The figure shows the variation of $R$,$X_L$,and $X_C$ with frequency $f$ in a series $L-C-R$ circuit. For what frequency point is the circuit capacitive?

As given in the figure,a series circuit connected across a $200\, V$,$60\, Hz$ line consists of a capacitor of capacitive reactance $30\,\Omega$,a non-inductive resistor of $44\,\Omega$,and a coil of inductive reactance $90\,\Omega$ and resistance $36\,\Omega$. The power dissipated in the coil is......$W$

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 . . . . . . .

In the series $L-C-R$ circuit shown,the impedance is (in $\Omega$)

An inductor coil takes a current of $8 \, A$ when connected to a $100 \, V$ and $50 \, Hz$ $AC$ source. $A$ pure resistor under the same condition takes a current of $10 \, A$. If the inductor coil and resistor are connected in series to a $100 \, V$ and $40 \, Hz$ $AC$ supply, then the current in the series combination of the above resistor and inductor is:

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