I'm not sure if this scenario is an important one or not, but I'm curious, in an ideal circuit where a wire has no resistance (I know in practice wires have a little bit of resistance), if we had two wires in parallel would the current split?

For example, in the circuit shown below the total current would be 3A. Would each wire 1 and wire 2 each experience half of this current? Or would all of the current go through the shortest path, which is wire 1 with no current through wire 2?
What if wire 1 and wire 2 were the same sized paths?

 

If you follow Kirchoff's current law, yes the current splits, but not necessarily equally.

The sum of all currents out from the node must equal the sum of all currents into the node.

Another way of putting it, the sum of all currents in and out of the node must equal zero if you apply a signed value to differentiate between input and output currents.

 

In an ideal circuit, you cannot determine how the current divides. In a real circuit, where wire have small amount of resistance, the current divides inversely to the resistance.

 

Here is a thought experiment.

Imagine you add more and more wires beside the original two. How much current flows through each individual wire?
Now make the number of wires infinite to the point where they merge into a flat surface.
Plot the current density in a flat infinitely large surface from point A to point B.

 

Here is a thought experiment.

Imagine you add more and more wires beside the original two. How much current flows through each individual wire?
Now make the number of wires infinite to the point where they merge into a flat surface.
Plot the current density in a flat infinitely large surface from point A to point B.

Interesting thought.

Next question:
What would happen if one wire was connected, and the other was disconnected. Then suddenly the other connects. Does the same concept apply?

 

In the case with two wires with one disconnected, all the current will flow through the one connected wire.

When both wires are connected the current will revert back to the same situation when the two wires were first connected.

(Note that the current is inversely proportional to the resistance of the wire as mike pointed out.)

 

Interesting thought.

Next question:
What would happen if one wire was connected, and the other was disconnected. Then suddenly the other connects. Does the same concept apply?

There are factors other than resistance at play. For instance, each wire has inductance and you have a magnetic field that is going to want to distribute the currents so as to minimize the energy involved. As soon as you start talking about these kinds of scenarios in which you don't have any resistance to determine the distribution, something else (which was previously a negligible higher-order effect) will rise to dominance and take over.

 

One consideration that is often ignored but is important in low resistance circuits is connection resistance.

This can lead to incorrect circuit measurements or burnt out components.

Every 'split' or branch you introduce reuqires two additional connections.

Have you thought about this?

Another consideration is that the situation you describe is widely used in the UK (but not in the US or Europe) in building wiring.

It is called the ring main and parallel paths are indeed provided for electrical supply.
Competent electricians cope with this every day of their working lives.

 

One consideration that is often ignored but is important in low resistance circuits is connection resistance.

This can lead to incorrect circuit measurements or burnt out components.

Every 'split' or branch you introduce requires two additional connections.

Have you thought about this?

Interesting, I never learned that there is increased connection resistance when there are additional connections before. I didn't know about connection resistance. I think you're referring to practical circuits rather than ideal wiring?

Another consideration is that the situation you describe is widely used in the UK (but not in the US or Europe) in building wiring.

It is called the ring main and parallel paths are indeed provided for electrical supply.
Competent electricians cope with this every day of their working lives.

So they place wires in parallel the way I described in the original post in the picture? Why do they do this?

 

So they place wires in parallel the way I described in the original post in the picture? Why do they do this?

This method essentially provides a 'circular' path for the circuit, a pair of conductors leave the breaker and are wired to each outlet in turn, the pair then continue back to the service panel essentially providing two supply paths for each of the outlets, spurs are allowed but a maximum of two outlets on a spur, (at least it was).
Max.

 

Connection resistance applies to all connections, not just additional ones.

What do you think four terminal measurements are all about?

Ringmains allow alternative paths to supply current when another load is drawing a high current thereby causing an unacceptable voltage drop.



The standard voltage at the dist board feeding the ringmain is 230Vac.

Now supposing that outlets A has a 3kW load connected.
This draws 13 amps in the leg from the distboard to A.
This will introduce a voltage drop in that section to say 220Vac.

But C can also be fed via E and D.

Now something known as electrical diversity syas that it is unlikely that a user will want to plug a 3kW device into each of A, B, C D and E at the same time.
So to save wiring and allow for this we use a ringmain.

Infact the standard fusing is either 30 amps or 45 amps so if the user did he would blow the distboard fuse anyway.

Diversity is also used when establishing the fuse and cable sizing for electric cookers.
Current due to a load at B may reduce still further the voltage available at C.