Power of Electrical Circuit: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Power of Electrical Circuit. Understanding the underlying formula is key to arriving at the correct answer below:

The current in the circuit is \(I = E / (R + r)\). For \(I\) to be maximum, the denominator \((R + r)\) must be minimum. This occurs when \(r = 0\), not \(r = R\). So, Assertion (A) is false. The power produced across \(R\) is \(P_R = I^2 R = (E / (R + r))^2 R\). As \(r\) increases, \(R+r\) increases, so \(P_R\) decreases. Thus, \(P_R\) is minimum when \(r\) is maximum (approaching infinity), not at \(r = R\). So, Reason (R) is also false.