In an $ac$ circuit,the current lags behind the voltage by $\pi /3$. The components in the circuit are

$A$ resistor of $20 \ \Omega$ and a capacitor are connected in series with an $AC$ current source of $50 \ Hz$. What should be the capacitance to produce a phase difference of $30^\circ$ between the voltage and current?

For a series $LCR$ circuit, inductive reactance $X_L$ is equal to resistance $R$ and also equal to twice the capacitive reactance $X_C$. The impedance of the circuit and the phase difference between voltage $V$ and current $i$ are respectively

An $AC$ generator $10 \, V$ (rms) at $200 \, rad/s$ is connected in series with a $50 \, \Omega$ resistor, a $400 \, mH$ inductor, and a $200 \, \mu F$ capacitor. The rms voltage across the inductor is (in $V$)

$A$ coil has an inductance of $0.7 \, H$ and is joined in series with a resistance of $220 \, \Omega$. When an alternating $emf$ of $220 \, V$ at $50 \, Hz$ is applied to it,the phase angle by which the current lags behind the applied $emf$ and the wattless component of the current in the circuit are respectively:

$A$ circuit contains an inductance of $\frac{1}{6 \pi} \text{ H}$ and a resistance of $15 \text{ } \Omega$ in series. If an $AC$ voltage of $100 \text{ V}$ and $60 \text{ Hz}$ is applied to the circuit,then the current in the circuit and the phase difference between voltage and current are,respectively: