Solving voltage divider involving capacitors

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SUMMARY

The discussion focuses on solving a voltage divider problem involving capacitors and complex impedance. Given the values ZV1 = ZV2 = 100Ω and ZCCV = ZCV = -2000jΩ, the user attempts to derive the ratio VV/VC, which is calculated as 0.02499, significantly lower than the expected result. The user employs the equation 1/ZV = 1/ZV1 + 1/ZV2 + 1/ZCV and applies Kirchhoff's laws but struggles with the arithmetic leading to the discrepancy in the expected outcome.

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wu_weidong
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Homework Statement


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Given ZV1 = ZV2 = 100Ω,
ZCCV = ZCV = 2000/j = -2000j, and
VV/VC = 0.04789.

I'm trying to get the given VV/VC result.

Homework Equations


I know that
1/ZV = 1/ZV1 + 1/ZV2 + 1/ZCV
VV = ZV / (ZV + ZCCV) * VC

The Attempt at a Solution


1/ZV = 1/ZV1 + 1/ZV2 + 1/ZCV = 1/100 + 1/100 + j/2000
|1/ZV| = √(0.022 + (1/2000)2) = 0.02
ZV = 50Ω

VV/VC = ZV / (ZV + ZCCV) = 50 / (50 - 2000j)
VC/VV = (50 - 2000j) / 50 = 1 - 40j
|VC/VV| = √(12 + 402) = 40.01
VV/VC = 1/40.01 = 0.02499
which is about half of the value I should get.

Where did I go wrong?
 
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Kirkoffs laws - check arithmetic.
 
Simon Bridge said:
Kirkoffs laws - check arithmetic.
Can I please have a bit more hint?

The voltage through ZV1, ZV2 and CV is the same (VV), right?
 

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