Two identical cells each of emf E and interna | vedclass

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(A) For two identical cells of emf $E$ and internal resistance $r$ connected in parallel, the equivalent emf $E_{eq} = E$ and the equivalent internal

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$R = r / 2$

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(A) For two identical cells of emf $E$ and internal resistance $r$ connected in parallel, the equivalent emf $E_{eq} = E$ and the equivalent internal resistance $r_{eq} = r / 2$.The current $I$ flowing through the external resistance $R$ is given by $I = \frac{E}{R + r_{eq}} = \frac{E}{R + r/2} = \frac{2E}{2R + r}$.The power $P$ developed across the external resistance $R$ is $P = I^2 R = \left( \frac{2E}{2R + r} \right)^2 R$.To maximize power, we set $\frac{dP}{dR} = 0$, which leads to the condition $R = r_{eq}$.Substituting $r_{eq} = r / 2$, we get $R = r / 2$.

Two identical cells each of emf $E$ and internal resistance $r$ are connected in parallel with an external resistance $R$. To get maximum power developed across $R$, the value of $R$ is

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