In the $AC$ circuit shown,$E = E_0 \sin(\omega t + \phi)$ and $i = i_0 \sin(\omega t + \phi + \frac{\pi}{4})$. Then,the box contains:

$A$ sinusoidal voltage of peak value $283 \, V$ and angular frequency $320 \, rad/s$ is applied to a series $LCR$ circuit. Given that $R = 5 \, \Omega$,$L = 25 \, mH$,and $C = 1000 \, \mu F$. The total impedance and the phase difference between the voltage across the source and the current will respectively be:

When a $60 \text{ mH}$ inductor and a resistor are connected in series with an $AC$ voltage source, the voltage leads the current by $60^{\circ}$. If the inductor is replaced by a $0.5 \text{ } \mu\text{F}$ capacitor, the voltage lags behind the current by $30^{\circ}$. What is the frequency of the $AC$ supply?

An $a.c.$ circuit contains a resistance of $12 \ \Omega$ and an inductor of inductive reactance $5 \ \Omega$. The phase angle between current and potential difference will be

$A$ resistance of $300\,\Omega$ and an inductance of $\frac{1}{\pi}\,H$ are connected in series to an $AC$ voltage source of $20\,V$ and $200\,Hz$ frequency. The phase angle between the voltage and current is:

The current $I$,potential difference $V_L$ across the inductor,and potential difference $V_C$ across the capacitor in the circuit as shown in the figure are best represented vectorially as: