A series $$R-L-C$$ circuit when excited by a $$10$$ $$V$$ sinusoidal voltage source of variable frequency, exhibits resonance at $$100$$ $$Hz$$ and has a $$3$$ $$dB$$ bandwidth of $$5$$ $$Hz.$$ The voltage across the inductor $$L$$ at resonace is

The current in the circuit shown in figure is

A fixed capacitor of reactance –$$j0.02$$ $$\Omega $$ is connected in parallel across a series combination of a fixed inductor of reactance $$j0.01$$ $$\Omega $$ and a variable resistance $$R.$$ As $$R$$ is varied from zero to infinity, the locus diagram of the admittance of this $$L-C-R$$ circuit will be

The voltage phasor of a circuit is $$10\angle {15^0}\,V$$ and the current phasor is $$2\,\,\angle - {45^0}A.$$ The active and the reactive powers in the circuit are