A cell of emf E is connected across an external resistance R. When a current 'I' is drawn from the cell, the potential difference across the electrodes of the cell drops to 'V'. The internal resistance 'r' of the cell is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( \left[\frac{E-V}{V}\right]R \)
When a current \( I \) is drawn, the terminal voltage is less than the emf by the drop across the internal resistance.
\( \displaystyle V = E - I r \;\Rightarrow\; r = \frac{E - V}{I} \)
The same current flows through the external resistance, so \( I = V/R \). Substituting,
\( \displaystyle r = \frac{E - V}{V/R} = \left[\frac{E-V}{V}\right] R \)