Which of the following statements is true about electromotive force (emf) of a cell?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → emf is the potential difference between positive and negative terminals of a cell in an open circuit.
The emf of a cell is the potential difference between its terminals when no current is drawn from it. When a current \( I \) flows, the terminal voltage is less than the emf by the drop across the internal resistance \( r \):
\( V = E - Ir \)
Option (1) It depends on external resistance. — Incorrect. The emf is fixed by the chemistry of the cell and does not depend on the external resistance; only the terminal voltage changes with it.
Option (2) emf is the potential difference between positive and negative terminals of a cell in a closed circuit. — Incorrect. In a closed circuit the terminal potential difference is \( V = E - Ir \), which is less than the emf.
Option (3) It has electrostatic origin. — Incorrect. The emf has a non-electrostatic (chemical) origin: it is the work done per unit charge by the chemical forces inside the cell.
Option (4) emf is the potential difference between positive and negative terminals of a cell in an open circuit. — Correct. In an open circuit \( I = 0 \), so \( V = E \).
NCERT (2026-27):
Cells, Emf, Internal Resistance – “… Thus, emf ε is the potential difference between the positive and negative electrodes in an open circuit, i.e., when no current is flowing through the cell. If however R is finite, I is not zero. In that case the potential difference between P and N is
\( \displaystyle V = V_+ + V_- - I r = \varepsilon - I r \qquad (3.38) \)”