In the figure the current source is $$1\,\,\angle \,0\,A,$$ $$R = \,1\,\,\Omega ,$$ the impedances are $${Z_C} = - j\,\,\Omega ,$$ and $${Z_L} = 2\,j\,\,\Omega .$$ The Thevenin equivalent looking into the circuit across $$X-Y$$ is.

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