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Q & A: Does current take the path of least resistance?

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Most recent answer: 11/13/2015
Q:
doubt on electrical currrent flow through resistance question : if current takes the path of the least resistance , then why cannot all the current pass through the first resistance in a parallel resistance connection instead of going through all the resistances?
- hari menon (age 12)
TRICHUR,INDIA
A:

This is a great question. It makes you wonder what phrases like "takes the path of least resistance" mean. If you think of a path as being a sort of line from one spot to another, then that saying is obviously false. The current spreads out if it can.  So it's probably best to just forget about those "current takes the path of the least resistance" words, since it's not clear what they mean or if they're true. Instead, you can think of the basic mathematical rules.

For resistors, the current is given by I=V/R, where V is the voltage across the resistor. Combined with the rule (Kirchhoff's) that over time the average current into some spot equals the average current out of it, that's enough equations to fix the current pattern for any resistor circuit, once you know the applied voltage. For a bunch of parallel resistors (R1, R2, R3,...) they each have the same voltage drop, so they have currents V/R1 , V/R2, V/R3,...

Mike W.


(published on 01/25/2014)

Follow-Up #1: Way to picture current flow

Q:
When the bell rings the kids run out of school by "taking the paths of least resistance", i.e., whatever door (or as I remember from my school, even window!) they can exit. If the main gate is already crowded with kids, then other kids go through smaller gates. The same is true of water you pour downhill; it takes several paths; as soon as a path is crowded, the water opens up a new branch. If you touch an equipment that is short-circuited, even if it is grounded still some current passes through you (you get a tingling feeling); again because a few electrons find your body as unoccupied exit (a small door) that they can exit.
- Mehran
Arlington Heights, IL
A:

Thanks Mehran, that's a nice way to help people think about how the current distributes. There's one little difference between your example and the current. You've got the flow of kids being non-linear, so that they don't take side door unless the main one fills up. Even a small current, however, branches out through all the paths.

Mike W.


(published on 11/13/2015)

Follow-up on this answer.