Question

At very high frequencies, the current (i) in the given circuit is:

• A. 4A
• B. 0.4 A
• C. 44 A
• D. 4.4 A

Answer 1

The Correct Option is C

To solve the problem, we need to analyze the behavior of the given AC circuit at very high frequencies and determine the current flowing through it.

1. Behavior of Components at High Frequencies:
At very high frequencies: - Inductive reactance $X_L = \omega L \rightarrow \infty$ (inductors behave like open circuits) - Capacitive reactance $X_C = \frac{1}{\omega C} \rightarrow 0$ (capacitors behave like short circuits)

2. Analyzing the Circuit:
Given these behaviors: - All inductors (20 mH, 50 mH) will act as open circuits and hence block current in their branches. - All capacitors (0.8 µF, 0.5 µF) will act as short circuits and can be replaced with wires.
With inductors acting as open circuits, the paths containing them become irrelevant for current flow. Therefore, current only flows through the branches that have only resistors and shorted capacitors**.

3. Remaining Effective Circuit:
After simplification: - The remaining path includes: 220V source → 1Ω resistor → shorted capacitors (negligible resistance) → 4Ω resistor → total resistance = 5Ω.

4. Calculating Current:
Using Ohm's law: $I = \frac{V}{R} = \frac{220}{5} = 44 \, \text{A}$

Final Answer:
The current in the circuit at very high frequencies is 44 A.