A series LCR circuit with resistance (R) $$500 ~\mathrm{ohm}$$ is connected to an a.c. source of $$250 \mathrm{~V}$$. When only the capacitance is removed, the current lags behind the voltage by $$60^{\circ}$$. When only the inductance is removed, the current leads the voltage by $$60^{\circ}$$. The impedance of the circuit is $$\left(\tan \frac{\pi}{3}=\sqrt{3}\right)$$

When a d.c. voltage of $$200 \mathrm{~V}$$ is applied to a coil of self-inductance $$\left(\frac{2 \sqrt{3}}{\pi}\right) \mathrm{H}$$, a current of $$1 \mathrm{~A}$$ flows through it. But by replacing d.c. source with a.c. source of $$200 \mathrm{~V}$$, the current in the coil is reduced to $$0.5 \mathrm{~A}$$. Then the frequency of a.c. supply is

An inductor coil wound uniformly has self inductance 'L' and resistance 'R'. The coil is broken into two identical parts. The two parts are then connected in parallel across a battery of 'E' volt of negligible internal resistance. The current through battery at steady state is

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