$A$ $\frac{2.5}{\pi} \mu F$ capacitor and $3000 \, \Omega$ resistor are joined in series to an $AC$ source of $200 \, V$ and $50 \, Hz$ frequency. The power factor of the circuit and the power dissipated in it will respectively be:

There is a $100\,\Omega$ resistance in an $L-C-R$ $AC$ circuit. An $AC$ $emf$ of $200\,V$ and $\omega = 300\,rad/s$ is applied to this circuit. When only the capacitor is removed,the current lags the voltage by $60^o$. When only the inductor is removed,the current leads the voltage by $60^o$. The current in this $L-C-R$ circuit will be.....$A$

$A$ direct current of $10 \,A$ is superimposed on an alternating current $I = 40 \cos \omega t \; (A)$ flowing through a wire. The effective value of the resulting current will be ....... $A$.

At very high frequencies, the current $(i)$ in the given circuit is (in $A$)

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.

Give the name of the physical quantity in an $LCR$ circuit that corresponds to mass $m$ in forced oscillations.