Maximum power delivered by battery is

Explanation

It states that the output power of a source of current is maximum, when the internal resistance of the source is equal to the external resistance in the circuit. So, if R is the external resistance of the circuit and r is the internal resistance of the source of current (i.e. a battery) then the output power is maximum, when R = r.This theorem is applicable to all types of source of e.m.f. and is related with the output power and NOT with the power dissipated.If E is the applied e.m.f. of the source of e.m.f. i.e. a battery of internal resistance r and R is the external resistance then current in the circuit is given as:I = E/(R + r)At the maximum output power, R = r, so we have:I = E/(r + r) = E/(2r) and maximum output power:Pmax = I2r = E2/(4r)