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(C) According to the maximum power transfer theorem,the power delivered to an external circuit is maximum when the external resistance $R_{	ext{ext}}

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$R = 3r$

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(C) According to the maximum power transfer theorem,the power delivered to an external circuit is maximum when the external resistance $R_{	ext{ext}}$ is equal to the internal resistance $r$ of the cell,i.e.,$R_{	ext{ext}} = r$.First,we determine the equivalent external resistance $R_{	ext{ext}}$ between terminals $A$ and $B$. The circuit consists of three resistors of resistance $R$ connected in parallel. For three resistors $R$ in parallel,the equivalent resistance $R_{	ext{ext}}$ is given by:$\frac{1}{R_{	ext{ext}}} = \frac{1}{R} + \frac{1}{R} + \frac{1}{R} = \frac{3}{R}$Therefore,$R_{	ext{ext}} = \frac{R}{3}$.Setting $R_{	ext{ext}} = r$ for maximum power transfer:$\frac{R}{3} = r$$R = 3r$Thus,the value of $R$ for which the power is maximum is $3r$.

Consider a circuit where a cell of emf $E_0$ and internal resistance $r$ is connected across the terminals $A$ and $B$ as shown in the figure. The value of $R$ for which the power generated in the circuit is maximum is given by

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