A series LCR circuit with $$R = {{250} \over {11}}\,\Omega $$ and $${X_L} = {{70} \over {11}}\,\Omega $$ is connected across a 220 V, 50 Hz supply. The value of capacitance needed to maximize the average power of the circuit will be _________ $$\mu$$F. (Take : $$\pi = {{22} \over 7}$$)

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 ____________ $$\times$$ 10^{2} Hz.

The intensity of the light from a bulb incident on a surface is 0.22 W/m^{2}. The amplitude of the magnetic field in this light-wave is ______________ $$\times$$ 10^{$$-$$9} T.

(Given : Permittivity of vacuum $$\in$$_{0} = 8.85 $$\times$$ 10^{$$-$$12} C^{2} N^{$$-$$1}-m^{$$-$$2}, speed of light in vacuum c = 3 $$\times$$ 10^{8} ms^{$$-$$1})

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 ____________.