Step 1: Understanding the Concept:
Kirchhoff’s circuit laws are fundamental tools for analyzing electrical networks.
The Loop Rule (or Voltage Law) states that if you start at any point in a closed loop and sum all the potential differences (voltages) around the loop, the total sum is zero:
\[ \sum \Delta V = 0 \]
This implies that all energy provided by sources (like batteries) is exactly consumed by the components (like resistors) within that specific loop.
Step 2: Detailed Explanation:
Electric potential at a point is defined as the electrical potential energy per unit charge.
The electrostatic field inside a circuit is a conservative field.
In any conservative field, the work done in moving a test charge around a closed path—starting and ending at the same point—is always zero.
Mathematically, the line integral of the electric field around a closed path is zero:
\[ W_{\text{loop}} = \oint q \vec{E} \cdot d\vec{r} = 0 \]
This means a unit charge gains no net energy and loses no net energy after completing a full cycle through the circuit.
Since the potential difference is just the work done per unit charge, the sum of potential changes must be zero to satisfy the Law of Conservation of Energy.
If the sum were not zero, it would mean energy is being created or destroyed out of nowhere as charges flow, which violates the laws of thermodynamics.
Step 3: Final Answer:
Kirchhoff’s Loop Rule is a direct consequence of the Conservation of Energy.