Choose the correct statements, when a cell of emf E and internal resistance r connected to external resistance R having current I flowing through the circuit is:
A. Potential difference across the terminals of the cell in a closed circuit having resistance R is always less than the emf.
B. For practical calculations, the internal resistance of the cells in the circuits may be neglected when the current I is such that \( E \gg Ir \)
C. Terminal potential difference in a closed circuit is always more than emf E.
D. Terminal potential difference versus current graph for a cell with closed circuit having resistance R is a straight line with a negative slope.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A, B and D only
When the cell drives a current \( I \) through the external resistance, part of its emf is used up across its own internal resistance. The terminal potential difference is
\( \displaystyle V = E - I r, \qquad I = \frac{E}{R + r} \)
(A) Potential difference across the terminals of the cell in a closed circuit having resistance R is always less than the emf. — Correct. In a closed circuit \( I \gt 0 \), so \( V = E - Ir \lt E \).
(B) For practical calculations, the internal resistance of the cells in the circuits may be neglected when the current I is such that \( E \gg Ir \) — Correct. Then the drop \( Ir \) is negligible and \( V \approx E \).
(C) Terminal potential difference in a closed circuit is always more than emf E. — Incorrect. A cell supplying current has \( V = E - Ir \), which is less than \( E \).
(D) Terminal potential difference versus current graph for a cell with closed circuit having resistance R is a straight line with a negative slope. — Correct. \( V = E - rI \) is a straight line of intercept \( E \) and slope \( -r \).
NCERT (2026-27):
Cells, Emf, Internal Resistance – “… If however R is finite, I is not zero. In that case the potential difference between P and N is
\( \displaystyle V = V_+ + V_- - I r = \varepsilon - I r \qquad (3.38) \)
… In practical calculations, internal resistances of cells in the circuit may be neglected when the current I is such that ε >> I r.”