$A$ coil has inductance of $0.4 \text{ H}$ and resistance of $8 \Omega$. It is connected to an $AC$ source with peak emf $4 \text{ V}$ and frequency $\frac{30}{\pi} \text{ Hz}$. The average power dissipated in the circuit is (in $\text{ W}$)

$A$ series $LR$ circuit is connected to a voltage source with $V(t) = V_0 \sin \omega t$. After a very large time,how does the current $I(t)$ behave? (Given: $t_0 \gg \frac{L}{R}$)

$A$ $\frac{2.5}{\pi} \mu F$ 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:

An $AC$ generator consists of a coil of $100$ turns and is of cross-sectional area $3 \ m^2$. It is rotating at a constant angular speed of $60 \ rad \ s^{-1}$ in a uniform magnetic field of $0.04 \ T$. The resistance of the coil is $360 \ \Omega$. What is the maximum power dissipation in the coil (in $W$)?

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

Given below are two statements:
Statement $I$: An $AC$ circuit undergoes electrical resonance if it contains either a capacitor or an inductor.
Statement $II$: An $AC$ circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor.
In the light of the above statements,choose the correct answer from the options given below: