Question

Find the amplitude response $|\frac{V_2}{V_1}|$ for the circuit shown in figure. Determine the half-power frequency.

• A. $\frac{1}{RC}$
• B. $\frac{\sqrt{2}}{RC}$
• C. $\frac{\sqrt{3}}{RC}$
• D. $\frac{2}{RC}$

Answer 1

Answer: (B)

$\frac{\sqrt{2}}{RC}$

Amplitude response for the given circuit$|\frac{V_2}{V_1}|=|\frac{R}{R+R/(1+jwRC)}|=|\frac{1+jwRC}{2+jwRC}|$

$=\frac{\sqrt{1+(wRC{)}^2}}{\sqrt{4+(wRC{)}^2}}$.

Now the maximum value of response is 1.

For half power frequency ,

Amplitude response should be $\frac{1}{\sqrt{2}}$ times its maximum value.

$\frac{1+(wRC{)}^2}{4+(wRC{)}^2}=\frac{1}{2}$

$⟹wRC=\sqrt{2}$

or ,$w=\frac{\sqrt{2}}{RC}$

Answer is B.