Question

In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current (in Amperes) through the resistor is $2\sin(t + \pi/2)$. The displacement current (in Amperes) through the capacitor is ________________.

• A. $2\sin(t)$
• B. $2\sin(t + \pi)$
• C. $2\sin(t + \pi/2)$
• D. 0

Hint:

In any series circuit involving a capacitor, the conduction current and displacement current are always identical because no actual charge flows through the dielectric.

Answer 1

The Correct Option is C

In a series $RC$ circuit, the same current flows through the resistor and the capacitor at every instant. The current through the resistor is called \textit{conduction current}, while the current through the capacitor is the \textit{displacement current}.
Step 1: Given conduction current.
\[ i_R(t) = 2\sin\left(t + \frac{\pi}{2}\right) \]
Step 2: Displacement current equals conduction current.
For an ideal capacitor in a series connection, the displacement current equals the conduction current: \[ i_C(t) = i_R(t). \]
Step 3: Substitute the given expression.
Thus, \[ i_C(t) = 2\sin\left(t + \frac{\pi}{2}\right). \]
Hence, the displacement current is the same sinusoid as the resistor current.
Final Answer: $2\sin(t + \pi/2)$