Question

A 15.0 $\mu$F capacitor is connected to a 220 V, 50 Hz source. Then capacitive reactance of the circuit is ______ $\Omega$.

• A. 2.12
• B. 212
• C. 21.2
• D. 2120

Hint:

In a DC circuit, frequency $f = 0$, so $X_C$ becomes infinite. This is why capacitors block DC!

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Capacitive reactance ($X_C$) is the opposition offered by a capacitor to the flow of alternating current. It is inversely proportional to frequency and capacitance.
Step 2: Calculation:
Formula: $X_C = \frac{1}{2\pi f C}$ Given: $f = 50$ Hz, $C = 15 \times 10^{-6}$ F. $$X_C = \frac{1}{2 \times 3.14 \times 50 \times 15 \times 10^{-6}}$$ $$X_C = \frac{1}{314 \times 15 \times 10^{-6}} = \frac{10^6}{4710} \approx 212.3 \text{ }\Omega$$
Step 3: Final Answer:
The capacitive reactance is approximately 212 $\Omega$.