Circuit, One resistor, two paths

nealh149

In a circuit where there is one resistor in one path and a seperate path with no resistance, will all of the current go through the second path?

chroot

Yes. The parallel combination of two resistors, one with resistance R ohms and the other with resistance 0 ohms, is:

[latex]\frac{1}{\frac{1}{R} + \frac{1}{0}} = \frac{1}{\infty} = 0[/latex]

- Warren

nealh149

Good intuitively it made sense, I didn't even try it mathematically. Thanks.

arunma

As Chroot said, the current will go through the wire, and won't even bother with the resistor. But I'd just like to add that you should remember this if you ever have to deal with things called Thévenin circuits. In order to compute a circuit's Thévenin equivalent, you actually need to short-circuit two terminals (don't worry, you only do it on paper). I actually spent a couple weeks being confused about this, because I didn't understand that the current will bypass the resistor completely.

Da-Force

Short-circuit means a 0 resistance wire (a perfect ammeter, I believe) is placed across two points... All the current will go through this wire (which is kinda how ammeters work LOLz, if that's an easy way to remember).

Mathmatically, don't rely on it... The idea is simple, current wants to go through the FASTEST possible way it can... If you have 1000 ohms in one wire and 0 ohms in another, it wants to go through the 0 ohms because... nothing resists it :-P (excuse the pun e_e)

chroot

You should rely on mathematics more than any kind of intuition. Intuition can lead you astray, while mathematics cannot.

Also, the use of the word "FASTEST" above is incorrect. Resistance has nothing to do with the "speed" of current, whatever that is.

- Warren

Da-Force

I meant charges e_e

But anyways, resistances can be thought of as 'slowing or resisting' charges which creates a voltage... High resistances like a voltmeter means no (or neglible) current goes through the wire.

And mathmatics never explain negative/positive signs in magnetism or electricity for that matter, trust me ;-)

chroot

Slowing down charge carriers does not 'create' a voltage.

Mathematics thoroughly explains the difference between positive and negative charges; it just happens that the assignment of negative charge to the electron was arbitrary, and we preserve it for historical reasons.

- Warren