Current calculation of a Y-junction

In Summary, The person is trying to solve a circuit but there is something wrong. They made a delta-Y conversion and their new impedances are Z_A, Z_B, and Z_C. The current I0 that flows between nodes A and B is not accounted for in their equation. They need to find the potentials at points B and C and then find I_0.
  • #1
simphysics
7
0
Homework Statement
Find I0 in the following circuit
Relevant Equations
I used the delta-Y conversion
Hello everyone!
I've been trying to solve this circuit but there's something wrong. Firstly, I made a Delta-Y conversion so that1 and zA were in series, and so were z5 and zb. I really don't know if writing "I0=IA-IB" is correct, cause basically I0 is the current that flows between the nodes A and B. Can someone help me, please?
Thank you!
EXERCISE.png
 
Physics news on Phys.org
  • #2
It is possible that you are getting few answers because the drawing is nearly illegible. Not all of the circuit elements seem to be resistors either. So that scares me away. I can make out (I think) ##Z_1## and ##Z_2## on the left hand side, ##Z_3## in the middle and ##Z_4## and ##Z_5## on the right.

Then in the equivalent Y layout we have some other symbols that I cannot make out.

Type in your equations. Explain what they mean and what justifies them and we can talk.
 
  • #3
Thank you.
I'll try to reupload the pics.
This is the circuit:
Screenshot_2022-08-25-16-27-41-763.jpeg

I did a delta-Y conversion
Screenshot_2022-08-25-16-27-58-026.jpeg

and the new impedances are:
Screenshot_2022-08-25-16-28-14-984.jpeg

I hope that the rest is pretty legible.
Thank you, again
 
  • #4
Much more legible, yes. Although the forum guidelines ask that you type in your work rather than import images.
https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/ said:
Core post content should be typed out and not solely contained in an image, PDF, or other attachment. (Exceptions at Mentor's discretion.) Use images for supporting figures. Use LaTeX to type mathematical expressions and equations. (See: Learn LaTeX for Math Equations)
[emphasis mine]
With the images made legible, I can see that ##Z_1## is an inductor and ##Z_5## is a capacitor. So this is beyond what I am competent to analyze.

I can see that you've transformed to something that might be a taus (##\dot{\tau_A}##, ##\dot{\tau_B}## and ##\dot{\tau_C}##) with bars through the symbols. But those equations would be a lot prettier if rendered in ##\LaTeX##.

See the LaTeX guide that is linked here, in the quote above and which is also linked below the edit window when you respond.
 
  • #5
simphysics said:
I really don't know if writing "I0=IA-IB" is correct, cause basically I0 is the current that flows between the nodes A and B.
That doesn't seem correct (though I'm no expert). There is a junction between ##Z_A## and ##Z_B## and your equation doesn't take account of the current flowing from the junction into ##Z_C##.

I think you need to find the potentials at points B and C. This gives the potential difference between B and C (##V_{BC} = V_C - V_B##). Then ##I_0 = \frac {V_{BC}}{R_3}##.

Notes

A, B and C are the names of points in the circuit So calling the Y-impedances ##Z_A, Z_B## and ##Z_C## isn't a good idea!. Maybe something like ##Z_P, Z_Q## and ##Z_R## would be better.

Your handwriting is difficult to read. Have some sympathy for whoever is marking your work! (And if they can't read it, you may lose marks.) For posting here, you should use Latex for equations (not that hard) as already noted by @jbriggs444.
 

FAQ: Current calculation of a Y-junction

1. How is the current calculated in a Y-junction?

The current in a Y-junction is calculated using Kirchhoff's Current Law (KCL), which states that the sum of currents entering a junction must equal the sum of currents leaving the junction. This means that the total current entering the junction must be equal to the total current leaving the junction.

2. What factors affect the current calculation in a Y-junction?

The current calculation in a Y-junction is affected by the resistances and voltage sources connected to the junction. The current will be higher if there is a lower resistance or a higher voltage source connected to the junction, and vice versa.

3. Can the current in a Y-junction be negative?

No, the current in a Y-junction cannot be negative. KCL states that the sum of currents entering and leaving a junction must be equal, so if one current is negative, another current must be positive to balance it out.

4. How does the number of branches in a Y-junction affect the current calculation?

The number of branches in a Y-junction does not affect the current calculation. KCL still applies, and the total current entering the junction must equal the total current leaving the junction, regardless of the number of branches.

5. What happens to the current if a branch is added or removed from a Y-junction?

If a branch is added or removed from a Y-junction, the total current entering and leaving the junction will still be equal. However, the current in each individual branch may change, depending on the resistance and voltage sources connected to the junction.

Back
Top