# V= IR So a circuit with no resistance has no current or voltage?

1. May 23, 2014

### jaredvert

If you had a voltage v and wanted to know current, would the current be infinity ? Do we just call it 0 because it is insignifant to find such a useless number because since there is no resistance it would be too high. I figure if r=0 then I = v/0 so infinity?

2. May 23, 2014

### phinds

In an ideal circuit, having a non-zero voltage across a short circuit would, mathematically, give you infinite current but that's a pointless exercise since it is impossible in the real world.

3. May 23, 2014

### jaredvert

Haha yeah I know but I wasn't sure. So does that mean a constant over 0 really isn't undefined? It is always infinity? Or does undefined just mean infinity?

4. May 23, 2014

### Matterwave

A number divided by 0 is undefined. It's not infinity, it's undefined.

5. May 23, 2014

### ModusPwnd

When he says "mathematically it will give you infinity" what he means is that under the real number set the limit as R approaches zero of 1/R [strike]is[/strike] approaches infinity. Not sure if you know limits or not... But saying all that is cumbersome so we just shorthand the saying to 1/0 is infinity (where there technicalities behind that are usually taken to be understood). As stated above, 1/0 is undefined. Limiting behavior can still be discussed.

Last edited: May 23, 2014
6. May 23, 2014

### Matterwave

This is not true. The limit as R approaches 0 of 1/R is undefined. Not only does it diverge, it diverges to positive infinity from the positive side and to negative infinity from the negative side. Additionally, infinity is not a real number, and so it doesn't make sense to think of the limit as approaching any real number.

If we really wanted to discuss limiting behavior, we should not say that the current approaches infinity (infinite currents don't make sense at all), but that it approaches a large number and then we expect Ohm's law to break down at some point, depending on the material.

7. May 23, 2014

### ModusPwnd

I believe that saying "approaches infinity" is generally taken to be the same as meaning "diverges" in this context (though not the other way around). I should edit my post accordingly though.

Last edited: May 23, 2014
8. May 23, 2014

### AlephZero

A zero voltage can give you a finite current in the real world: http://en.wikipedia.org/wiki/Superconductivity

But understanding that needs a bit more physics than just Ohm's law.

9. May 23, 2014

### Matterwave

I suppose for the function 1/R, you might be able to get away with it, since R is assumed positive. But I did not want OP to go away with the thinking that the function 1/x, where x can be any non zero real number, "approaches infinity" at x=0, since it diverges in two different directions. The two sided limit doesn't exist, the one sided limit doesn't exist either, but at least for the one sided limit you might be able to say something like "approaches infinity".

10. May 23, 2014

### jaredvert

Yeah I know what limits are and I understand what everyone is saying. I just finished calc bc

11. May 23, 2014

### Drakkith

Staff Emeritus
I don't think Ohm's law applies in the case of zero resistance circuits.

12. May 23, 2014

### Maxo

This made me think of something. Is it physically possible to have resistances less than 1 Ohm? And does Ohm's law still apply then?

13. May 23, 2014

### Matterwave

Of course it is. And Ohm's law will apply. You just use fractions. A short length of copper wire, for example, will have resistance much less than 1 ohm.

Another way to think about it. The Ohm, like the meter, or second, is an arbitrary unit defined by humans. It would be very weird indeed if nature cared enough about this unit to put a break down of a natural law based on a human unit of measurement!

This would be like saying "velocity=distance/time doesn't work for times less than 1 second". Huh?

14. May 23, 2014

### D H

Staff Emeritus
The title to the thread is "V= IR ... So a circuit with no resistance has no current or voltage?" This is a much better question than the question raised in the opening post. The answer to the question raised by the title is that a circuit with no resistance has zero voltage.

This essentially asks, "What happens when an ideal voltage source is applied against an ideal short circuit"? Let me reword that slightly by changing "ideal voltage source" to "unstoppable force" and "ideal short circuit" to "immovable object". The result is "What happens what an unstoppable force meets an immovable object?" Unless Zeus intervenes and turns both the unstoppable force and immovable object into stars and casts them into the heavens, the answer is "something is going to break."

AlphaZero mentioned superconductors. It's best to use a current source rather than a voltage source to establish the current flow in a superconducting magnetic. What if you use a voltage source? Something is going to break. The voltage source can fry, it can reach some breakdown current that makes it act more like a current source than a voltage source, or the induced magnetic field in the superconductor will become so high as to make the superconductor stop being a superconductor. Whatever happens, something is going to break. Truly unstoppable forces and immovable objects don't exist.

15. May 23, 2014

### BruceW

V=IR, and if R=0, this means V=0. The equation can't tell us anything about I, because R is zero.

16. May 23, 2014

### AlephZero

Sure. As the other answer said, there is nothing in definition of the Ohm that makes "1 Ohm" a special value.

You can buy resistors down to 0.01 ohms, for example http://uk.farnell.com/panasonic/erjm03nf10mv/resistor-low-r-0-01ohm-1/dp/2145282

Below 0.01 ohms, the notion of an "electronic component with a given resistance" becomes a bit vague, because the connecting wires, soldered joints, etc all have resistances that can't be ignored. For example, even the relatively thick copper wire used for house wiring has a resistance of about 0.005 ohms per meter of length.

17. May 24, 2014

### Maxo

So let's say we have a circuit with a 0.01 Ohm resistance connected to a 9 V battery. Does that mean we will have I = V/R <=> a current of I = 9/0.01 = 900 Amps? I guess in reality the circuit will just burn up, but let's say we have some super durable material, does there exist 900 Amps for some time (if only a split second) before it burns up? I mean if Ohm's law applies, it should.

18. May 24, 2014

### Matterwave

The battery cannot output 900 amps. It will simply short circuit. I'm not a battery engineer, so I don't know what exactly will happen to it.

You can try (if you have the equipment anyways) this effect with two big capacitor plates made of aluminum foil, connected to a power supply. As long as the aluminum foil is insulated from each other, the power supply will put a constant voltage across the two plate. Once you touch one plate to the other, you will see that the voltage on the power supply drops to ~0V because the power supply has been short circuited.

19. May 24, 2014

### CWatters

Indeed.

However a "9V battery" (eg a PP9) is not an ideal voltage source, it has some internal resistance that has to be added to the 0.01 ohms to calculate the maximum current. The internal resistance of a battery depends on the type of battery and it's state of charge.

Something like a 12V car battery has a very low internal resistance. If you were to accidentally drop a good conductor (like a spanner/wrench) across the terminals the battery could indeed deliver very high current, possibly enough to melt the tool or parts of the battery.

The current delivered can be high enough to weld metal although I do NOT recommend you try this because car batteries can produce hydrogen gas...

Last edited by a moderator: Sep 25, 2014
20. May 24, 2014

### phinds

As matterwave pointed out, in the real world a battery will see that low a resistance as a short circuit and cannot put out that much current. BUT ... an ideal battery absolutely has no problem with the situation.

Why do you have some believe that Ohms Law should be restricted in some way? Why would it not apply in all non-infinite situations (using ideal components)