In an ac circuit, the applied instantaneous voltage equal to the algebraic sum of the instantaneous voltages across the series elements of the circuit? IS the same true for rms voltage?

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Solution

Yes, in a series LCR circuit, applied instantaneous voltage is equal to the algebraic sum of the instantaneous voltage across all the series elements in the circuits.
$E = E_{L} + E_{C} + E_{R}$
where, E is the instantaneous voltage.

But, the same is not true for r.m.s. voltage.
In Case of r.m.s. voltage, we have,
$E = \sqrt{E_{R}^{2} + (E_{L} - E_{C})^{2}}$

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