Question

In an AC circuit containing only a capacitor, the current

• A. lags the voltage by $\pi/2$
• B. leads the voltage by $\pi/2$
• C. is in phase with the voltage
• D. lags the voltage by $\pi$
• E. leads the voltage by $\pi$

Hint:

Use the mnemonic \textbf{ELI} the \textbf{ICE} man:

• \textbf{ELI}: In an Inductor (\textbf{L}), Voltage (\textbf{E}) leads Current (\textbf{I}).
• \textbf{ICE}: In a Capacitor (\textbf{C}), Current (\textbf{I}) leads Voltage (\textbf{E}).

Answer 1

The Correct Option is B

Concept:
Physics - AC Circuits (Pure Capacitive Circuit).
Step 1: Set up the equations.
Let the applied alternating voltage be $V = V_0 \sin(\omega t)$. The charge on the capacitor is $Q = CV$.
Step 2: Determine the current.
Current $I$ is the rate of flow of charge: $$ I = \frac{dQ}{dt} = \frac{d}{dt} (C V_0 \sin \omega t) $$ $$ I = C V_0 \omega \cos \omega t $$
Step 3: Convert to sine form for comparison.
Using the identity $\cos \theta = \sin(\theta + \pi/2)$: $$ I = I_0 \sin(\omega t + \pi/2) $$ where $I_0 = \omega C V_0$.
Step 4: Compare phases.
The phase of the voltage is $\omega t$, while the phase of the current is $(\omega t + \pi/2)$. This shows that the current leads the voltage by a phase angle of $\pi/2$ (or $90^{\circ}$).