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Q. In an $LCR$ series $AC$ circuit the voltage across $L, C$ and $R$ is $10\,V$ each. If the inductor is short circuited, the voltage across the capacitor would become on

KEAMKEAM 2009Alternating Current

Solution:

Circuit is resonant, hence supply voltage equals to
$ {{V}_{R}} $ . $ {{V}_{R}}=10 $
volt Also, $ {{X}_{C}}=R $
As the voltage drops are equals across L, C and R then when L is short
$ Z=\sqrt{{{R}^{2}}+X_{C}^{2}} $
$ =\sqrt{2}R $
$ {{V}_{C}}=i{{X}_{C}} $
$ \left[ \because i=\frac{V}{Z} \right] $
Or $ {{V}_{C}}=\frac{V}{Z}{{X}_{C}} $
Or $ =\frac{10}{\sqrt{2}R}R $
Or $ {{V}_{C}}=\frac{10}{\sqrt{2}}volt $