Question

In an A.C.circuit containing only capacitance, the current

• A. leads the voltage by $180^{\circ }$
• B. lags the voltage by $90^{\circ }$
• C. leads the voltage by $90^{\circ }$
• D. remains in phase with the voltage

Answer 1

Answer: (C)

In a purely capacitive circuit, where there is no resistance, the current i flowing through it deposits a charge dq on the capacitor in time that is
$dq=idt$
$\Rightarrow i=\frac{dq}{dt}$

Now using Kirchoff's law, if total charge deposited on the capacitor is $q$ then
$\frac{q}{C}=E_0\sin \omega t$
$\Rightarrow q=C{E}_0\sin \omega t$
$\Rightarrow i=\frac{dq}{dt}=C{E}_0\omega \cos \omega t=i_0\cos \omega t$ where
$i_0=\frac{E_0}{\left(1/C_{\omega }\right)}$ = peak current
$\therefore i=i_0\cos \omega t=i_0\sin \left(\omega +\frac{\pi }{2}\right)t$
and $E=E_0\sin \omega t$
Hence current is leading the voltage in phase by $\frac{\pi }{2}$