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(C) The voltage across an inductor in an $AC$ circuit is given by $V_{L} = I X_{L}$,where $I$ is the current and $X_{L}$ is the inductive reactance.Th

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$10 \,A$

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(C) The voltage across an inductor in an $AC$ circuit is given by $V_{L} = I X_{L}$,where $I$ is the current and $X_{L}$ is the inductive reactance.The inductive reactance is defined as $X_{L} = \omega L = 2 \pi f L$.Given values are $V_{L} = 31.4 \,V$,$L = 10 \,mH = 10 	imes 10^{-3} \,H$,and $f = 50 \,Hz$.Substituting these values into the formula:$31.4 = I 	imes (2 	imes 3.14 	imes 50 	imes 10 	imes 10^{-3})$$31.4 = I 	imes (314 	imes 10 	imes 10^{-3})$$31.4 = I 	imes 3.14$$I = \frac{31.4}{3.14} = 10 \,A$.Therefore,the current in the circuit is $10 \,A$.

$A$ series $LCR$ circuit is subjected to an $AC$ signal of $200 \,V, 50 \,Hz$. If the voltage across the inductor $(L=10 \,mH)$ is $31.4 \,V$,then the current in this circuit is $\qquad$

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