Solve Delta-to-Y Circuit: Find Current & Voltage Across R5

  • Thread starter FilthyOtis
  • Start date
In summary, the conversation is about solving a circuit problem where the goal is to calculate the current through R5 and the voltage across R5. The speaker has not yet solved for the current through R5 and is struggling with working backwards through a delta-to-Y transformation. Another person suggests using the Kirkhoff current law to solve the problem.
  • #1
FilthyOtis
15
0
I'm really having troubles figuring this stuff out. Here's a question and what I've done..

a) Calculate current through R5

b) Determine Voltage across R5

I haven't gotten a) yet so haven't even tried b). I made a crude drawing of the original circuit in mspaint.


So... I did a delta-to-y on resisters 1, 2 and 5. Ra = R5, Rb = R2, Rc = R1

running the formulas

R1 = [(18)(12)] / [18 + 12 + 24] = 4 ohms

R2 = [(24)(12)] / 54 = 5.33 ohms

R3 = [(24)(18)] / 54 = 8 ohms


I redrew the picture with the 4ohms at the top splitting into the 5.33 on the left, 8 on the right and continuing down into the other 2 original resistors.

at this point I combined them all into one resistor by going
|| = parallel

4 ohms + [(5.33 ohms + 6 ohms) || (8 ohms + 6 ohms)] = 10.32 ohms


total current(I) = 15 V / 10.32 ohms = 1.46 A

and this is where my problem occurs... I don't know how to work backwards through this delta-to-Y transformation and properly find out how the current is splitting up. Can anyone help make sense of this? Thank you!

- Otis
 

Attachments

  • Circuit.GIF
    Circuit.GIF
    1.3 KB · Views: 528
Physics news on Phys.org
  • #2
Hi, the circuit drawn is known as brigde circuit. I'm not sure whether your working is wrong or correct. But I try to solve this question by the method below. It will be simpler. The V5 is 1.25v with I= 52.08mA.

First, i knew that V5= R3(15)/(R3+R1)-R4(15)/(18+6)
= 5-3.75
= 1.25v

Here a note attached here, and I hope it is useful for you.
Please correct me if I'm wrong.
 

Attachments

  • Bridge Circuit.pdf
    162.8 KB · Views: 363
  • #3
I think the standard way to solve this problem is to use the Kirkhoff current law, i.e., the sum of all currents flowing in and out of the node is zero. Denote x and y the unknown voltages on the left and right node, respectively. Assume that currents flow down trough resistors R1, R2, R3, and R4, and that the current flows from left to right through resistor R5. (It doesn't matter if this guess is wrong: your calculated currents will be negative then.) Then zero current condition in the node x leads to the following equation

[tex] \frac{15-x}{12} -\frac{x}{6} - \frac{x-y}{24} = 0 [/tex]

The similar condition for the node y yields

[tex] \frac{15-y}{18} -\frac{y}{6} + \frac{x-y}{24} = 0 [/tex]

Now you have 2 equations with two unknowns. The rest is just math.

Eugene.
 

FAQ: Solve Delta-to-Y Circuit: Find Current & Voltage Across R5

What is a Delta-to-Y circuit?

A Delta-to-Y circuit, also known as a Delta-to-Star or Delta-to-Wye circuit, is a type of electrical circuit used to connect three resistive elements in a triangular shape. It is commonly used in power systems and can be converted to a Y or star configuration for analysis purposes.

How do I solve a Delta-to-Y circuit?

To solve a Delta-to-Y circuit, you can use a variety of methods such as Kirchhoff's laws, Ohm's law, or the delta-star transformation. Begin by labeling the resistors as R1, R2, and R3 in a clockwise direction. Then, use the appropriate equations to calculate the equivalent resistance, current, and voltage across each resistor.

What is the delta-star transformation?

The delta-star transformation is a method used to convert a Delta-to-Y circuit into a Y or star configuration. It involves replacing the delta or triangular-shaped resistors with equivalent Y or star-shaped resistors. This transformation helps simplify circuit analysis and calculations.

How do I find the current and voltage across individual resistors in a Delta-to-Y circuit?

To find the current and voltage across individual resistors in a Delta-to-Y circuit, you can use Ohm's law (V=IR) or Kirchhoff's laws. First, calculate the equivalent resistance of the circuit using the delta-star transformation. Then, use the appropriate equations to calculate the current and voltage for each resistor.

What is the purpose of solving a Delta-to-Y circuit?

The purpose of solving a Delta-to-Y circuit is to determine the current, voltage, and power across individual resistors in the circuit. This information can be used to analyze the circuit's behavior, identify potential issues, and make necessary adjustments for optimal performance.

Similar threads

Replies
3
Views
1K
Replies
15
Views
2K
Replies
8
Views
2K
Replies
22
Views
3K
Replies
34
Views
5K
Replies
7
Views
3K
Back
Top