A cell of internal resistance r drives a current through an external r

1.	A cell of internal resistance r drives a current through an external resistance R. The power delivered by the cell to the external resistance is maximum when (a) R = r (b) R >> r (c) R << r (d) R = 2r
Answer» Correct Answer is: (a) R = r Let ℰ = emf of the cell, i = current in the circuit i = ℰ / R + r. Power delivered to R = P = i²R = ℰ²R/(R + r)² = f(R). For P to be maximum, dP/dR = 0 = ℰ² [1 / (R + r)² - 2R / (R + r)³] or 2R = R + r or R = r

A cell of internal resistance r drives a current through an external resistance R. The power delivered by the cell to the external resistance is maximum when (a) R = r (b) R >> r (c) R << r (d) R = 2r

Answer»

Correct Answer is: (a) R = r

Let ℰ = emf of the cell, i = current in the circuit

i = ℰ / R + r.

Power delivered to R = P = i²R = ℰ²R/(R + r)² = f(R).

For P to be maximum, dP/dR = 0 = ℰ² [1 / (R + r)² - 2R / (R + r)³]

or 2R = R + r

or R = r