The phase angle between $e.m.f.$ and current in an $LCR$ series $ac$ circuit is:

The coil of an $A.C.$ generator has $100$ turns, each of cross-sectional area $2 \, m^2$. It is rotating at a constant angular speed of $30 \, rad/s$ in a uniform magnetic field of $2 \times 10^{-2} \, T$. If the total resistance of the circuit is $600 \, \Omega$, then the maximum power dissipated in the circuit is: (in $W$)

You are given many resistances,capacitors and inductors. These are connected to a variable $DC$ voltage source (the first two circuits) or an $AC$ voltage source of $50 \ Hz$ frequency (the next three circuits) in different ways as shown in Column $II$. When a current $I$ (steady state for $DC$ or rms for $AC$) flows through the circuit,the corresponding voltage $V_1$ and $V_2$ (indicated in circuits) are related as shown in Column $I$. Match the two.

An electrical device draws $2 \, kW$ power from $AC$ mains $(V_{rms} = 223 \, V = \sqrt{50000} \, V)$. The current lags in phase by $\tan \phi = -\frac{3}{4}$ compared to the voltage. Find $(i)$ $R$,$(ii)$ $X_C - X_L$,and $(iii)$ $I_M$. Another device has twice the values for $R$,$X_C$,and $X_L$. How are the answers affected?

In an $LCR$ circuit $R = 100 \ \Omega$. When capacitance $C$ is removed,the current lags behind the voltage by $\pi /3$. When inductance $L$ is removed,the current leads the voltage by $\pi /3$. The impedance of the circuit is......$\Omega$.

In the circuit shown,$L = 1 \mu H$,$C = 1 \mu F$,and $R = 1 k\Omega$. They are connected in series with an $a.c.$ source $V = V_0 \sin \omega t$ as shown. Which of the following options is/are correct?
[$A$] The frequency at which the current will be in phase with the voltage is independent of $R$.
[$B$] At $\omega \sim 0$,the current flowing through the circuit becomes nearly zero.
[$C$] At $\omega \gg 10^6 \text{ rad } s^{-1}$,the circuit behaves like a capacitor.
[$D$] The current will be in phase with the voltage if $\omega = 10^6 \text{ rad } s^{-1}$.