Help on thevenizing a Scheering Bridge

[degs2k4]

Help on "thevenizing" a Scheering Bridge

Homework Statement

Under the following conditions: C1=C, C2=0, Cx=2C, R2=R3=R, Rx=0, find the magnitude and phase of the sinusoidal current flowing through the galvanometer D (ID) whose internal resistance is neglibly small.

The Attempt at a Solution

We have an unbalanced condition. We can determine ID by means of the Thevenin equivalent circuit:

Steps:
1) get Vth:

VTH = VCB = VC - VB = VAC - VAB

(Z1= 1/jwC, Zx=1/jw2C, Z3=Z2=R)

2) Now let's calculate Zth, which will have a real part (resistor) and imaginary part (capacitor)

ZTH = (Z1 || Z2) + (Zx || Z3)

3) Finally let's form the Thevenin equivalent circuit:

ID = VTH / ZTH

ok, up to this point I think we have got the magnitude of ID. What about the phase ? Since a capacitor delays voltage 90 degrees, I believe that the phase of ID is 90, but I am not sure...

Would this work as a solution?

Thanks in advance...

 

[The Electrician]

Your method will work. The expressions involved are rather complicated and you will have to be very careful with your algebra to get the final result, which is surprisingly simple.

The phase is not 90 degrees; it depends on the frequency. You will have to derive an expression involving jw: Arctan(Imaginarypart/Realpart)

 

[degs2k4]

Your method will work. The expressions involved are rather complicated and you will have to be very careful with your algebra to get the final result, which is surprisingly simple.

The phase is not 90 degrees; it depends on the frequency. You will have to derive an expression involving jw: Arctan(Imaginarypart/Realpart)

Thanks for your comment! I also thought that the calculations were very complicated...