Internal resistance

Question

When a 12 V batter with 1Ω internal resistance is connected to a motor, it delivers a current of 2.4 A. The battery is now replaced with a new battery with the same emf but a different internal resistance and the resistor of the motor dissipates 16 W. What is the internal resistance of the new battery?

Answer 1

Write 12 Volts = (2.4 Ampères)[(1+R_Motor) Ohms] which simplifies to R_Motor equal to 4 Ohms.

Then write 12 Volts = (I Ampères)[(R_Internal+4) Ohms] where 16 Watts equals (I Ampères)²(4 Ohms)

or I = 2 Ampères.

Finally, equate 12 Volts to 2 Ampères Times [(R_Internal+4) Ohms] to obtain R_Internal = 2 Ohms.