# 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 (VA) is equal to the sum of the voltage drops (V1, V2 and V3) in that circuit. The mathematical expression is given below.

VA = V1 + V2 + V3

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

Σ V = VA – (V1 + V2 + V3) = VA – 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