A capacitor has a reactance of \( 100\,\Omega \) at 50 Hz. Its reactance at 125 Hz would be
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 40\,\Omega \)
The capacitive reactance is inversely proportional to the frequency, with the capacitance fixed.
\( \displaystyle X_C = \frac{1}{2\pi f C} \;\Rightarrow\; X_C \propto \frac{1}{f} \)
\( \displaystyle \frac{X_2}{X_1} = \frac{f_1}{f_2} = \frac{50}{125} = \frac{2}{5} \)
\( \displaystyle X_2 = 100\,\Omega \times \frac{2}{5} = 40\,\Omega \)