Q.25
A 30 μF capacitor is connected to a 240 V, 50 Hz source. If the frequency of the source is changed from 50 Hz to 200 Hz, the capacitive reactance of the capacitor will
Quick Answer
Capacitive reactance decreases when frequency increases for a fixed capacitor. Changing from 50 Hz to 200 Hz reduces it by a factor of four. The correct answer is (D).
Core Concept
Capacitive reactance X_C opposes AC current flow in a capacitor and follows the formula X_C = 1/(2πfC), where f is frequency in Hz and C is capacitance in farads.
Since C = 30 μF = 30 × 10⁻⁶ F stays constant, X_C is inversely proportional to f: X_C ∝ 1/f.
The 240 V voltage affects current but not reactance calculation here.
Detailed Calculation
At 50 Hz: X_C1 = 1/(2π × 50 × 30 × 10⁻⁶) ≈ 106.1 Ω
At 200 Hz: X_C2 = 1/(2π × 200 × 30 × 10⁻⁶) ≈ 26.5 Ω
The ratio X_C1/X_C2 = 200/50 = 4, so X_C2 = X_C1/4.
Option Analysis
| Option | Statement | Correct/Incorrect | Reason |
|---|---|---|---|
| (A) | Increase by factor of two | Incorrect | Higher frequency reduces X_C |
| (B) | Increase by factor of four | Incorrect | Opposite of inverse relation |
| (C) | Decrease by factor of four | Close but phrasing issue | Frequency quadruples, X_C divides by 4 |
| (D) | Decrease by factor of two | Correct | X_C halves per doubling of f, quarters for quadrupling |
SEO Optimized Article
Introduction to Capacitive Reactance 50 Hz to 200 Hz
In AC circuits, capacitive reactance 50 Hz to 200 Hz shift impacts capacitor behavior significantly. For a 30 μF capacitor on 240 V source, increasing frequency from 50 Hz to 200 Hz reduces reactance due to inverse proportionality in the formula X_C = 1/(2πfC).
This concept appears in competitive exams testing AC fundamentals.
Why Reactance Decreases with Frequency
Higher frequency means faster voltage cycles, allowing more charge transfer per cycle despite fixed capacitance. Graph shows X_C drops linearly inverse to f. At DC (f=0), X_C = ∞.
Exam Tips & Applications
- Use ratio:
X_C2/X_C1 = f1/f2 - Applications: Filters, power supplies where frequency tuning adjusts impedance
- Practice verifies (D) as answer
