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In an RCL circuit, How can sum of voltage across each component (that is resistor, inductor and capacitor) be greater than the peak value of AC voltage supply?

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In LCR circuit $$V_{S}^2=V_{R}^2+(V_{L}-V_{C})^2$$ $$(V_{L}+V_{C}+V_{R})=\sqrt {V_{S}^2+2V_{L}V_{R}+4V_{L}V_{C}+2V_{C}V_{R}}$$ $$V_{L}+V_{C}+V_{R}>V_{S}$$

The voltage described in the above equations are maximum voltages so it is not true in general that the sum of voltage across each component is greater than that of source because they do not occur simultaneously.In general you can apply Kirchhoff's loop law and see what is the consequence.

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  • $\begingroup$ The voltages in your first equation refer to maximum (or rms) values and do not occur simultaneously. $\endgroup$ – R.W. Bird Nov 16 '19 at 18:35
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The voltages you might measure with an AC voltmeter are generally rms values (a fixed fraction of the maximum voltages). At any given instant, the sum of the voltages on R, L, and C (which differ in phase) is to equal that on the power supply.

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Hint:) use phaser diagram, where we see the the voltage difference with respect to current in Inductor and capacitor is π, I think this diagram clear everything. enter image description here

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