Question

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 1

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