Mesh Analysis: Converting from Time to Frequency Domain with Correct Equations

Join the discussion
Ask a follow-up here, or get your own question answered by working scientists, mathematicians and engineers — people, not an autocomplete.
Real named experts · corrections over time · the nuance an AI answer skips
Sign up Log in
18 replies · 2K views
eehelp150
Messages
235
Reaction score
0

Homework Statement


pHJ8FSj.png
[/B]
1. Convert from time to freq domain
2. Use mesh analysis to find I1, I2, I3
3. Find Ve and convert it to time domain

Homework Equations


KVL
V=IR

The Attempt at a Solution


Are these mesh equations correct?
45cos(500t) -> 45V
80mH -> 40j
50mH -> 25j
25uF -> -80j
12.5uF -> -160j

Mesh1
(100+40j+25j+200)I1 - 200I2 - 400jI3 = 0
Mesh2
-45 + (200-80j)I2 - (200I1) + 80jI3 = 0
Mesh3
(-80j-160j+25j)I3 + 80jI2 -25jI1 = 0
 
Last edited:
on Phys.org
I don't see the 200 Ω resistor being affected by I1 in the first mesh equation.
 
gneill said:
I don't see the 200 Ω resistor being affected by I1 in the first mesh equation.
Can't believe I missed that. Do the other two look fine?
Are there any "shortcut strategies" for solving a system of three equations with complex variables?
 
eehelp150 said:
Can't believe I missed that. Do the other two look fine?
Are there any "shortcut strategies" for solving a system of three equations with complex variables?
The others look okay to me.

No shortcuts other than using a software package to do the heavy lifting. I'm partial to Mathcad myself, putting the equations into matrix form and using the built in solver.
 
gneill said:
The others look okay to me.

No shortcuts other than using a software package to do the heavy lifting. I'm partial to Mathcad myself, putting the equations into matrix form and using the built in solver.
For mesh1, it should be -25jI3 instead of 400jI3
I used an online calculator and got this:
upload_2016-10-11_10-59-40.png
 

Attachments

  • upload_2016-10-11_10-50-14.png
    upload_2016-10-11_10-50-14.png
    4.8 KB · Views: 430
Last edited:
Your 1,3 entry of the matrix should be identical to the 3,1 entry.

Here's a Mathcad version:
upload_2016-10-11_14-1-3.png
 
gneill said:
Your 1,3 entry of the matrix should be identical to the 3,1 entry.

Here's a Mathcad version:
View attachment 107300
Is the voltage across Ve simply (I3-I2) * Impedance of 25uF capacitor?
 
eehelp150 said:
Is the voltage across Ve simply (I3-I2) * Impedance of 25uF capacitor?
Make that (I2 - I3)*Z25μF. I2 flows into the top of the capacitor, so it'll produce a voltage drop in the correct direction.
 
gneill said:
Make that (I2 - I3)*Z25μF. I2 flows into the top of the capacitor, so it'll produce a voltage drop in the correct direction.
I ended up getting 9.988 < -43.347 volts.
Converting to time domain would give: 9.988cos(500t - 43.347) right?
 
eehelp150 said:
I ended up getting 9.988 < -43.347 volts.
Converting to time domain would give: 9.988cos(500t - 43.347) right?
That looks a bit small. Can you show that calculation in detail?
 
gneill said:
That looks a bit small. Can you show that calculation in detail?
(I2-I3) * (-j80)
= (0.086 + 0.091j) * (-j80)
= -6.88j - 7.248j^2
=7.248-6.88j

sqrt(7.248^2 + 6.88^2) = 9.99 < -43.5 degrees
 
gneill said:
What values are you using for I2 and I3?
I2 = 0.1188 + 0.1314j
I3 = 0.0329 + 0.0408j

EDIT:
Are these the correct values?
I2 = 0.52013055631408 +0.24535752634041i
I3=0.15152422756397 +0.07991035923825i
 
eehelp150 said:
I2 = 0.1188 + 0.1314j
I3 = 0.0329 + 0.0408j
They don't match your results from post #5. Has something changed?
 
gneill said:
They don't match your results from post #5. Has something changed?
Lack of sleep I guess :P
I plugged in the wrong value to the calculator.

New value for Ve: 32.3<65.88 degrees
 
eehelp150 said:
Lack of sleep I guess :P
I plugged in the wrong value to the calculator.

New value for Ve: 32.3<65.88 degrees
Better. Confirm the sign of the angle.
 
gneill said:
Better. Confirm the sign of the angle.
Why is it -65.88 instead of 65.88? I recall this being covered in class but I forgot. The calculator spits out 65.88
 
eehelp150 said:
Why is it -65.88 instead of 65.88? I recall this being covered in class but I forgot. The calculator spits out 65.88
What are the Cartesian components of the complex value?
 
gneill said:
What are the Cartesian components of the complex value?
Fourth quadrant.
I get it now.