When the $$rms$$ voltages $${V_L},{V_C}$$ and $${V_R}$$ are measured respectively across the inductor $$L,$$ the capacitor $$C$$ and the resistor $$R$$ in a series $$LCR$$ circuit connected to an $$AC$$ source, it is found that the ratio $${V_L}:{V_C}:{V_R} = 1:2:3.$$ If the $$rms$$ voltage of the $$AC$$ sources is $$100\,V,$$ the $${V_R}$$ is close to :
A.
$$50\,V$$
B.
$$70\,V$$
C.
$$90\,V$$
D.
$$100\,V$$
Answer :
$$90\,V$$
Solution :
$$\eqalign{
& {\text{Given,}}\,{V_L}:{V_C}:{V_R} = 1:2:3 \cr
& V = 100\,V \cr
& {V_R} = ? \cr} $$
As we know, $$V = \sqrt {V_R^2 + {{\left( {{V_L} - {V_C}} \right)}^2}} $$
Solving we get, $${V_R} \simeq 90\,V$$
Releted MCQ Question on Electrostatics and Magnetism >> Alternating Current
Releted Question 1
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