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

Click For Summary

Discussion Overview

The discussion revolves around the application of Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL) in a series-parallel RC circuit. Participants are exploring issues related to vector addition of voltages and currents, and the calculations involved in proving these laws.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant reports that their calculated voltages and currents do not satisfy KVL and KCL, stating that the sum of voltages does not equal the total voltage.
  • Another participant requests to see the analysis steps to understand the discrepancies in the results, noting potential issues with the calculated values.
  • A participant provides a formula for calculating total impedance and breaks it down into polar form, presenting their calculations for total impedance.
  • Further calculations for current through specific components are shared, including the use of Ohm's Law to derive values for current through R2 and the capacitive reactance.
  • One participant corrects the AC voltage input value mentioned earlier, indicating it was initially misstated.
  • Another participant questions the application of KVL in the context of the circuit configuration, suggesting that the participant may be incorrectly adding voltages across components that are in parallel.

Areas of Agreement / Disagreement

Participants express differing views on the application of KVL and KCL in the circuit, with no consensus reached on the correct approach to resolving the discrepancies in the calculations.

Contextual Notes

There are unresolved issues regarding the assumptions made in applying KVL and KCL, particularly concerning the identification of closed paths in the circuit and the treatment of parallel components.

Yarnzorrr
Messages
11
Reaction score
0
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°
 

Attachments

  • Screen Shot 2012-09-27 at 4.38.07 PM.png
    Screen Shot 2012-09-27 at 4.38.07 PM.png
    3.4 KB · Views: 502
Physics news on Phys.org
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)
 

Attachments

  • Screen Shot 2012-09-27 at 10.05.34 PM.png
    Screen Shot 2012-09-27 at 10.05.34 PM.png
    6.4 KB · Views: 463
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?