Does Wire Length Affect Current Flow Due to Potential Difference?

[Joshua_T]

Hi,

I have a question about something that I was recently told. They said that if you have a positive charge on one end of a wire and the other end is connected to ground, which they said was negatively charged, a current will be produced due to potential difference. Is this true, and does making the wire longer increase current? Thanks.

 

[TomHart]

Welcome to Physics Forums!

If you apply a voltage differential across a wire, it will produce a current in the wire. All wire has some resistance per unit length, so the longer the wire the greater the resistance. Additionally, a thicker wire has a lower resistance per unit length than a thinner wire. So if you maintain a constant potential and a constant wire thickness, a longer wire will produce a lower current because of greater total resistance from one end of the wire to the other end.

However, it probably is not wise to take a power supply and set it to, say, 10 V and connect a wire to it. Your power supply will either current limit or you could end up fusing the wire, depending on the various parameters.

 

[Bandit127]

To explain it another way.

A useful formula is V=IR.
V is the voltage between the top and bottom of the wire and can be considered constant for this situation. Normally Earth is 0V, not negatively charged so V is the voltage at the top of the wire since the bottom is at 0V.
I is the current (you could use A for Amps but I is the proper letter).
R is the resistance in the length of the wire.

If you increase the the length of the wire you increase the resistance. Since V is constant in the equation the current has to decrease. As we shorten the wire R decreases so I increases.

However, R is a very small number for normal lengths of wire so I is going to be a very big number. Increasing a very small number a bit still gives you a small number so current is going to be high for all outcomes of an experiment using normal lengths of wire.

Long lengths of very thin wire have real resistances. Transformers and speaker coils are good examples.

 

[Joshua_T]

Thank you both for the help, I understand this a lot better now.

So let's say that one end of a 10' wire is +12v and the other end is in the ground. The wire is single-strand insulated copper wire (Its pretty thick (8-10 gauge) so I would think that resistance is negligible). What modifications (like length, thickness, single vs multi stranded) would increase the current (and resulting wattage) going through the wire? Also, does the orientation of the wire influence anything? (vertical, horizontal, coil, etc.)

 

[TomHart]

It seems very unusual that you would want to connect +12V across a 10 foot wire. Are you sure that is correct? Or are you just using that 10-foot wire to convey the power from the +12V source to some load?

 

[Joshua_T]

It seems very unusual that you would want to connect +12V across a 10 foot wire. Are you sure that is correct? Or are you just using that 10-foot wire to convey the power from the +12V source to some load?

Well I'm asking this as more of a conceptual question. The numbers I gave are just for the hypothetical situation. Sorry if that was misleading.

 

[TomHart]

It wasn't misleading; I was just curious as to why you were asking. But depending on the capacity of the source, connecting a wire across a voltage like that can be very interesting, or even dangerous.

As an example, for work a number of years ago, we were doing a type of demo on the New York subways. In order to be allowed to walk out on the tracks, we had to take safety training. One particular slide they showed us was of a man who was bandaged up like a mummy. What happened was that he dropped a crowbar and it shorted across the third rail to ground. Due to the extremely high current capacity, the crowbar became like a fuse and exploded into molten iron. Unfortunately, the man ended up dying from his injuries.

 

[Joshua_T]

Well that's unfortunate. I'm guessing that it was the electrical resistivity of the crowbar that caused the conversion of electric energy into thermal energy, which melted the iron.

 

[TomHart]

Well that's unfortunate. I'm guessing that it was the electrical resistivity of the crowbar that caused the conversion of electric energy into thermal energy, which melted the iron.

Exactly.

 

[davenn]

Well that's unfortunate. I'm guessing that it was the electrical resistivity of the crowbar that caused the conversion of electric energy into thermal energy, which melted the iron.

and the same will happen to your 10 ft of wire if the PSU is capable of supplying enough current for the wire to fuse and melt

 

[Joshua_T]

and the same will happen to your 10 ft of wire if the PSU is capable of supplying enough current for the wire to fuse and melt

Well I'm not actually doing anything with 10' of wire or a PSU. I'm just curious as to what properties (length, thickness, wire type, orientation) of a wire in this hypothetical situation would increase the wattage flowing through it.

 

[davenn]

Well I'm not actually doing anything with 10' of wire or a PSU. I'm just curious as to what properties (length, thickness, wire type, orientation) of a wire in this hypothetical situation would increase the wattage flowing through it.

no problem, good to hear and ohhh ... wattage doesn't flow through anything. Watts is just the amount of power used / dissipated

Also, does the orientation of the wire influence anything? (vertical, horizontal, coil, etc.)

no, it doesn't affect the flow of charge ( current) nor the potential difference between the ends of the wireDave

 

[Joshua_T]

no problem, good to hear and ohhh ... wattage doesn't flow through anything. Watts is just the amount of power used / dissipated
no, it doesn't affect the flow of charge ( current) nor the potential difference between the ends of the wireDave

Thanks for the help Dave!