Resistance of an interesting circuit

In summary, the conversation discusses finding the resistance between points A and B in a circuit with multiple boxes, each with resistance R. The equations R=R1+R2 and 1/R=1/R1+1/R2 are used to determine the equivalent resistance, which is found to be 3.5R by taking advantage of the symmetry of the circuit. It is noted that the problem would become more complex if the resistances were different.
  • #1
fawk3s
342
1

Homework Statement



vivalaresistance.png


So each box in the picture has resistance R. Find the resistance between A and B.

Homework Equations



R=R1+R2
1/R=1/R1+1/R2

The Attempt at a Solution



I got the answer to be 3,5R. But as I am not sure if I approached the problem correctly, I would like to hear what you guys got for the answer.

Thanks in advance
 
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  • #2
I don't see any picture.
 
  • #3
You dont? Thats weird, because I do. Anyway, here's the link:
http://s17.postimage.org/pj88qy16l/vivalaresistance.png
 
Last edited by a moderator:
  • #4
fawk3s said:
You dont? Thats weird, because I do. Anyway, here's the link:
http://s17.postimage.org/pj88qy16l/vivalaresistance.png

Ok, thanks for the link. But i still don't see the image in your main post.
To find the equivalent resistance, you see that there is some kind of symmetry. You can break the circuit as shown in the attachment.
 

Attachments

  • eq.png
    eq.png
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  • #5
Thats what I did, and got 3,5R. Wasnt sure it was correct. Thanks =)

Guess it would get more interesting if the resistances were different.
 
  • #6
I get that too, taking advantage of the symmetry of the problem.
 
  • #7
fawk3s said:
Thats what I did, and got 3,5R. Wasnt sure it was correct. Thanks =)

Guess it would get more interesting if the resistances were different.

You are welcome! :smile:
 

1. What is resistance and how is it measured in a circuit?

Resistance is the measure of how much a material or component resists the flow of electric current. It is measured in units called Ohms (Ω) and can be calculated using Ohm's Law, which states that resistance equals voltage divided by current.

2. How does adding resistors affect the overall resistance of a circuit?

When resistors are added in series, the total resistance increases as the individual resistances add up. When resistors are added in parallel, the total resistance decreases as the inverse of the individual resistances add up.

3. Can the resistance of a circuit change over time?

Yes, the resistance of a circuit can change over time due to factors such as temperature, material degradation, and external influences. This is why components like resistors are given a tolerance value to account for potential changes in their resistance.

4. How does the length and thickness of a wire affect its resistance?

The length of a wire is directly proportional to its resistance, meaning a longer wire will have a higher resistance. The thickness or cross-sectional area of a wire is inversely proportional to its resistance, meaning a thicker wire will have a lower resistance.

5. How does the type of material used in a circuit affect its resistance?

Different materials have different resistivities, which is a measure of how easily a material allows electric current to flow through it. Materials with higher resistivities will have higher resistance, while materials with lower resistivities will have lower resistance.

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