An inductor of 0.5 mH, a capacitor of 200 $$\mu$$F and a resistor of 2 $$\Omega$$ are connected in series with a 220 V ac source. If the current is in phase with the emf, the frequency of ac source will be ____________ $$\times$$ 10² Hz.

In the given circuit, the magnitude of V_L and V_C are twice that of V_R. Given that f = 50 Hz, the inductance of the coil is $${1 \over {K\pi }}$$ mH. The value of K is ____________.

An AC source is connected to an inductance of 100 mH, a capacitance of 100 $$\mu$$F and a resistance of 120 $$\Omega$$ as shown in figure. The time in which the resistance having a thermal capacity 2 J/$$^\circ$$C will get heated by 16$$^\circ$$C is _____________ s.

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 $$\pi$$ = $$\sqrt{10}$$)