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

let E = e.m.f. of cell and r = its internal resistance. Current through the cell i=ER+rP = Power delivered to .R=i2R=E2R(R+r)2Power delivered will be maximum, whendPdR=E21(R+r)2−2R(R+r)3=0Solving, we get E = r