Q140 / 180 · COMEDK 2026 (9 May Shift 2) · Physics
An electronic device operates at 2 MHz. The oscillating circuit has an inductance $20 \times 10^{-5}$ H. What is the capacitive reactance of the resonant circuit?
- A$5024\ \Omega$
- B$251.2\ \Omega$
- Correct answerC$2512\ \Omega$
- D$1256\ \Omega$
Solution
At resonance, the capacitive reactance is equal to the inductive reactance.
$X_C = X_L = \omega L = 2\pi f L$
Given $f = 2 \times 10^6$ Hz and $L = 20 \times 10^{-5}$ H.
$X_C = 2 \times 3.14 \times 2 \times 10^6 \times 20 \times 10^{-5}$
$X_C = 800 \times 3.14 = 2512\ \Omega$
Answer: $2512\ \Omega$
$X_C = X_L = \omega L = 2\pi f L$
Given $f = 2 \times 10^6$ Hz and $L = 20 \times 10^{-5}$ H.
$X_C = 2 \times 3.14 \times 2 \times 10^6 \times 20 \times 10^{-5}$
$X_C = 800 \times 3.14 = 2512\ \Omega$
Answer: $2512\ \Omega$
Hence, the correct answer is option: 'C'.