 #1
 217
 61
 Homework Statement:

In the given RC network, for an input signal of angular frequency w=1/RC, the voltage gain Vo/Vi and the phase angle between Vo and Vi, respectively are:
1/2 and 0
1/3 and 0
1/2 and pi/2
1/3 and pi/2
 Relevant Equations:

Xc = j/(wC)
where j is the imaginary unit.
Kirchhof's Law:
Vi  IR  IXc  Vo = 0
The impedance Z = R j/wC + ##\frac{1}{\frac{1}{R}  \frac{\omega C}{j}}##
But,1/wC=R
So, solving this, I find:
Z= 3R/2(1j)
Z =##\frac{3R}{\sqrt 2}##
I =##\frac{V_i \sqrt 2} {3R}##
Vi  IRIXc =Vo
Solving this,
##Vo = V_i \frac {V_i \sqrt 2}{3}  \frac{V_i \sqrt 2}{3R} \frac{j}{wC}##
##Vo = V_i(1 \frac {\sqrt 2}{3}  \frac{+j \sqrt 2}{3})##
This is something that doesn't match the options.
I think I am doing something conceptually wrong( like parallel addition of resistance and reactance maybe..). Please guide me.
Last edited by a moderator: