1. The power P delivered to a variable resistor R by a battery of emf V and a constant internal resistance r is given by

Question

P= V^2R / (R + r)^2
Find dP/dR and hence the value of R when the power delivered is a maximum.

Answer 1

using the quotient rule,

dP/dR = -V^2(R-r)/(R+r)^3

so, max power when R=r

I think you'll find this discussed somewhere in your text.