Kirchhoff's Laws

Understand Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL) with formulas and examples.

Kirchhoff's Voltage Law (KVL)

Kirchhoff's Voltage Law (KVL) states that the sum of all voltages around any closed loop in a circuit is zero.

Formula:

  • Σ V = 0
    • Where Σ V = sum of all voltages in the loop.

**Explanation**: In any closed circuit loop, the total voltage provided by sources (e.g., batteries) is equal to the total voltage drop across the resistors and other components.

KVL Example Circuit

**Example**: For the above circuit, if we have resistors and voltage sources, applying KVL gives:
V1 - IR1 - IR2 - V2 = 0

Kirchhoff's Current Law (KCL)

Kirchhoff's Current Law (KCL) states that the sum of currents entering a junction is equal to the sum of currents leaving the junction.

Formula:

  • Σ I (in) = Σ I (out)

**Explanation**: At any node in an electric circuit, the total current entering the node is equal to the total current leaving the node.

KCL Example Circuit

**Example**: In the circuit above, if I1, I2, and I3 are currents entering or leaving the junction, then:
I1 + I2 - I3 = 0