NEET Physics Question - Current Electricity - Power of Electrical Circuit

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.

(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)

(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

(3) (A) is true but (R) is false

(4) Both (A) and (R) are false

Solution:

Concept: Maximum power transfer theorem for cells.
Formula: For a source with EMF \(E_{eq}\) and internal resistance \(r_{eq}\), maximum power is transferred when load \(R_L = r_{eq}\), and \(P_{max} = \frac{E_{eq}^2}{4r_{eq}}\).
Solution: For 2 cells in series: \(E_{eq} = 2E\), \(r_{eq} = 2r\). \(P_{max, series} = \frac{(2E)^2}{4(2r)} = \frac{E^2}{2r}\). Load \(R_L = 2r\).
For 2 cells in parallel: \(E_{eq} = E\), \(r_{eq} = r/2\). \(P_{max, parallel} = \frac{E^2}{4(r/2)} = \frac{E^2}{2r}\). Thus, maximum power transferred is same, so A is true. Load resistances for max power transfer are different, so R is false.

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Solution:

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