Table of Contents

# Kirchhoff’s Voltage Law (KVL)

Kirchhoff’s Voltage Law (KVL) is one of the fundamental principles in electrical circuit theory. It states that the sum of all electrical potential differences (voltages) around any closed network (or loop) is zero. This law is based on the principle of energy conservation, implying that the total energy gained per charge around a loop is equal to the total energy lost per charge.

Mathematically, for a closed loop with \( n \) elements, KVL can be expressed as:

\[ \sum_{i=1}^{n} V_i = 0 \]

where \( V_i \) represents the voltage across the \( i \)-th element in the loop.

## Key Points of KVL:

**Closed Loop**: The law applies to any closed loop within a circuit, meaning the loop must return to the starting point.**Direction**: When summing voltages, attention must be paid to the polarity (direction) of each voltage drop or rise. Typically, voltage drops (positive to negative) are considered positive, and voltage rises (negative to positive) are considered negative.**Conservation of Energy**: KVL is derived from the principle of conservation of energy, which asserts that energy cannot be created or destroyed within an isolated system.

## Example:

Consider a simple circuit with a battery and two resistors in series.

- Let \( V \) be the voltage of the battery.
- Let \( V_1 \) and \( V_2 \) be the voltages across the two resistors.

According to KVL:

\[ V – V_1 – V_2 = 0 \]

This equation shows that the total voltage provided by the battery is equal to the sum of the voltage drops across the resistors.

## Application:

KVL is widely used in electrical engineering and physics to analyze and solve circuit problems. It helps in:

- Determining unknown voltages in a circuit.
- Verifying the correctness of calculated voltages.
- Analyzing complex circuits by breaking them down into simpler loops.

Understanding and applying KVL is essential for anyone working with electrical circuits, whether in theoretical analysis or practical design.