Electrical eng, my vectors for KVL and KCL aren't adding up - no errors in math

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SUMMARY

The discussion centers on the application of Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL) in a series-parallel RC circuit. The user reports discrepancies in their vector calculations for voltage and current, specifically noting that the sum of voltages (Vr1 + Vr2 + Vc1 + Vc2) does not equal the total voltage (Vtotal). The user has verified their calculations with a lab supervisor and utilized a vector addition calculator. Key values include a total voltage of 4.75<0° and total current of 1.956<49.9°.

PREREQUISITES
  • Understanding of Kirchhoff's Voltage Law (KVL)
  • Understanding of Kirchhoff's Current Law (KCL)
  • Proficiency in complex number arithmetic for electrical engineering
  • Familiarity with series-parallel RC circuit analysis
NEXT STEPS
  • Review the principles of KVL and KCL in the context of AC circuits
  • Learn about complex impedance calculations in series-parallel circuits
  • Study vector addition techniques specific to electrical engineering
  • Explore common pitfalls in applying KVL and KCL to circuits with parallel components
USEFUL FOR

Electrical engineering students, circuit designers, and professionals troubleshooting AC circuit analysis issues will benefit from this discussion.

Yarnzorrr
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I've been asked to prove KVL and KCL using this circuit, but my vectors don't add up.
ei Vr1+ Vr2 + Vc1+Vc2 ≠ Vtotal, same goes for Current, but I at least got the correct angle for the current
Tried using vector addition, using addition of the vectors in complex form and even tried using this http://www.1728.org/vectors.htm vector addition calculator

I know my calculation are correct, I got my lab supervisor to check them.

Noting works, I don't know what I'm doing wrong, please help!

These are the values that I've got for my series parallel RC circuit (attached a photo of the circuit diagram)

Voltage (V)
R1 1.60< 49.97°
C1 2.78 < - 40.03°
R1 1.68 <19.4°
C2 1.68 <19.4°
Total 4.75< 0°

Currant (mA)
R1 1.956 < 49.97°
C1 1.956 < 49.97°
R2 1.68<19.4°
C2 0.995< 109.4°
Total 1.956 < 49.9°

Impedance (Ω)
R1 820 < 0°
C1 1421< -90°
R2 1000 < 0°
C2 1693< -90°
Total 2427.6 < - 49.9°
 

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Yarnzorrr said:
I've been asked to prove KVL and KCL using this circuit, but my vectors don't add up.
ei Vr1+ Vr2 + Vc1+Vc2 ≠ Vtotal, same goes for Current, but I at least got the correct angle for the current
Tried using vector addition, using addition of the vectors in complex form and even tried using this http://www.1728.org/vectors.htm vector addition calculator

I know my calculation are correct, I got my lab supervisor to check them.

Noting works, I don't know what I'm doing wrong, please help!

These are the values that I've got for my series parallel RC circuit (attached a photo of the circuit diagram)

Voltage (V)
R1 1.60< 49.97°
C1 2.78 < - 40.03°
R1 1.68 <19.4°
C2 1.68 <19.4°
Total 4.75< 0°

Currant (mA)
R1 1.956 < 49.97°
C1 1.956 < 49.97°
R2 1.68<19.4°
C2 0.995< 109.4°
Total 1.956 < 49.9°

Impedance (Ω)
R1 820 < 0°
C1 1421< -90°
R2 1000 < 0°
C2 1693< -90°
Total 2427.6 < - 49.9°

Can you show your analysis steps? I can see issues with your result values, but without seeing how you got there it's difficult to know how to help you.
 
Forgot to mention that the AC voltage input value on the diagram is wrong, its actually 4.75 < 0° sorry!

first found Z with:

Ztotal = (R2*Xc2)/(√(R2^2+Xc2^2) + R1 + Xc1

Where
R2 = 1000
Xc2 = -j 1693
R1 = 820
Xc2 = -j 1421

break it down to polar form to get

861 < 30.57° + 820 <0° + 1421 <-90° = 2427.6 < - 49.97°

Then made a table and using Ohm's Law got the following (attached)
 

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and to get the current through R2 and Xc2:

Itotal * (R2/(-jxc2+R2) = 1.956 < 49.97° * (1000 /-j1693+1000)

then to get IXc swapped the value for R2 on the denominator for Xc

got the following answers:
IR2 = 0.999 <109.4°
IXc2 = 1.68 < 19.4°
 
Yarnzorrr said:
Forgot to mention that the AC voltage input value on the diagram is wrong, its actually 4.75 < 0° sorry!
In that case, your individual calculated values look fine.

Perhaps your issue lies with using the calculated values with KVL and KCL. For example, in your original post you wrote: "Vr1+ Vr2 + Vc1+Vc2 ≠ Vtotal". The question is what closed KVL path does this expression correspond to in the circuit? After all, R2 and C2 are in parallel, so why would you add the voltage across them twice?