Help on thevenizing a Scheering Bridge

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SUMMARY

This discussion focuses on the process of "thevenizing" a Scheering Bridge to find the magnitude and phase of the sinusoidal current (ID) flowing through the galvanometer D. The solution involves calculating the Thevenin equivalent circuit, which includes determining the Thevenin voltage (VTH) and Thevenin impedance (ZTH). The phase of ID is not a fixed 90 degrees but varies with frequency, requiring the use of the arctangent function to derive the correct phase angle based on the real and imaginary components of the impedance.

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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.

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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)

cum50.png


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

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

2jescqg.png


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...
 
Last edited:
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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)
 


The Electrician said:
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...
 

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