Question

A battery has an emf of 15.0 V. The terminal voltage of the battery is 13.0 V when it is delivering 16.0 W of power to an external load resistor R.

(a) What is the value of R?
?

(b) What is the internal resistance of the battery?
?

Answer 1

Vt=Vb+VL where
Vt - no load voltage = 15V
Vb - Voltage across the battery under load = 13 V
VL - load voltage = (15- 13 )V

The circuit current is (it is a series circuit)
I=Vt/(Rb +RL)

The power supplied to the load is
PL=VL^2/RL then
RL= PL/VL^2= 16/(15 - 13)^2=4 ohms

Current I is
I= PL/VL=16/(15 - 13)= 8 A

Finally we have
Rb= (Vt - I RL)/I=(15 - 8 x 4)/8=
Rb=0.375 ohms