An ac circuit has an inductor and a resistor resistance R in series, such that X_L = 3R. Now, a capacitor is added in series such that X_C = 2R. The ratio of new power factor with the old power factor of the circuit is $$\sqrt 5 :x$$. The value of x is ___________.

The alternating current is given by $$i = \left\{ {\sqrt {42} \sin \left( {{{2\pi } \over T}t} \right) + 10} \right\}A$$

The r.m.s. value of of this current is ................. A.

Consider an electrical circuit containing a two way switch 'S'. Initially S is open and then T₁ is connected to T₂. As the current in R = 6$$\Omega$$ attains a maximum value of steady state level, T₁ is disconnected from T₂ and immediately connected to T₃. Potential drop across r = 3$$\Omega$$ resistor immediately after T₁ is connected to T₃ is __________ V. (Round off to the Nearest Integer)

Two circuits are shown in the figure (a) & (b). At a frequency of ____________ rad/s the average power dissipated in one cycle will be same in both the circuits.