Question

Same current is flowing in two different a.c. circuits. First circuit contains only inductance and second contains only capacitance. If the frequency of a.c. is increased in both circuits, the current will

• A. increase in the first circuit and decrease in second.
• B. increase in both circuits.
• C. decrease in both circuits.
• D. decrease in first circuit and increase in second.

Hint:

Inductors block high frequencies (low-pass), while capacitors pass high frequencies (high-pass).

Answer 1

The Correct Option is D

Step 1: Inductive Reactance
$X_L = 2\pi f L$. As $f$ increases, $X_L$ increases.
Since $I = V/X_L$, current \textit{decreases} in the inductive circuit.
Step 2: Capacitive Reactance
$X_C = \frac{1}{2\pi f C}$. As $f$ increases, $X_C$ decreases.
Since $I = V/X_C$, current \textit{increases} in the capacitive circuit.
Step 3: Comparison
Inductor circuit: $I \propto 1/f$. Capacitor circuit: $I \propto f$.
Step 4: Conclusion
Current decreases in the first (L) and increases in the second (C).
Final Answer:(D)