Waste less time on Facebook — follow Brilliant.
×

Equivalent Resistance!

In question \(3.153\) . Find \(R_{eq}\) between the points \(A\) and \(B\)

Note by Advitiya Brijesh
4 years, 2 months ago

No vote yet
8 votes

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

Sort by:

Top Newest

http://img22.imageshack.us/img22/1256/dmj1.png

Log in to reply

thnks a lot! :)

Advitiya Brijesh - 4 years, 2 months ago

Log in to reply

This link has a lot of information on this and related problems. It gives \(R_{eq}=R/2\) in this case, and proves it first in a simple (albeit non-rigorous) way, and then provides rigorous justification. It also gives equivalent resistances for other points \(A\) and \(B\).

Ricky Escobar - 4 years, 2 months ago

Log in to reply

" Thus the direct link carries the same current as all the other paths, so the resistance of the direct link equals the effective resistance of the entire grid excluding that link. The direct link is in parallel with the remainder of the grid, so the combined resistance is simply R/2. " - why the resistance of the direct link is equally to the effective resistance of the entire grid EXCLUDING that link?

Andu Ouatu - 4 years, 2 months ago

Log in to reply

Let potential difference V be applied across A and B and i be the current in wires. Assume A is isolated positive terminal, so in every direction it sends out a current of i/4 (as there are 4 directions current at a junction can take). Similarly assume B is an isolated negative terminal, so from every direction it recieves an incoming current of i/4. Therefore, in the wire between A and B, net current is i/2 from A to B and hence resistance between A and B is R(0)/2

Utkarsh Sahu - 4 years, 2 months ago

Log in to reply

irodov right??

Varnika Chaturvedi - 4 years, 2 months ago

Log in to reply

Yes

Rishabh Deep Singh - 1 year, 10 months ago

Log in to reply

A Twist : What if these points A and B were diagonally opposite??

Rahul Nahata - 4 years, 2 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...