Question

In a detector, the output circuit consists of \( R = 10 \, \text{k}\Omega \) and \( C = 100 \, \text{pF} \). The frequency of carrier signal it can detect is:

• A. \( \gg 1 \, \text{MHz} \)
• B. 0.1 kHz
• C. \( \gg 1 \, \text{GHz} \)
• D. \( 10^3 \, \text{Hz} \)

Hint:

Use \( f = \frac{1}{2\pi RC} \) to find cut-off frequency in RC detectors.

Answer 1

The Correct Option is A

The cut-off frequency of an RC circuit is: \[ f = \frac{1}{2\pi RC} \] Given: - \( R = 10^4 \, \Omega \) - \( C = 100 \times 10^{-12} \, \text{F} \) \[ f = \frac{1}{2\pi \cdot 10^4 \cdot 100 \times 10^{-12}} = \frac{1}{2\pi \cdot 10^{-6}} \approx \frac{10^6}{2\pi} \approx 1.6 \, \text{MHz} \] So it can detect frequencies greater than 1 MHz.