Kirchoff's Laws using Phasors

Consider a household circuit where an AC power supply from the distribution panel is wired to appliances in parallel.

Analyzing an AC circuit involves replacing loads with impedance equivalents and transforming voltages and currents to phasor forms.

This AC circuit can be analyzed using Kirchhoff's voltage and current laws.

When Kirchhoff's voltage law is applied to the first loop in the circuit, it mandates that the sum of phasor voltages in a closed loop equals zero.

In a sinusoidal steady state, these voltages can be represented in the time domain and converted into phasor equivalents.

As the frequency factor cannot be null, the aggregate of the phasor voltages equals zero.

Now, applying Kirchhoff's current law at a node asserts that the total current entering the circuit node is equal to the total current exiting the node.

Expressed in phasor notation, the sum of phasor currents at the node equals zero.

So, Kirchhoff's laws apply to any AC circuit, ensuring zero sums for both phasor voltages in closed loops and phasor currents at nodes.