Question:

A cell of internal resistance r drives current through an external resistance R. The power delivered by the cell to the external resistance will be maximum when:

R=1000r

R=0.001r

R=2r

R=r

Correct option is D. R=r
Current i=E/(r+R)
Power generated in R P=i²R
P=E²R/(r+R)²
For maximum power dP/dR=0
E²[(r+R)²×1−R×2(r+R)/(r+R)⁴]=0
→r=R