Question
A small signal voltage $$V\left( t \right) = {V_0}\sin \omega t$$ is applied across an ideal capacitor $$C$$ :
A.
Current $$I\left( t \right),$$ lags voltage $$V\left( t \right)$$ by $${90^ \circ }.$$
B.
Over a full cycle the capacitor $$C$$ does not consume any energy from the voltage source.
C.
Current $$I\left( t \right)$$ is in phase with voltage $$V\left( t \right).$$
D.
Current $$I\left( t \right)$$ leads voltage $$V\left( t \right)$$ by $${180^ \circ }.$$
Answer :
Over a full cycle the capacitor $$C$$ does not consume any energy from the voltage source.
Solution :
As we know, power $$P = {V_{rms}} \cdot {I_{rms}}\cos \phi $$
$${\text{as}}\,\cos \phi = 0\,\,\left( {\because \phi = {{90}^ \circ }} \right)$$
$$\therefore $$ Power consumed $$= 0$$ (in one complete cycle)