Question

The storage battery of a car has an emf of 12V . If the internal resistance of the battery is 0.4 Ohm , what is the maximum current that can be drawn from the battery?

Answer 1

The maximum current that can be drawn from the battery is 30 Amperes (A).

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Detailed Explanation

1. Understand the Concepts

• EMF (Electromotive Force, $\mathcal{E}$): This is the total voltage the battery can supply. In this case, $\mathcal{E}$ = 12 V.
• Internal Resistance (r): Every real battery has some internal resistance, which opposes the flow of current. Here, r = 0.4 Ω.
• Maximum Current ($I_{max}$): The current drawn from a battery depends on the external circuit (the "load") connected to it. To get the maximum possible current, you need the minimum possible total resistance.

2. The Formula

The current (I) flowing from a battery is given by Ohm's Law, applied to the entire circuit:

$I = \frac{\text{Total Voltage}}{\text{Total Resistance}}$

In this case:
$I = \frac{\mathcal{E}}{r + R_{load}}$

Where:
$I$ is the current.
$\mathcal{E}$ is the EMF of the battery (12 V).
$r$ is the internal resistance (0.4 Ω).
$R_{load}$ is the resistance of the external circuit (the device being powered).

3. Finding the Maximum Current

To maximize the current ($I$), we need to make the denominator ($r + R{load}$) as small as possible. Since the internal resistance ($r$) is a fixed property of the battery, the only way to minimize the denominator is to make the external load resistance ($R{load}$) as small as possible.

The smallest possible value for $R_{load}$ is 0 Ω. This situation is called a short circuit.

So, for maximum current, we set $R_{load} = 0$. The formula becomes:

$I_{max} = \frac{\mathcal{E}}{r + 0} = \frac{\mathcal{E}}{r}$

4. Calculation

Now, we can plug in the given values:

• $\mathcal{E}$ = 12 V
• $r$ = 0.4 Ω

$I_{max} = \frac{12 \text{ V}}{0.4 \text{ Ω}}$

$I_{max} = 30 \text{ A}$

The maximum current that can be drawn from the battery is 30 Amperes.

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Important Safety Note: A short circuit, as described here, is extremely dangerous with a car battery. The large current (30 A) would generate immense heat, potentially causing the wires to melt, the battery to overheat, and even explode. This calculation is a theoretical maximum. Never attempt to short-circuit a car battery.