Path of least resistance

[Ethanadams]

I am just really curious about this.

electricity will always follow the path of least resistance right? So what would it do if we had a grid that had a hight of 10 cm land a length of 10 cm. inside the grid wires cross at every 1cm. Let's say the wires are made out of super cooled silver for next to no resistance. Now if this grid represented the top right quadrant of a graph what path would an eletric charge take if it went from (5,5) to (10,5) or (8,4) to (3,6).

 

Sorry of I did not explain this well enough if you have trouble understanding I can try and show it on graph paper what I mean

 

 

Edited September 30, 2016 by Ethanadams

[Shpaget]

That's an old puzzle, or variation of it.

http://www.mathpages.com/home/kmath668/kmath668.htm

[mhoram]

XKCD says it all ;-)

 

[peadar1987]

Saying electricity follows the path of least resistance is a little misleading, as it makes it sound like all the electricity flows through whichever channel happens to be easiest. The actual current will split, based on the resistance. When you have things like copper wire and air, the difference in resistance between the copper and the air is so big that the proportion of current that flows through the air is completely negligible, but in networks of conductors it's not

[Nuke]

you can pretty much take every short maxim (< 1 paragraph) about electronics and throw it out. they are all oversimplified, misleading lies, and they have screwed me over so much its not funny. then go watch all of afroman's videos on youtube.

8 hours ago, peadar1987 said:

Saying electricity follows the path of least resistance is a little misleading, as it makes it sound like all the electricity flows through whichever channel happens to be easiest. The actual current will split, based on the resistance. When you have things like copper wire and air, the difference in resistance between the copper and the air is so big that the proportion of current that flows through the air is completely negligible, but in networks of conductors it's not

pretty much this, use the voltage divider formula:

vout = (r2 / (r1+r2)) * vin

note that wire is not free of resistance, its just very low. you can break down any resistor network (or wire grid for that matter) into a system of voltage dividers. i actually had to go through the trouble of that to design a ladder dac for some a/v projects.

 

Edited September 30, 2016 by Nuke

[Talavar]

Occam's razor: It will simply take all equal available paths simultaneously. "Any time you encounter an electrical flow question, First think of the flow of water in a similar downhill simulation. If that fails, then apply mathematics" ~Mr Batronis, my highschool electrical tech teacher~

Edited October 1, 2016 by Talavar

[mhoram]

18 hours ago, WildLynx said:

What is solution of XCD resistor grid question?

Have a look at the explanation section here: " 4/π − 1/2 ohms". There is also a link to a page detailing the math behind it.

[Superfluous J]

18 hours ago, WildLynx said:

What is solution of XCD resistor grid question?

Keep walking until you're out of the street.