Choose the correct option from the following.
(A) The internal resistance of a cell depends on its distance between electrodes and on the area of the electrodes.
(B) The emf of a cell is measured when it is used in series in an electrical circuit carrying current I.
(C) If a cell of emf E and of internal resistance r is providing current I through a resistance R then the potential difference across the cell is \( V = I(R + r) \).
(D) The emf of a cell is 1 V, if 1 J of work is done by the cell to drive 1 C of charge in the whole circuit.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A) and (D) only
The emf \( E \) of a cell is the work done per unit charge carried round the complete circuit. With a current \( I \), the terminal potential difference is \( V = E - I r = I R \).
(A) The internal resistance of a cell depends on its distance between electrodes and on the area of the electrodes. — Correct. It is the resistance of the electrolyte between the electrodes: it grows with their separation and falls as the electrode area increases.
(B) The emf of a cell is measured when it is used in series in an electrical circuit carrying current I. — Incorrect. The emf is the terminal potential difference when no current is drawn (open circuit).
(C) If a cell of emf E and of internal resistance r is providing current I through a resistance R then the potential difference across the cell is \( V = I(R + r) \). — Incorrect. \( I(R + r) \) is the emf itself; the potential difference across the cell is \( V = E - Ir = IR \).
(D) The emf of a cell is 1 V, if 1 J of work is done by the cell to drive 1 C of charge in the whole circuit. — Correct. Emf is work per unit charge: \( E = W/q = 1\,\mathrm{J}/1\,\mathrm{C} = 1\,\mathrm{V} \).
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
\( \displaystyle V = V_+ + V_- - I r = \varepsilon - I r \qquad (3.38) \)”
Summary – “… The work done per unit charge by the source in taking the charge from lower to higher potential energy (i.e., from one terminal of the source to the other) is called the electromotive force, or emf, of the source.”