(D) For element $X$,the current is in phase with the voltage,so $X$ is a resistor.The resistance $R = \frac{V_0}{I_0} = \frac{100}{5} = 20\,\Omega$.Fo

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(D) For element $X$,the current is in phase with the voltage,so $X$ is a resistor.The resistance $R = \frac{V_0}{I_0} = \frac{100}{5} = 20\,\Omega$.For element $Y$,the current lags behind the voltage by $\frac{\pi}{2}$,so $Y$ is an inductor.The inductive reactance $X_L = \frac{V_0}{I_0} = \frac{100}{5} = 20\,\Omega$.When $X$ and $Y$ are connected in series,the total impedance $Z = \sqrt{R^2 + X_L^2} = \sqrt{20^2 + 20^2} = 20\sqrt{2}\,\Omega$.The peak current in the series circuit is $I_0 = \frac{V_0}{Z} = \frac{100}{20\sqrt{2}} = \frac{5}{\sqrt{2}}\,A$.The rms current is $I_{rms} = \frac{I_0}{\sqrt{2}} = \frac{5/\sqrt{2}}{\sqrt{2}} = \frac{5}{2}\,A$.

Class 12 Physics Alternating Current RL, RC and LC AC Circuits

Medium

$A$ circuit element $X$ when connected to an a.c. supply of peak voltage $100\,V$ gives a peak current of $5\,A$ which is in phase with the voltage. $A$ second element $Y$ when connected to the same a.c. supply also gives the same value of peak current which lags behind the voltage by $\frac{\pi}{2}$. If $X$ and $Y$ are connected in series to the same supply,what will be the rms value of the current in ampere?

JEE MAIN 2022 All JEE MAIN

A
$\frac{10}{\sqrt{2}}$
B
$\frac{5}{\sqrt{2}}$
C
$5 \sqrt{2}$
D
$\frac{5}{2}$

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Alternating Current

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RL, RC and LC AC Circuits

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