With an increase in the frequency of an $A.C.$ supply,the impedance of an $L-C-R$ series circuit

An $LCR$ series circuit with a resistance of $100 \, \Omega$ is connected to an $ac$ source of $200 \, V \, (r.m.s.)$ and angular frequency $300 \, rad/s$. When only the capacitor is removed, the current lags behind the voltage by $60^o$. When only the inductor is removed, the current leads the voltage by $60^o$. The average power dissipated is.....$W$

In the circuit shown,$C = \frac{\sqrt{3}}{2} \times 10^{-3} \, F$,$R_2 = 20 \, \Omega$,$L = \frac{\sqrt{3}}{10} \, H$,and $R_1 = 10 \, \Omega$. The current in the $L-R_1$ branch is $I_1$ and in the $C-R_2$ branch is $I_2$. The voltage of the $A.C.$ source is given by $V = 200\sqrt{2} \sin(100t) \, V$. The phase difference between $I_1$ and $I_2$ is:

In a given series $LCR$ circuit,$R = 4\,\Omega ,$ $X_L = 5\,\Omega $ and $X_C = 8\, \Omega ,$ the current:

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

An inductor of $10 \text{ mH}$, capacitor of $0.1 \text{ } \mu\text{F}$ and a resistor of $100 \text{ } \Omega$ are connected in series across an $a.c.$ power supply of $220 \text{ V}$, $70 \text{ Hz}$. The power factor of the given circuit is $0.5$. The difference between the inductive reactance and capacitive reactance is $\sqrt{3}\alpha \text{ } \Omega$. The value of $\alpha$ is . . . . . . .