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

[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?

 

[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.

 

[jaredvert]

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.

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?

 

[Matterwave]

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

 

[ModusPwnd]

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?

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.

 

[Matterwave]

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 is 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.

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.

 

[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.

 

[AlephZero]

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.

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.

 

[Matterwave]

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.

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".

 

[jaredvert]

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".

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

 

[Drakkith]

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

 

[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?

 

[Matterwave]

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?

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?

 

[D H]

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.

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?

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.

 

[BruceW]

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?

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

 

[AlephZero]

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?

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.

 

[Maxo]

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.

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.

 

[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.

 

[CWatters]

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.

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...

 

[phinds]

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.

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)

 

[stevendaryl]

It's a little bit misleading to try to imagine a battery connected in a circuit with zero resistance, because batteries themselves have an internal resistance.

If we try to imagine a voltage source with no internal resistance, possibly the best model would be a capacitor: two parallel metal plates, with opposite charges. The voltage $V$ on the capacitor is proportional to the charge $Q$ via: $Q = CV$.

Now, if you connected a capacitor to a circuit with zero resistance, then the meaning of $V = I R$ in the case where $R=0$ becomes clear: Immediately after making the connection, the voltage on the capacitor will be zero (because the charge will flow instantly from the positively charged plate to the negatively charged plate, making both become neutral).

 

[UltrafastPED]

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

Correct - Ohm's law applies to situations with that are called "Ohmic" - there is a linear relation between voltage and current that is controlled by the resistance.

Other passive linear elements can be included: capacitors and inductors along with resistance. This combination is called impedance, and Ohm's law reads V=Z*I.

 

[nsaspook]

A battery is a hybrid. It's not a pure voltage or current source. The internal resistance is a factor of the electrochemical reaction so it's not purely electronic and Ohmic in the way it supplies voltage and current. The voltage output is fairly stable as long as the cell can maintain equilibrium due to the charge separation of the redox at the rate of current but if you exceed that rate the output voltage will fall and cell reactions will increase as it tries to rebalanced it's charge separation turning the battery into a current source that can supply very large amounts of current into a short causing conductors to literally explode from heat and the intense magnetic field if the battery doesn't explode first as it's internal heating makes the reactions even more intense.

 

[enorbet]

Ohms Law describes a relationship between the elements of an electronic circuit in the real world, primarily at STP. If you were somehow to create a power source capable of sustaining 900 amps into 0.01 Ohms it would be useless for anything but an 8.1KW heater. As it is commonly the resistance in a circuit that does useful work, 0.01 Ohms is what makes it expensive and therefore useless. I can think of nothing, at room temperature, that can utilize 0.01 Ohms. It would be far easier and more useful to do the same job with, say, 0.1 Ohm device and drop current to 90 Amps, or better, 1 Ohm and 9 Amps. See? Relationships. Aside from the purely theoretical, Ohms Law is superbly useful in the design of efficient systems factored by work required and strength of materials.

Incidentally one can buy commercial resistors that measure below 1 Ohm. I have seen 0.27 Ohm resistors in commercial equipment.

 

[nsaspook]

If you were somehow to create a power source capable of sustaining 900 amps into 0.01 Ohms it would be useless for anything but an 8.1KW heater. As it is commonly the resistance in a circuit that does useful work, 0.01 Ohms is what makes it expensive and therefore useless. I can think of nothing, at room temperature, that can utilize 0.01 Ohms.

I have 10kW power supplies with 6/0 cables for several ton beam analyzer magnets with fractional ohm values that can easily generate 1T plus fields for ions at 90kev. Resistors that low are not something commonly seen in consumer electronics but that we have banks of resistors in that range for dumping energy from large DC motor driven processing disks that spin at high speed when we need to stop them quickly.

 

[enorbet]

I have 10kW power supplies with 6/0 cables for several ton beam analyzer magnets with fractional ohm values that can easily generate 1T plus fields for ions at 90kev. Resistors that low are not something commonly seen in consumer electronics but that we have banks of resistors in that range for dumping energy from large DC motor driven processing disks that spin at high speed when we need to stop them quickly.

This is extremely interesting but also puzzling. How is it that in a real world circuit, a resistance of 0.01 Ohms is not the lesser of the resistance of the connecting wire? Even #1AWG Oxygen Free Copper has a resistance of roughly 0.1 ohms per 1000 feet... or are we talking about extremely heavy gauges and extremely short runs?

 

[nsaspook]

This is extremely interesting but also puzzling. How is it that in a real world circuit, a resistance of 0.01 Ohms is not the lesser of the resistance of the connecting wire? Even #1AWG Oxygen Free Copper has a resistance of roughly 0.1 ohms per 1000 feet... or are we talking about extremely heavy gauges and extremely short runs?

This is typical of the magnet interconnect cables with stacked parallel cores. The small one is a 4/0 cable. Yes, it's a short run (~10 foot loop) with big cables.
https://flic.kr/p/7RTdjF

Magnet on a typical 'small' low current machine. A gauss probe feedback loop is used to control the power supply.
http://images.caeonline.com/im.php?id=180248

 

[enorbet]

Thank you nsaspook. You certainly get to work with some serious "iron".

 

[Maxo]

nsaspook your pictures look interesting, I just wish I understood what they are. ;) Did you explain it in some other thread maybe?

 

[nsaspook]

Thank you nsaspook. You certainly get to work with some serious "iron".

The things I play with are nothing compared to the research class machines the scientists on this forum use. Our highest energy machine at 3mev is only a injector stage for those guys.