Battery Voltage Behavior Under Load

In practical applications, understanding how a battery's voltage behaves under varying load conditions is essential. A battery is not an ideal voltage source; it inherently possesses internal resistance, which plays a significant role in determining its terminal voltage.

Internal Resistance and Battery Voltage Drop

Every real-world battery has an internal resistance, often denoted as \(\text{R}_{\text{int}}\). When a load is connected to the battery, current (\(\text{I}\)) flows from the battery to the load. This current must pass through the battery's own internal resistance, leading to a voltage drop across it.

According to Ohm's Law, the voltage drop (\(\text{V}_{\text{drop}}\)) across the internal resistance is given by: \[ \text{V}_{\text{drop}} = \text{I} \times \text{R}_{\text{int}} \]

The terminal voltage (\(\text{V}_{\text{terminal}}\)) that you measure across the battery's terminals while it is supplying current to a load is the battery's electromotive force (EMF, or open-circuit voltage) minus this internal voltage drop: \[ \text{V}_{\text{terminal}} = \text{EMF} - \text{V}_{\text{drop}} \] Substituting the expression for \(\text{V}_{\text{drop}}\): \[ \text{V}_{\text{terminal}} = \text{EMF} - (\text{I} \times \text{R}_{\text{int}}) \]

Effect of Increasing Load on Battery Voltage

When the load increases, it means that the effective resistance of the external circuit connected to the battery decreases. According to Ohm's Law (\(\text{I} = \text{V}/\text{R}_{\text{total}}\)), a decrease in total circuit resistance (assuming constant EMF) leads to a higher current being drawn from the battery.

• As the load increases, more current (\(\text{I}\)) is drawn from the battery.
• Since the battery's internal resistance (\(\text{R}_{\text{int}}\)) is relatively constant for a given battery, an increase in the current (\(\text{I}\)) directly causes a larger voltage drop (\(\text{V}_{\text{drop}}\)) across this internal resistance.
• Consequently, because the terminal battery voltage is calculated by subtracting this internal voltage drop from the EMF (\(\text{V}_{\text{terminal}} = \text{EMF} - \text{V}_{\text{drop}}\)), a larger \(\text{V}_{\text{drop}}\) results in a lower observed terminal battery voltage.

Therefore, in practical application, battery voltage is lowered as the load increases. This is a fundamental characteristic of how real batteries perform under various operating conditions.

Analysis of Options

• Option 1: is restored as soon as disconnect occurs

  This statement describes the open-circuit voltage recovery. When a load is disconnected, current flow stops, and the internal voltage drop across \(\text{R}_{\text{int}}\) becomes zero. The terminal voltage then recovers to the battery's open-circuit voltage or EMF. While true, this doesn't describe the behavior *as the load increases*.

• Option 2: is lowered as the load increases

  This statement is correct. As explained above, an increased load leads to a higher current draw, which causes a larger voltage drop across the battery's internal resistance. This results in a decrease in the terminal battery voltage.

• Option 3: May be stored indefinitely

  This statement is incorrect. Batteries, over time, undergo a process called self-discharge. Due to internal chemical reactions, batteries gradually lose their charge and voltage even when they are not in use or connected to any load. Therefore, they cannot store energy indefinitely.

• Option 4: Will be reduced to zero as power is drawn

  This statement is incorrect. While battery voltage does decrease when power is drawn, it does not immediately reduce to zero under normal operating conditions. The voltage reduces progressively as the battery discharges, eventually reaching a very low level or zero only when the battery is completely depleted or subjected to a short circuit. For typical power draw, the voltage lowers but remains above zero for the majority of the battery's operational life.