The figure shows the variation of $R$,$X_L$,and $X_C$ with frequency $f$ in a series $LCR$ circuit. For which frequency point is the circuit inductive?

In an $LCR$ series circuit,if $V$ is the effective value of the applied voltage,$V_R$ is the voltage across $R$,and $V_L$ and $V_C$ are the effective voltages across $L$ and $C$ respectively,then:

An inductor and a resistor are connected in series to an ac source of variable frequency. When the frequency of the applied ac is $50 \ Hz$,the power factor of the circuit is $\frac{\sqrt{3}}{2}$. If the frequency of the ac is increased by $200 \%$,the power factor of the circuit is . . . . . . .

An inductor of inductive reactance $R$,a capacitor of capacitive reactance $2R$,and a resistor of resistance $R$ are connected in series to an $AC$ source. The power factor of the series $LCR$ circuit is

$A$ coil of resistance $450 \Omega$ and self-inductance $1.5 \text{ H}$ is connected to an $A$.$C$. source of frequency $\frac{150}{\pi} \text{ Hz}$. The phase difference between voltage and current is

In a series $LCR$ circuit,the $rms$ voltage across the resistor and the capacitor are $30 \ V$ and $90 \ V$ respectively. If the applied voltage is $V = 50 \sqrt{2} \sin \omega t$,then the peak voltage across the inductor is