Question

Why the emf of a cell is greater than its terminal voltage?

Answer 1

The electromotive force (emf) of a cell is the maximum potential difference it can provide when no current is flowing through the circuit. On the other hand, the terminal voltage is the potential difference measured across the terminals of the cell when current is actually flowing.

Here’s why the emf is greater than the terminal voltage:

1. Internal Resistance: Every real battery or cell has some internal resistance (denoted as \(r\)). This resistance causes a voltage drop when current flows through the cell.
   

1. Current Flow and Voltage Drop: When a current \(I\) flows through the cell, the voltage drop across the internal resistance is given by \(V_{\text{drop}} = I \times r\). This voltage drop reduces the voltage available at the terminals of the cell.
   

1. Relation Between emf and Terminal Voltage:
   

   - The emf (\(E\)) is the potential difference when no current is flowing (i.e., the ideal voltage of the cell).
   - The terminal voltage (\(V_{\text{terminal}}\)) when current flows is given by:
     \[
     V_{\text{terminal}} = E - I \times r
     \]
   Since \(I \times r\) is always a positive quantity (assuming current is flowing), the terminal voltage is always less than the emf.

Thus, when a current flows, the internal resistance of the cell causes a voltage drop inside the cell, making the terminal voltage lower than the emf. If no current is flowing, there is no voltage drop, and the terminal voltage is equal to the emf.