Unbalanced Scheering Bridge and Thevenin

[degs2k4]

Homework Statement

Find the magnitude and phase of the current flowing through the galvanometer whose internal resistance is negligible.C1=C, C2=0, Cx=2C, R2=R3=R, Rx=0

http://www.freeimagehosting.net/uploads/4ce4800510.png

The Attempt at a Solution

Magnitude of the current:

Using the Thevenin equivalent circuit,Z1 = 1/jwC1 = 1/jwC
Z2 = R2 || 1/jwC2 = R
Zx = Rx + 1/jwCx = 1/jw2C
Z3 = R3 = R

Rth = (Z1 || Z2) + (Zx || Z3)
Vth = V from c to b = Vc - Vb = Vac - Vab = E (Z1/(Z1+Z2) - Zx/(Zx+Z3))
Ig = Vth/Rth

Would this be correct?

Have no idea on how to get the phase of the current...

Thanks!

 

[KataKoniK]

Hello,

Your approach to finding the magnitude of the current using Thevenin's theorem is correct. However, to find the phase of the current, you need to use the impedance triangle method. This method involves drawing a triangle with the three impedances (Z1, Z2, Zx) as the sides and the current (Ig) as the hypotenuse. The phase angle can then be found using the tangent function, as shown below:

Phase angle = tan^-1 (Zx/Z1+Z2)

I hope this helps! Let me know if you have any other questions. Good luck with your calculations!