Kirchhoff’s Voltage Law (KVL)

1. Definition

Kirchhoff’s second law, or Kirchhoff’s loop rule, states that the sum of all voltages around any closed loop in a circuit is equal to zero.
This means the total voltage rises are equal to the total voltage drops in that loop.
It is based on the principle of conservation of energy.

1.1. Visualization

KVL Example

  • The sum of all the voltages around a loop is equal to zero. v1 + v2 + v3 + v4 = 0
  • When you go around a closed circuit loop, every increase in electric potential (voltage rise) is balanced by a decrease in electric potential (voltage drop).
  • The algebraic sum of voltages in a closed loop is zero.

1.2. In Formula Form

Sum of Voltage Rises; Sum of Voltage Drops = 0

Or equivalently:

Sum of Voltages = 0

Where:

  • V = Voltage (in volts, V)
  • The sign of V depends on whether you move from the negative to positive terminal (rise) or from positive to negative terminal (drop).

1.3. Example

Consider a simple loop with a 12 V battery and two resistors with voltage drops of 7 V and 5 V:

12 - 7 - 5 = 0

KVL confirms the loop is balanced because the total sum is zero.

2. Usage

  • Calculating unknown voltages in a circuit.
  • Verifying that a circuit is wired correctly.
  • Analyzing multi-loop circuits with mesh analysis.
  • Troubleshooting voltage drops in wiring or components.

3. Limitations

  • Assumes steady-state DC or low-frequency AC circuits where inductive and capacitive effects are negligible.
  • For high-frequency circuits, parasitic inductance and capacitance can cause small deviations from the law.
  • Requires a clearly defined loop and consistent sign convention for rises and drops.

4. Video Explanation

video coming soon