In Kirchhoff's loop rule

The correct answer is Option (4) → The algebraic sum of changes in potential around any closed loop involving resistors and cells in the loop is zero.

Kirchhoff's loop rule follows from the conservation of energy: the potential is a single-valued function, so on returning to the starting point after going round a closed loop, the total change in potential must be zero.

Option (1) The currents entering the junction are not equal to the sum of currents leaving the junction. — Incorrect. This contradicts the junction rule.

Option (2) In a circuit, charge is accumulated at a point. — Incorrect. In steady state no charge piles up at any point.

Option (3) In a closed circuit, the potential difference across the cell is equal to the electromotive force of the cell. — Incorrect. When a current flows, the terminal potential difference is \( E - Ir \), not \( E \).

Option (4) The algebraic sum of changes in potential around any closed loop involving resistors and cells in the loop is zero. — Correct. This is the loop rule, \( \sum \Delta V = 0 \).

NCERT (2026-27):
Kirchhoff’s Rules – “… (b) Loop rule: The algebraic sum of changes in potential around any closed loop involving resistors and cells in the loop is zero (Fig. 3.15). This rule is also obvious, since electric potential is dependent on the location of the point. Thus starting with any point if we come back to the same point, the total change must be zero. In a closed loop, we do come back to the starting point and hence the rule.”