Combined resistance in this circuit

In summary: YIn summary, the homework statement is trying to find the combined resistance once the switch is closed. The student used a spread sheet to find the resistance and then used Kirchoff's law to find the voltages.
  • #1
Eitan Levy
259
11

Homework Statement


Find the combined resistance once the switch is closed.

Homework Equations


V=IR

The Attempt at a Solution


I tried applying Kirchoff’s law but I got many equations, I am sure there is a more efficient way. I also tried to re-draw the circuit, but wasn't sure how to do so. The answer is 4Ω.
 

Attachments

  • ‏‏לכידה.PNG
    ‏‏לכידה.PNG
    2.6 KB · Views: 407
Physics news on Phys.org
  • #2
The resistance is measured from top to bottom.
I do not get exactly 4.

I used a spread sheet.
I took node C as the top and D as the bottom, and assumed the current through the network was 1.
Then I set current CA to an estimated value and deduced all other currents (CB, AB, BD, and AD) based on that. Then, given the resistances, I computed all 5 of those voltages. Then I computed the total voltages CA+AB+BD and CB-AB+AD. Then I adjusted my original estimate for CA current to make those two total voltages equal.

That's probably as awkward as any other method. But it gave me an answer.
 
Last edited:
  • #3
.Scott said:
The resistance is measured from top to bottom.
I do not get exactly 4.
Perhaps it was rounded. Could you explain how you got it?
 
  • #4
Eitan Levy said:
Perhaps it was rounded. Could you explain how you got it?
I just edited post #2 with details.
If you're handy with Excel (or other spread sheet), it is pretty straight forward.
 
  • #5
Eitan Levy said:
Could you explain how you got it?
Resistors28628.png


Cells F18:21 are copies of F17.
Cells H23:J23 are copies of G23

All 4 values on row 22 should be the total voltage (and therefore impedance) from top (node C) to bottom (node D)

The 0.023 factor in line 25 results from experimentation. I did a few E23 adjustments manually until I saw what the approximate correction factor was. Then I put that into the "Improved Estimate" calculation.
 

Attachments

  • Resistors28628.png
    Resistors28628.png
    21.9 KB · Views: 238
  • #6
Eitan Levy said:
I am sure there is a more efficient way.
check out delta / Y transforms (or in your case, Y / delta transforms)
 
  • Like
Likes .Scott

1. What is combined resistance in a circuit?

Combined resistance in a circuit refers to the overall resistance encountered by an electric current as it flows through a circuit containing multiple resistors. It is the total opposition to the flow of current in a circuit and is measured in Ohms (Ω).

2. How is combined resistance calculated in a series circuit?

In a series circuit, the combined resistance is equal to the sum of all the individual resistances. This means that if there are two resistors with values R1 and R2, the combined resistance would be R1 + R2. In general, for n number of resistors in series, the combined resistance would be R = R1 + R2 + ... + Rn.

3. How is combined resistance calculated in a parallel circuit?

In a parallel circuit, the combined resistance is calculated using the formula 1/R = 1/R1 + 1/R2 + ... + 1/Rn. This means that the reciprocal of the combined resistance is equal to the sum of the reciprocals of all the individual resistances. The combined resistance can then be found by taking the reciprocal of the result.

4. What is the relationship between combined resistance and current in a circuit?

According to Ohm's Law, the current in a circuit is directly proportional to the voltage and inversely proportional to the combined resistance. This means that as the combined resistance in a circuit increases, the current decreases and vice versa.

5. Can the combined resistance in a circuit ever be lower than the lowest individual resistance?

No, the combined resistance in a circuit can never be lower than the lowest individual resistance. This is because adding more resistors in parallel or series will always increase the overall resistance, making it impossible for the combined resistance to be lower than any of the individual resistances.

Similar threads

  • Introductory Physics Homework Help
2
Replies
42
Views
1K
  • Introductory Physics Homework Help
Replies
12
Views
1K
  • Introductory Physics Homework Help
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
266
  • Introductory Physics Homework Help
Replies
3
Views
252
  • Introductory Physics Homework Help
Replies
2
Views
918
  • Introductory Physics Homework Help
Replies
3
Views
564
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
218
  • Introductory Physics Homework Help
Replies
3
Views
1K
Back
Top