Question

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How long can a car with a 12V battery of 60 A h capacity have the lights, of total resistance of 4 ohms, on before the battery runs down?

Answer 1

Convert the voltage and capacity of the battery into energy units: 12V, 60A·h are

$$E=12·60·3600=2592·10^3\text{ J}.$$

The power the lights consume is

$$P=\frac{V^2}{R}.$$

The energy, on the other hand, is

$$E=Pt,\\\space\\ t=\frac EP=\frac{ER}{V^2}=72000\text{ s},$$

or 20 h.