An inductor of inductance $2 \mu \mathrm{H}$ is connected in series with a resistance, a variable capacitor and an a.c. source of frequency 5 kHz . The value of capacitance for which maximum current is drawn into the circuit is $\frac{1}{\mathrm{x}} \mathrm{F}$, where the value of ' $x$ ' is (Take $\pi^2=10$)

When 80 volt d.c. is applied across a solenoid, a current of 0.8 A flows in it. When 80 volt a.c. is applied across the same solenoid, the current becomes 0.4 A . If the frequency of a.c. source is 50 Hz , the impedance and inductance of the solenoid is nearly

A transformer is used to set up an alternating e.m.f. of 220 V to 4.4 kV to transmit 6.6 kW of power. The primary coil has 1000 turns. The current rating of the secondary coil is (Transformer is ideal)

A series LCR circuit containing a resistance ' R ' has angular frequency ' $\omega$ '. At resonance the voltage across resistance and inductor are ' $\mathrm{V}_{\mathrm{R}}$ ' and ' $V_L$ ' respectively, then value of inductance ' $L$ ' will be