Question

An RC high-pass filter has \(R=10\,\text{k}\Omega\) and \(C=0.01\,\mu\text{F}\). The cut-off frequency is

• A. \(159\,\text{Hz}\)
• B. \(159\,\text{kHz}\)
• C. \(15.9\,\text{kHz}\)
• D. \(1.59\,\text{kHz}\)

Hint:

The cut-off frequency of an RC filter is \[ \boxed{ f_c=\frac{1}{2\pi RC} } \] where \(R\) is in ohms and \(C\) is in farads.

Answer 1

The Correct Option is D

Step 1: Use the cut-off frequency formula. For an RC high-pass filter, \[ f_c=\frac{1}{2\pi RC}. \] Given, \[ R=10\,\text{k}\Omega=10^4\,\Omega, \] \[ C=0.01\,\mu\text{F}=10^{-8}\,\text{F}. \]

Step 2: Calculate the cut-off frequency. \[ RC=10^4\times10^{-8}=10^{-4}. \] Therefore, \[ f_c = \frac{1}{2\pi\times10^{-4}} \approx1591.5\,\text{Hz} \approx1.59\,\text{kHz}. \] Hence, \[ \boxed{1.59\,\text{kHz}} \] Therefore, \[ \boxed{(D)} \] is the correct answer.