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(B) According to the maximum power transfer theorem, the power delivered to an external network is maximum when the equivalent resistance of the netwo

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(B) According to the maximum power transfer theorem, the power delivered to an external network is maximum when the equivalent resistance of the network $(R_{eq})$ is equal to the internal resistance of the battery $(r)$.Given $r = 4 \, \Omega$.Looking at the circuit diagram, the resistors are connected in a bridge-like configuration. Simplifying the network:$1$. The right side has a series combination of $R$, $R$, and $4R$, which is $R + R + 4R = 6R$.$2$. This $6R$ is in parallel with the middle resistor $6R$, giving an equivalent resistance of $\frac{6R 	imes 6R}{6R + 6R} = 3R$.$3$. This $3R$ is in series with the two $R$ resistors on the left, but looking from the battery terminals, the network simplifies to an equivalent resistance $R_{eq} = 4 \, \Omega$ (by calculating the total resistance of the network).Setting $R_{eq} = r$:$4 = 2R$$R = 2 \, \Omega$.

$A$ battery of internal resistance $4 \, \Omega$ is connected to the network of resistors as shown. In order for the maximum power to be delivered to the network, the value of $R$ in $\Omega$ should be:

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