Question

According to Kirchhoff's Loop Rule (Second Law) applied across a closed network mesh, the algebraic sum of all potential variations around any closed loop must equal zero. This fundamental circuit law is a direct consequence of which physical conservation principle?

• A. \( \text{Conservation of Linear Momentum} \)
• B. \( \text{Conservation of Electric Charge} \)
• C. \( \text{Conservation of Mass} \)
• D. \( \text{Conservation of Energy} \)

Hint:

Remember this reliable pairing for exams: Junction Rule maps to Charge (JC), and Loop Rule maps to Energy (LE). These are among the most frequently asked conceptual points in CUET physics modules.

Answer 1

The Correct Option is D

Concept: Kirchhoff's circuit laws keep track of currents and voltages within electrical networks. The loop rule states that the algebraic sum of the electromotive forces (\( \text{EMFs} \)) plus the algebraic sum of the potential drops across all resistors in any closed loop must equal zero: \[ \sum \Delta V = 0 \]

Step 1: Link electrostatic potential to work and energy definitions. Electric potential difference is defined as the work done per unit charge by electrostatic forces to move a test charge between two points. The electrostatic field is conservative, meaning the total work done moving a charge around any closed loop path, starting and ending at the exact same point, is always zero. \[ W_{\text{loop}} = \oint q \cdot \vec{E} \cdot d\vec{r} = 0 \]

Step 2: Match the loop rule to its conservation law. Since the net work done on a unit charge around a closed loop is zero, the charge gains no net energy, and loses no net energy once it completes a full loop. This makes Kirchhoff's Loop Rule a direct statement of the Conservation of Energy.