$A$ resistor of resistance $30 \Omega$, an inductor of reactance $10 \Omega$, and a capacitor of reactance $10 \Omega$ are connected in series to an $AC$ voltage source $V = 300 \sqrt{2} \sin(\omega t)$. The current in the circuit is . . . . . . (in $\text{ A}$)

Draw phasor diagrams for $X_C > X_L$ and $X_C < X_L$,and state the disadvantages of the phasor method.

The power factor of the given $LCR$ circuit is $1/\sqrt{2}$. Find the capacitance $C$ of the circuit in $\mu F$.

$A$ series $LCR$ circuit consists of an inductor $L$,a capacitor $C$,and a resistor $R$ connected across a source of emf $\varepsilon = \varepsilon_0 \sin \omega t$. When $\omega L = \frac{1}{\omega C}$,the current in the circuit is $I_0$. If the angular frequency of the source is changed to $\omega^{\prime}$,the current in the circuit becomes $\frac{I_0}{2}$. Then,the value of $\left|\omega^{\prime} L - \frac{1}{\omega^{\prime} C}\right|$ is

An inductor of reactance $100 \text{ } \Omega$, a capacitor of reactance $50 \text{ } \Omega$, and a resistor of resistance $50 \text{ } \Omega$ are connected in series with an $AC$ source of $10 \text{ V}$, $50 \text{ Hz}$. Average power dissipated by the circuit is (in $\text{ W}$)

In a parallel $AC$ circuit with $R_1 = R_2 = R$ and $X_L = X_C = X$. An $AC$ source $V = V_0 \sin(\omega t)$ is connected across the circuit as shown in the figure. The $RMS$ value of the potential difference $V_A - V_B$ will be: