A telegraph line of length 100 km has a capacity of 0.01 $$\mu$$F/km and it carries an alternating current at 0.5 kilo cycle per second. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is _____________ mH. (if $$\pi$$ = $$\sqrt{10}$$)

A 220 V, 50 Hz AC source is connected to a 25 V, 5 W lamp and an additional resistance R in series (as shown in figure) to run the lamp at its peak brightness, then the value of R (in ohm) will be _____________.

A 110 V, 50 Hz, AC source is connected in the circuit (as shown in figure). The current through the resistance 55 $$\Omega$$, at resonance in the circuit, will be __________ A.

In a series LCR circuit, the inductance, capacitance and resistance are L = 100 mH, C = 100 $$\mu$$F and R = 10 $$\Omega$$ respectively. They are connected to an AC source of voltage 220 V and frequency of 50 Hz. The approximate value of current in the circuit will be ___________ A.