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 ____________.

All resistances in figure are 1 $$\Omega$$ each. The value of current 'I' is $${a \over 5}$$ A. The value of a is _________.

A capacitor C₁ of capacitance 5 $$\mu$$F is charged to a potential of 30 V using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor C₂ of capacitance 10 $$\mu$$F as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor C₂ is __________ $$\mu$$C.

A tunning fork of frequency 340 Hz resonates in the fundamental mode with an air column of length 125 cm in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is ___________ cm.

(Velocity of sound in air is 340 ms^$$-$$1)