$A$ series $LCR$ circuit has $L=0.01\,H$,$R=10\,\Omega$,and $C=1\,\mu F$ and it is connected to an $AC$ voltage of amplitude $V_m = 50\,V$. At a frequency $60\%$ lower than the resonant frequency,the amplitude of the current will be approximately $...............\,mA$.

Assertion : In the purely resistive element of a series $LCR$ $AC$ circuit,the maximum value of $rms$ current increases with an increase in the angular frequency of the applied $e.m.f$.
Reason : $I_{\max} = \frac{\varepsilon_{\max}}{Z}$,where $Z = \sqrt{R^2 + (\omega L - \frac{1}{\omega C})^2}$ and $I_{\max}$ is the peak current in a cycle.

In the given circuit,the $AC$ source has $\omega = 100 \, rad \, s^{-1}$. Considering the inductor and capacitor to be ideal,what will be the current $I$ flowing through the circuit? (in $A$)

In an $LCR$ series circuit,when $L$ is removed from the circuit,the phase difference between voltage and current is $\frac{\pi}{3}$. If $C$ is removed from the circuit instead of $L$,the phase difference is again $\frac{\pi}{3}$. The power factor of the circuit is $(\tan 60^{\circ}=\sqrt{3})$.

$A$ series $RLC$ circuit is shown here. The source frequency $f$ is varied, but the current is kept unchanged. Which of the curves showing changes of $V_C$ and $V_L$ with frequency would be valid for the circuit under consideration?

$L$,$C$,and $R$ represent the physical quantities inductance,capacitance,and resistance,respectively. Which of the following combinations has the dimensions of frequency?