When a $DC$ voltage of $200\, V$ is applied to a coil of self-inductance $\frac{2\sqrt{3}}{\pi}\,H$,a current of $1\, A$ flows through it. When the $DC$ source is replaced by an $AC$ source of $200\, V$,the current in the coil is reduced to $0.5\, A$. The frequency of the $AC$ supply is......$Hz$.

If $i$ is the current in an $L-C-R$ series $AC$ circuit,what are the formulas for:
$(i)$ Voltage across resistance.
$(ii)$ Voltage across inductor.
$(iii)$ Voltage across capacitor.

An inductor and a resistor are connected in series to an ac supply. If the potential differences across the inductor and the resistor are $180 \ V$ and $240 \ V$ respectively,then the voltage of the ac supply is (in $V$)

An alternating emf given by the equation $E = 200 \sin(50 \pi t)$ (where $E$ is in volts and $t$ is in seconds) is applied across a series combination of an inductor and a resistor having inductive reactance $X_L = 40 \ \Omega$ and resistance $R = 30 \ \Omega$ respectively. At time $t = 1 \ s$,the power dissipated by the resistor is close to $(\cos 53^{\circ} = 0.6)$. (in $W$)

An inductor and a resistor are connected in series to an $AC$ source. The current in the circuit is $500 \,mA$, if the applied $AC$ voltage is $8 \sqrt{2} \,V$ at a frequency of $\frac{175}{\pi} \,Hz$, and the current in the circuit is $400 \,mA$, if the same $AC$ voltage at a frequency of $\frac{225}{\pi} \,Hz$ is applied. The values of the inductance and the resistance are respectively:

$A$ coil of inductance $0.1 H$ and resistance $110 \Omega$ is connected to a source of $110 V$ and $350 Hz$. The phase difference between the voltage maximum and the current maximum is