Question

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

• A. $\frac{1}{RC}$
• B. $\frac{2}{RC}$
• C. $\frac{4}{RC}$
• D. $0$

Answer 1

Answer: (B)

$\frac{2}{RC}$

Amplitude response for the circuit is actually ratio of impedences across source and across further points leaving one resistor component R ; $|\frac{V_2}{V_1}|=|\frac{R/(1+jwCR)}{R+R/(1+jwCR)}|=|\frac{1}{2+jwCR}|=\frac{1}{\sqrt{4+(wCR{)}^2}}$

Now for half power frequency,

$|\frac{V_2}{V_1}{|}_{max}=\frac{1}{2}$ at $w=0$.

Half power frequency is the frequency when response becomes $\frac{1}{\sqrt{2}}$ times its maximum value.

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

$⟹4+(wRC{)}^2=8$

or,$(wRC{)}^2=4$ or,$w=\frac{2}{RC}$

$\therefore$Answer is B.