Saturday, June 15, 2024

Are Ohm's law and Kirchhoff's law applicable to AC circuits?

 Are Ohm's law and Kirchhoff's law applicable to AC circuits?

Yes, if you properly examine all the resistances and reactances, taking into account phase of currents and voltages. Not just of the components, but parasitic and distributed parameters. Electrons can’t just disappear and reappear, therefore Kirchoff’s Current Law must be true; energy can’t just disappear and reappear and that is current times voltage, therefore Kirchoff’s Voltage Law must be true.

Steven J Greenfield's answer to Kirchoff's laws are invalid for AC. So why do books use Kirchoff's laws for an alternating current?

You must analyze the circuit correctly. It is not enough to simply take peak or RMS values and try to analyze it. Kirchoff's laws apply for a given instant in time. So the voltages at a given moment around a loop will all sum to zero, or currents in a node sum to zero if you look at the instantaneous voltage and current.

But they will be out of phase. So merely seeing 9Vrms on an inductor, 3Vrms on a capacitor, 5Vrms on a resistor, all connected in series to a 10Vrms AC source does not tell you the whole story.

It is simpler in a simulation program like Spice to measure the current individually in a parallel circuit, than the voltage in a series circuit. So here I have three components, a resistor, capacitor, and inductor in parallel. You can see the mess of currents out of phase. Yet the purple line, which is the sum of all currents, adds to zero at all times, within the limits of finite calculations.

You can click on that to see a larger image. Created in LTSpiceIV, thanks to Linear Technology for making their Spice front-end free for all.

You might notice that I(L) is greater than the total supply current. Watch what I(C) is doing and think about what happens when the reactance of the inductor and the capacitor are equal. This is a condition called resonance, and it only happens at one frequency for a given inductance and capacitance.

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