Question

A capacitor of capacitance ' C ' is connected across a.c. source of voltage V as \(\mathrm{V}=\mathrm{V}_0 \sin \omega \mathrm{t}\). The displacement current between the plates of the capacitor would be

• A. \(V_{0}\omega C\mathrm{cos}\omega t\)
• B. \(\frac{V_{0}}{\omega C}\mathrm{sin}\omega t\)
• C. \(\frac{V_{0}}{\omega C}\mathrm{cos}\omega t\)
• D. \(\mathrm{V}_{0}\omega \mathrm{Csin}\omega \mathrm{t}\)

Hint:

The displacement current equals the conduction current, which is C times dV/dt.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
Displacement current between the plates equals the conduction current in the wires.

Step 2: Conduction current
\(I=\dfrac{dq}{dt}=C\dfrac{dV}{dt}\).

Step 3: Differentiate
\(I=C\dfrac{d}{dt}(V_{0}\sin\omega t)=V_{0}\omega C\cos\omega t\).

Final Answer:
The displacement current is \(V_{0}\omega C\cos\omega t\). \[ \boxed{\text{(A) }V_{0}\omega C\cos\omega t} \]