An $AC$ generator $10 \, V$ (rms) at $200 \, rad/s$ is connected in series with a $50 \, \Omega$ resistor, a $400 \, mH$ inductor, and a $200 \, \mu F$ capacitor. The rms voltage across the inductor is (in $V$)

Which one of the following curves represents the variation of impedance $(Z)$ with frequency $(f)$ in a series $L-C-R$ circuit,when connected to an $AC$ source?

If the power factor is $1/2$ in a series $RL$ circuit with $R = 100\,\Omega$ connected to an $ac$ mains $(50\,Hz)$,find the value of $L$.

$A$ capacitor of capacitance $100 \mu F$ and a coil of resistance $20 \Omega$ and inductance $12.5 mH$ are connected in series with a $220 V, \frac{200}{\pi} Hz$ $AC$ source. The maximum value of instantaneous current in the circuit is (in $A$)

$A$ sinusoidal voltage $V(t) = 210 \sin(3000t) \text{ V}$ is applied to a series $LCR$ circuit in which $L = 10 \text{ mH}$,$C = 25 \mu\text{F}$,and $R = 100 \Omega$. The phase difference $(\Phi)$ between the applied voltage and resultant current will be

In a series $CR$ circuit shown in the figure,the applied voltage is $10 \, V$ and the voltage across the capacitor is found to be $8 \, V$. Then the voltage across $R$,and the phase difference between the current and the applied voltage will respectively be: