Circuit, One resistor, two paths

[nealh149]

In a circuit where there is one resistor in one path and a separate 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:

\frac{1}{\frac{1}{R} + \frac{1}{0}} = \frac{1}{\infty} = 0

- 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 (excuse the pun e_e)

 

[chroot]

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 (excuse the pun e_e)

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

 

[chroot]

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.

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

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

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