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(B) The power $P$ dissipated in an external resistance $R$ connected to a cell of electromotive force $E$ and internal resistance $r$ is given by the

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(B) The power $P$ dissipated in an external resistance $R$ connected to a cell of electromotive force $E$ and internal resistance $r$ is given by the formula:$P = I^2 R$Since the current $I = \frac{E}{R+r}$,we have:$P = \left( \frac{E}{R+r} ight)^2 R = \frac{E^2 R}{(R+r)^2}$To find the variation of $P$ with $R$,we analyze the function $P(R) = \frac{E^2 R}{(R+r)^2}$.$1$. When $R = 0$,$P = 0$.$2$. When $R 	o \infty$,$P 	o 0$.$3$. The maximum power is dissipated when $R = r$,where $P_{max} = \frac{E^2}{4r}$.This behavior corresponds to a curve that starts from the origin,increases to a maximum value at $R = r$,and then decreases asymptotically towards zero as $R$ increases further. This matches the shape of Graph $B$.

Which of the following graphs represents the variation of power loss in the external load with external resistance $R$?

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