2}} .$ Hence minimum value of n is 4.
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