Question

Obtain the formula for the internal resistance of a cell in terms of \( E \), \( V \), and \( R \), where \( E \), \( V \), and \( R \) are the electromotive force of the cell, potential difference across the external resistance, and external resistance, respectively.

Hint:

The internal resistance of a cell depends on the electromotive force \( E \), terminal voltage \( V \), and external resistance \( R \).

Answer 1

The total current in the circuit is: \[ I = \frac{E}{R + r}, \] where \( r \) is the internal resistance. The terminal voltage is given by: \[ V = IR = \frac{ER}{R + r}. \] Rearranging: \[ r = R \left( \frac{E}{V} - 1 \right). \]