Kirchhoff’s laws can also be used in ac electric circuit analysis. With the basic KVL and KCL from dc circuit, we can modify those two to be used for a sinusoidal electric circuit.

*Make sure to read what is ac circuit first.*

We cannot do circuit analysis in the frequency domain without Kirchhoff’s current and voltage laws. Hence, we need to express them in the frequency domain.

## Kirchhoff’s Laws for AC Circuit

For KVL, let *v _{1}*,

*v*, …,

_{2}*v*be the voltages around a close loop. Then

_{n}(1) |

In the sinusoidal steady-state, each voltage may be written in cosine form, so that Equation.(1) becomes

(5) |

indicating that Kirchhoff’s voltage law holds for phasors.

By following a similar procedure, we can show that Kirchhoff’s current law holds for phasors. If we let *i _{1}*,

*i*, …,

_{2}*i*be the current leaving or entering a closed surface in a network at time

_{n}*t*, then

Make sure to read:

And its applications:

- Phase shifter circuit and formula
- AC bridge
- AC op-amp
- Capacitance multiplier circuit
- Wien bridge oscillator

Learning Kichhoff’s laws for AC circuit will lead us to: