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  4. A series L-C-R circuit is connected to a source of alternating emf of 50 V and the potential difference across inductor and capacitor is 90 V and 60 V, respectively. The potential difference across the resistor is

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Q. A series $L-C-R$ circuit is connected to a source of alternating emf of $50 V$ and the potential difference across inductor and capacitor is $90 V$ and $60 V$, respectively. The potential difference across the resistor is

MHT CETMHT CET 2021

Solution:

Given, $V=50 V , V_L=90 V , V_C=60 V$
In $L-C-R$ circuit,
$ \therefore V=\sqrt{V_R^2+\left(V_L-V_C\right)^2} $
$ \Rightarrow V^2=V_R^2+\left(V_L-V_C\right)^2$
$ 50^2=V_R^2+(90-60)^2$
$\Rightarrow 2500=V_R^2+900$
$ \Rightarrow V_R^2=1600 $
$ \Rightarrow V_R=\sqrt{1600}=40 V$