Question

"A low voltage battery from which high current is required must have low internal resistance." Justify.

Hint:

To ensure a high current output, the internal resistance of the battery should be as low as possible.

Answer 1

The statement "A low voltage battery from which high current is required must have low internal resistance" is justified by considering the following factors:

1. Ohm’s Law and Internal Resistance:

According to Ohm's law, the total current (\(I\)) drawn from a battery is determined by the applied voltage (\(V\)) and the total resistance in the circuit, which includes the internal resistance of the battery (\(r_{\text{int}}\)) and the external resistance (\(R_{\text{ext}}\)):

\[ I = \frac{V}{R_{\text{ext}} + r_{\text{int}}} \]

If a high current is required, the current will be maximized when the total resistance in the circuit is minimized. This means that for a low voltage battery, if we need a high current, we must minimize the internal resistance \( r_{\text{int}} \) of the battery.

2. Impact of High Internal Resistance:

When a battery has a high internal resistance, a significant portion of the battery's voltage is "lost" within the battery itself. This is because the internal resistance causes a voltage drop (\( I \cdot r_{\text{int}} \)) inside the battery, which reduces the voltage available for the external circuit.

• If the internal resistance is too high, it limits the amount of current that can flow out of the battery, as much of the voltage is dropped across the internal resistance.
• This results in inefficient performance, especially when high current is required by the external load.

3. Low Internal Resistance for High Current:

To ensure that a low voltage battery can supply a high current, the internal resistance must be kept low so that a minimal voltage is lost inside the battery. A low internal resistance allows most of the battery's voltage to be applied across the external circuit, allowing for higher current flow as required by the load.

4. Practical Example:

Consider a low voltage battery, such as a 1.5 V AA battery, that needs to supply current to a motor. If the battery has a high internal resistance, much of the 1.5 V would be dropped inside the battery, leaving little voltage for the motor, which would result in low current and poor motor performance. However, if the battery has low internal resistance, it can supply the full 1.5 V (minus a small drop) to the motor, resulting in a higher current and better performance.

5. Conclusion:

For a low voltage battery that needs to supply high current, it is essential to have low internal resistance. This ensures that most of the voltage from the battery is applied to the external circuit, allowing for higher current flow and efficient operation of the load.