What is the Equivalent Resistance of Resistors in Series and Parallel?

In summary, the centre "diamond" has zero resistance and the right-hand sides of the "diamond" should short-out the four right-hand resistances.
  • #1
axleboy57
2
0

Homework Statement



All resistors have the same value, 'R'

Homework Equations



I don't think mesh/loop analysis or nodal analysis is applicable here, I think I'm just having a hard time seeing how the series-parallel connections work.

The Attempt at a Solution



I know the top left two are in parallel and then they come back together, and I know all the corners are in series, it's just the middle box that throws me.
 

Attachments

  • Untitled.jpg
    Untitled.jpg
    9.1 KB · Views: 384
Last edited:
Physics news on Phys.org
  • #2
My approach would be to redraw the circuit so it's a bit easier to see what's going on.

You are right that mesh and nodal don't apply- you have no need to find voltages or currents.

Now, lastly, why do you say the top left are in parallel and the rest are in series? Step through that thought process, it might help you. I'm not saying you're wrong, but I'm not saying you're right either- just walk through the process.
 
  • #3
Welcome to PF!

Hi axleboy57! Welcome to PF! :smile:

I don't normally do electricity questions unless they're really easy :rolleyes:

can someone tell me whether the centre "diamond" is supposed to have zero resistance, because if it is, why don't the right-hand sides of the "diamond" short-out the four right-hand resistances? :confused:
 
  • #4


tiny-tim said:
Hi axleboy57! Welcome to PF! :smile:

I don't normally do electricity questions unless they're really easy :rolleyes:

can someone tell me whether the centre "diamond" is supposed to have zero resistance, because if it is, why don't the right-hand sides of the "diamond" short-out the four right-hand resistances? :confused:

Yes, it has zero resistance (the diamond) but I don't want to say more lest I give away the answer. Think about when a source is applied, where is current going to flow?

This is a very common type of problem for intro courses to electronics. It's basically designed to force the student to think about parallel and series resistances (though, honestly, it's really just meant to confuse more than anything). I can PM you the solution, tiny-tim, so you can see what to do and I can explain what I can't in this thread if you want me to?
 
  • #5


Fronzbot said:
Yes, it has zero resistance (the diamond) but I don't want to say more lest I give away the answer. Think about when a source is applied, where is current going to flow?

This is a very common type of problem for intro courses to electronics. It's basically designed to force the student to think about parallel and series resistances (though, honestly, it's really just meant to confuse more than anything). I can PM you the solution, tiny-tim, so you can see what to do and I can explain what I can't in this thread if you want me to?

Good hint, TT :wink:
 

What is an equivalent resistance problem?

An equivalent resistance problem is a type of circuit problem where the goal is to find a single resistance value that can replace a complex circuit with multiple resistors. This simplifies the circuit and makes it easier to analyze.

How do you calculate the equivalent resistance?

The equivalent resistance can be calculated using Ohm's Law, which states that resistance is equal to voltage divided by current. In a series circuit, the equivalent resistance is the sum of all individual resistances. In a parallel circuit, the equivalent resistance is calculated using the formula 1/R = 1/R1 + 1/R2 + ... + 1/Rn.

Why is finding the equivalent resistance important?

Finding the equivalent resistance allows us to simplify complex circuits and make them easier to analyze. It also helps us understand the behavior of the overall circuit and how changing the resistance values may affect the circuit's performance.

What are the key principles to keep in mind when solving an equivalent resistance problem?

There are a few key principles to keep in mind when solving an equivalent resistance problem. These include understanding the difference between series and parallel circuits, knowing how to calculate equivalent resistance for each type of circuit, and being familiar with Ohm's Law and its applications.

Are there any useful tips for solving equivalent resistance problems?

Some useful tips for solving equivalent resistance problems include breaking down complex circuits into smaller, simpler parts, using diagrams or drawings to visualize the circuit, and double-checking your calculations to ensure accuracy. It may also be helpful to practice solving various types of equivalent resistance problems to become more familiar with the concepts and formulas.

Similar threads

  • Engineering and Comp Sci Homework Help
Replies
11
Views
5K
  • Engineering and Comp Sci Homework Help
Replies
2
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
5
Views
3K
  • Engineering and Comp Sci Homework Help
Replies
17
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
6
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
8
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
9
Views
4K
  • Engineering and Comp Sci Homework Help
Replies
8
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
17
Views
9K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
716
Back
Top