Question

When an alternating emf is applied across a capacitor \(C\), the graph of capacitive reactance \((X_C)\) with frequency \((f)\) of the source of alternating signal is

• A. (B)
• B. (A)
• C. (C)\
• D. (D)

Hint:

Capacitive reactance decreases inversely with frequency in AC circuits.

Answer 1

The Correct Option is A

Step 1: Expression for capacitive reactance.
Capacitive reactance is given by:
\[ X_C = \frac{1}{2\pi f C} \]
Step 2: Dependence on frequency.
From the formula,
\[ X_C \propto \frac{1}{f} \]
Step 3: Nature of graph.
As frequency increases, capacitive reactance decreases non-linearly.
The graph is a rectangular hyperbola.

Step 4: Conclusion.
The correct graph representing this variation is option (B).