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

$A$ 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 ....... $A$.

$A$ resistor $R$, an inductor $L$, and a capacitor $C$ are connected in series with an a.c. source. When $L$ is removed from the circuit, the phase difference between voltage and current in the circuit is $\pi/3$. If instead, $C$ is removed from the circuit, the phase difference is again $\pi/3$. The power factor of the circuit is

An initially charged undriven $LCR$ circuit having inductance $L$,capacitance $C$ and resistance $R$ will be:

Assertion: Ohm's law cannot be applied to $a.c.$ circuits.
Reason: Resistance offered by a capacitor for an $a.c.$ source depends upon the frequency of the source.

Three alternating voltage sources $V_1 = 3 \sin \omega t \text{ V}$,$V_2 = 5 \sin(\omega t + \phi_1) \text{ V}$,and $V_3 = 5 \sin(\omega t - \phi_2) \text{ V}$ are connected in series with a resistor $R = \sqrt{\frac{7}{3}} \, \Omega$ as shown in the figure (where $\phi_1 = 30^\circ$ and $\phi_2 = 127^\circ$). Find the peak current (in Ampere) through the resistor.