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?

When $100\, V$ $DC$ is applied across a solenoid,a current of $1\, A$ flows in it. When $100\, V$ $AC$ is applied across the same coil,the current drops to $0.5\, A$. If the frequency of the $AC$ source is $50\, Hz$,the impedance and inductance of the solenoid are:

An $AC$ voltage source of variable angular frequency $\omega$ and fixed amplitude $V_0$ is connected in series with a capacitance $C$ and an electric bulb of resistance $R$ (inductance zero). When $\omega$ is increased,

In a simple $L-R$ circuit with an $A.C.$ source,the potential difference at any instant across the inductor and the resistor are $V_L$ and $V_R$ respectively,and the $A.C.$ source has a potential difference $V_{AC}$ at the same instant. Then:

In an $LCR$ series circuit,an inductor $30 \, {mH}$ and a resistor $1 \, \Omega$ are connected to an $AC$ source of angular frequency $300 \, {rad/s}$. The value of capacitance for which the current leads the voltage by $45^{\circ}$ is $\frac{1}{x} \times 10^{-3} \, {F}$. Then the value of $x$ is ..... .

In a circuit,$L, C$ and $R$ are connected in series with an alternating voltage source of frequency $f$. The current leads the voltage by $45^o$. The value of $C$ is