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I was solving a steady state question with sinusoidal AC voltage source and the solution for the question used Kirchoff's current law to find the nodal voltage of a node. Now, I used to think that I could only use kcl for DC sources and not for AC as the polarity of the source does not stay the same and keeps on reversing, so obviously the kirchoff's current equation for a particular node will change when the polarity changes. Where am I wrong?

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    \$\begingroup\$ At steady state, amplitudes and phase angles are fixed. \$\endgroup\$
    – Chu
    Commented Jun 29, 2022 at 9:38

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Polarity is not a problem for Kirchhoff's laws. You don't have to change the polarity in the equations - if the actual polarity is different from what you drew, the calculation will say it's a negative number and that's fine.

There are two ways you could possibly use Kirchhoff's laws for AC circuits: they apply if you substitute all AC voltages with their instantaneous values, and they also apply if the AC voltages are phasors.

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