Problem 4: A typical 12 V automobile battery has a resistance of 0.012 Ω. What is the terminal voltage of this battery when the starter draws a current of 100 A. Also calculate R, P, P_{R} and P_{r}.

Solution

Given Electromotive force, emf = 12 V Internal resistance, r = 0.012 Ω

Current, I = 100 A

Required Starter resistance, R =? Power, P =? P_{R} =? P_{r} =?

Automobile battery provides current to the starter. The internal resistance of the battery (acting as emf), is 0.012 Ω. We know that

Put values in (A) to get terminal voltage.

Terminal voltage is the voltage applied across the resistance.

In order to calculate resistance (of the starter), we apply Ohm’s law.

V = IR. Put the values,

10.8 = 100R OR R = 10.8/100 = 0.108 Ω

Power is the rate of work done (energy conversion) in the circuit. It is given by P=IV.

Put the values, power = 100 * 12 = 1200 watt

To calculate power of the starter, P_{R} = 100 * 10.8 = 1080 watt

To calculate power of the battery, P_{r} = 100*1.2 = 120watt

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