Question

When discharging the terminal voltage of a battery can never be greater than the emf of the battery?

Answer 1

Correct! The terminal voltage of a battery can never be greater than its electromotive force (emf) during discharging. Here's why:

1. Definition of emf: The emf of a battery is the maximum potential difference between the battery's terminals when no current is flowing (i.e., when the battery is not under load). It's essentially the "ideal" voltage the battery could provide.
   

1. Terminal Voltage During Discharge: When the battery is supplying current (discharging), the terminal voltage is influenced by both the emf and the internal resistance of the battery. The battery has an internal resistance that causes a voltage drop when current flows. This means the terminal voltage will always be less than the emf when current is drawn from the battery.
   

1. Voltage Drop: The relationship between terminal voltage, emf, and internal resistance can be expressed as:
   

   
   \[
   V_{\text{terminal}} = \mathcal{E} - I \cdot r_{\text{internal}}
   \]
   
   Where:
   - \(V_{\text{terminal}}\) is the terminal voltage,
   - \(\mathcal{E}\) is the emf of the battery,
   - \(I\) is the current drawn,
   - \(r_{\text{internal}}\) is the internal resistance of the battery.
   
   When current flows, the internal resistance causes a voltage drop \(I \cdot r_{\text{internal}}\), which reduces the terminal voltage below the emf.

1. Why Terminal Voltage Can’t Exceed Emf: Since the internal resistance always causes a voltage drop when discharging, the terminal voltage will always be less than the emf. It can never exceed the emf because there’s no mechanism in the battery that would increase the terminal voltage beyond the emf, especially under normal conditions.
   

In summary, the terminal voltage will always be slightly lower than the emf when the battery is supplying current, due to the internal resistance.