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(C) According to the maximum power transfer theorem,the external resistance $R_{ext}$ must be equal to the internal resistance $r$ of the battery.Give

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$2$

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(C) According to the maximum power transfer theorem,the external resistance $R_{ext}$ must be equal to the internal resistance $r$ of the battery.Given internal resistance $r = 4\, \Omega$.From the circuit simplification shown in the image,the equivalent external resistance $R_{ext}$ is calculated as follows:The circuit simplifies to two parallel branches,one with resistance $(R + 2R) = 3R$ and the other with $(2R + 4R) = 6R$.The equivalent resistance $R_{ext} = \frac{(3R 	imes 6R)}{(3R + 6R)} = \frac{18R^2}{9R} = 2R$.Setting $R_{ext} = r$,we get $2R = 4\, \Omega$,which implies $R = 2\, \Omega$.

In the given circuit,for maximum power to be transferred from a battery with an internal resistance of $4\, \Omega$,what should be the value of $R$ in $\Omega$?

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