Maximum Power Transfer for Cells – Rankers Physics

Combination of Batteries: Practice Problem & Solution

Assertion (A): Two identical cells are connected in (a) series (b) parallel then maximum power transferred to the load is same in both cases. Reason (R): Value of load resistance for maximum power transfer for series and parallel combination of cells are same.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

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

Assertion (A) is true. For two identical cells (emf \(E\), internal resistance \(r\)), in series, \(E_{\text{eq}} = 2E\) and \(r_{\text{eq}} = 2r\). Max power \(P_{\text{max,s}} = (2E)^2 / (4 \cdot 2r) = E^2 / (2r)\). In parallel, \(E_{\text{eq}} = E\) and \(r_{\text{eq}} = r/2\). Max power \(P_{\text{max,p}} = E^2 / (4 \cdot r/2) = E^2 / (2r)\). The maximum power is indeed the same. Reason (R) is false. For series, the load resistance for max power is \(R_L = 2r\), while for parallel, it is \(R_L = r/2\). These are not the same.

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