Kirchhoff’s Circuit Laws

Kirchhoff’s circuit laws were first defined by a German physicist Gustav Kirchhoff in 1845.

Kirchhoff’s Voltage Law (KVL)

This law states that the voltage applied to any closed circuit (V_A) is equal to the sum of the voltage drops (V₁, V₂ and V₃) in that circuit. The mathematical expression is given below.

V_A = V₁ + V₂ + V₃

In other words, the algebraic sum of all voltages in the loop must be zero.

Σ V = V_A – (V₁ + V₂ + V₃) = V_A – V₁ – V₂ – V₃ = 0

In the circuit below, the resistors are connected in series across a voltage source. The voltage drops are shown as V₁, V₂ and V₃.

FIGURE

Kirchhoff’s Current Law (KCL)

This law states that the sum of the currents entering a junction is equal to the sum of the currents leaving the junction. This common meeting point is called as a node or junction, which is shown in the figure below.

FIGURE

The mathematical expression based the above circuit is given below.

I₁ + I₂ = I₃ + I₄ + I₅

In other words, the algebraic sum of all the currents at the node is zero.

Σ I = I₁ + I₂ – I₃ – I₄ – I₅ = 0