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 v1, v2, …, vn be the voltages around a close loop. Then
In the sinusoidal steady-state, each voltage may be written in cosine form, so that Equation.(1) becomes
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 i1, i2, …,in be the current leaving or entering a closed surface in a network at time t, then
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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: