The resistance of a series R-C circuit is 5 ω If the impedance of the circuit is 13 ω calculate the reactance of the capacitor

Analyze the question: In a series R-C circuit, you're given the resistance (R = 5 Ω) and the total impedance (Z = 13 Ω). You need to find the capacitive reactance (Xc).

Concept: In a series R-C circuit, the resistance and capacitive reactance are 90° out of phase, so they add as vectors (Pythagoras' theorem), not by simple addition:

Z² = R² + Xc²

So: Xc = √(Z² − R²)

Solution:

1. Z² = 13² = 169
2. R² = 5² = 25
3. Xc² = 169 − 25 = 144
4. Xc = √144 = 12 Ω

Answer: The reactance of the capacitor is 12 Ω, which is option A.

Tip: Watch for the (5, 12, 13) Pythagorean triple. Whenever you see numbers like 5 and 13 in an R-C, R-L, or R-L-C impedance question, the missing value is very likely 12. Other common triples to remember are (3, 4, 5), (8, 15, 17), and (7, 24, 25). Recognising them saves valuable time in the exam.