An ideal capacitor is charged to a voltage $${V_0}$$ and connected at $$t=0$$ across an ideal inductor $$L.$$ (The circuit now consists of a capacitor and inductor alone). If we let $${\omega _0} = 1/\sqrt {LC} ,$$ the voltage across the capacitor at time $$t>0$$ is given by

The circuit shown in the figure is energized by a sinusoidal voltage source $${V_1}$$ at a frequency which causes resonance with a current of $${\rm I}$$.

The phasor diagram which is applicable to this circuit is

A $$400V$$, $$50$$ $$Hz,$$ three phase balanced source supplies power to a star connected load whose rating is $$12\,\,\angle 3\,\,kVA,$$ $$0.8$$ $$pf$$ (lag). The rating $$($$in $$kVAR)$$ of the delta connected (capacitive) reactive power bank necessary to bring the $$pf$$ to unity is

The parameters of the circuit shown in the figure are
$${R_i} = 1\,\,M\,\Omega ,\,\,{R_0} = 10\,\Omega ,\,\,A = {10^6}\,\,V/V.$$ If $${V_i} = 1\,\,\mu V,\,\,$$ the output voltage, input impedance and output impedance respectively are