A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are 1 H, 1 F and 1Ω , respectively, the operating angular frequency (in rad/s) is ________.

The current I in the circuit shown is

An AC source of RMS voltage $$20$$ $$V$$ with internal impedance $${Z_s} = \left( {1 + 2j} \right)\Omega $$ feeds a load of impedance $${Z_L} = \left( {7 + 4j} \right)\Omega $$ in the figure below. The reactive power consumed by the load is

Two series resonant filters are as shown in the figure. Let the $$3$$-dB bandwidth of Filter $$1$$ be $${B_1}$$ and that of Filter $$2$$ be $${B_2}$$. The value of $${B_1}$$/$${B_2}$$ is