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Kirchhoff's Laws for AC Circuits

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.
kvl and kcl for ac circuits

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 v1v2, ..., vn be the voltages around a close loop. Then
kvl and kcl for ac circuits
In the sinusoidal steady-state, each voltage may be written in cosine form, so that Equation.(1) becomes
kvl and kcl for ac circuits
This can be written as
kvl and kcl for ac circuits
If we let Vk = Vmkejθk, then
kvl and kcl for ac circuits
Since ejωt ≠ 0,
kvl and kcl for ac circuits
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 i1i2, ...,in be the current leaving or entering a closed surface in a network at time t, then
kvl and kcl for ac circuits
If I1I2, ...., In are the phasor forms of the sinusoids i1i2, ...,in, then
kvl and kcl for ac circuits
which is Kirchhoff's current law in the frequency domain.
Once we have shown that both KVL and KCL hold in the frequency domain, it is easy to do many things, such as impedance combination, nodal and mesh analyses, superposition, and source transformation.

Have you understood what is kirchhoff's laws for ac circuit? Don't forget to share and subscribe! Happy learning!
Reference:  Fundamentals of electric circuits by Charles K. Alexander and Matthew N. O. Sadiku

Untuk Bahasa Indonesia baca Hukum Kirchhoff Rangkaian AC
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