NCERT Solutions

We need to determine the maximum current a car battery can supply given its electromotive force and internal resistance.

Concept: Maximum current

The maximum current ($I_{\text{max}}$) is drawn from a battery when the external resistance in the circuit is zero (a short circuit condition). According to Ohm's Law for a complete circuit:

$$I = \frac{\varepsilon}{R + r}$$

For maximum current, $R = 0$, thus:

$$I_{\text{max}} = \frac{\varepsilon}{r}$$

where $\varepsilon$ is the electromotive force (emf) and $r$ is the internal resistance.

Given:

• Electromotive force, $\varepsilon = 12\,\text{V}$
• Internal resistance, $r = 0.4\,\Omega$

Solving:

1. Identify the condition for maximum current:

   • The current is maximum when the external load resistance $R$ is negligible ($R = 0$).

2. Substitute the given values into the maximum current formula:

$$\begin{aligned} I_{\text{max}} &= \frac{12\,\text{V}}{0.4\,\Omega} \\[8pt] &= 30\,\text{A} \end{aligned}$$

Result:

The maximum current that can be drawn from the battery is

$$30\,\text{A}$$