Question

"A high voltage battery must have a large internal resistance." Justify.

Hint:

High voltage batteries often have a larger internal resistance to regulate the current and enhance safety.

Answer 1

High Voltage Battery and Its Internal Resistance 

A high voltage battery typically has a large internal resistance. This design choice serves several important purposes:

1. Limiting Current:

The internal resistance of the battery limits the amount of current that can be drawn from it. The current \( I \) supplied by a battery is determined by the battery’s voltage \( V \) and the total resistance \( R \) in the circuit: \[ I = \frac{V}{R} \] where \( R \) includes both the resistance of the circuit and the battery's internal resistance.

By having a large internal resistance, the current drawn from the battery is kept at a safe level. This is particularly important for high voltage batteries, as excessive current could lead to overheating, damage to the battery, or even dangerous conditions.

2. Preventing Overloading:

High voltage batteries are typically used to power devices that require a large voltage to operate. However, the power required by these devices is also dependent on the current drawn. If the battery had very low internal resistance, the current could easily exceed safe limits, especially if the external circuit’s resistance is low.

The large internal resistance of the battery ensures that the current remains within a safe range, preventing overloading of both the battery and any connected devices. This regulation helps prevent excessive heat generation and reduces the risk of battery failure.

3. Heat Generation and Damage Prevention:

When excessive current flows through a battery or a circuit, it leads to power dissipation in the form of heat. This is governed by the formula: \[ P = I^2 R \] where \( P \) is the power dissipated as heat. High current can lead to significant heat generation, which can damage the battery and other connected components.

By using a high internal resistance, the battery limits the current, thereby preventing the buildup of excessive heat and avoiding potential damage to the battery or the devices it powers.

Conclusion:

In summary, high voltage batteries are designed with large internal resistance to limit the current drawn, preventing overloading, excessive heat generation, and potential damage. This ensures the battery operates efficiently and safely, protecting both the battery and the connected devices.