Voltage and Current in Ohm's Law

[Shafia Zahin]

Hello,one thing really confuses me ,in an open circuit the value of resistance is 0 and so due to v=iR the voltage also becomes 0 but my question is how can a current flow in a circuit where there is no voltage Difference? Please help.
Shafia.

 

[EnEE]

in an open circuit the value of resistance is infinity, so voltage drop is zero(there is voltage difference) and i=0

 

[Shafia Zahin]

in an open circuit the value of resistance is infinity, so voltage drop is zero(there is voltage difference) and i=0

Oh,I am sorry I meant to say short circuit ,I have said it wrong

 

[lewando]

You are correct that a current cannot flow in a circuit where there is no voltage difference.

If you look at an ideal voltage source, short circuited by a less-than-ideal 0 Ω resistance--say 0.001 Ω, you will get a very large amount of current. Ohm's Law remains intact. The resistor might get hot or explode, but that is another subject.

If you look at a real voltage source (like a real battery), short circuited by a perfect 0 Ω resistance, you will have 0 V across the battery terminals-but some current still will flow due to internal resistance of the battery. This is equivalent to taking a perfect, ideal battery (with no internal resistance) and applying a resistance equivalent to the internal resistance of the real battery across the battery terminals.

What happens if you take an ideal voltage source and short circuit it with a perfect 0 Ω resistance? I = V/R = V/0 = ∞, which is not possible because ∞ is a concept, not a number, and because the scenario is not possible.

 

[davenn]

great response @lewando

 

[Shafia Zahin]

@lewando thank you so much for your response.Still to justify what I have understand I would like to repeat that the current in a short circuit will flow due to the internal resistance of the voltage source,isn't it?

 

[davenn]

I would like to repeat that the current in a short circuit will flow due to the internal resistance of the voltage source,isn't it?

and the small resistance of the wire causing the short circuit ... because it isn't an idea 0 Ohm
The internal resistance of the power source limits the current that can flow

 

[jim hardy]

One thousandth or one millionth of an ohm rounds off to zero. We don't very often point that out to beginners,

as Dave said we instead use "zero" as if it were ideal. That's because the resistance of a wire is usually so small compared to other circuit elements that including its small value wouldn't change results enough to notice.

One exception is in short circuit current calculations . If you look at the circuit breakers in your house panel you'll see a rating probably around ten thousand amps. At those currents the resistance of the wire is what limits the current.

 

[anorlunda]

I wish that teachers would simply say, "Any result that indicates infinite current or infinite voltage is bogus, and outside the range of Ohm's Law."

Equivalently, they could say, "Ohm's law is an approximation, linear only within a reasonable range of voltages and currents. If you get outside the reasonable range, forget ordinary circuit analysis."

Ditto for all ideal components. They are ideal only within a reasonable range of voltages and currents.

Instead, it appears that Ohm's law is being taught as an absolute truth with no boundaries.

Is that an unreasonable thing to demand of teachers?

 

[davenn]

@anorlunda

nice double post

 

[cabraham]

You are correct that a current cannot flow in a circuit where there is no voltage difference.

If you look at an ideal voltage source, short circuited by a less-than-ideal 0 Ω resistance--say 0.001 Ω, you will get a very large amount of current. Ohm's Law remains intact. The resistor might get hot or explode, but that is another subject.

If you look at a real voltage source (like a real battery), short circuited by a perfect 0 Ω resistance, you will have 0 V across the battery terminals-but some current still will flow due to internal resistance of the battery. This is equivalent to taking a perfect, ideal battery (with no internal resistance) and applying a resistance equivalent to the internal resistance of the real battery across the battery terminals.

What happens if you take an ideal voltage source and short circuit it with a perfect 0 Ω resistance? I = V/R = V/0 = ∞, which is not possible because ∞ is a concept, not a number, and because the scenario is not possible.

Actually a perfect superconducting short across a voltage source of 0 ohm internal resistance produces a current ramp. The current ramps up with time, I = Vt/L, where L is the loop inductance. Just thought it deserved to be mentioned. BR.

Claude

 

[OmCheeto]

Wouldn't the speed of light limit, also limit the current flow in a superconductor? I've never thought about it before.
Perhaps current flow in the vacuum of a CRT can be analyzed.
(pfoogle pfoogle pfoogle)
It looks like it's been discussed a couple of times.

Relativistic Currents
Relativistic effects of a current carrying wire
Is space a superconductor?

Regarding "space as a superconductor", I think I liked ZapperZ's comment the best:

"This is a perfect example of where, if you go beyond just the superficial, simplistic understanding and definition of something, you'll run into trouble if you don't have a more complete picture.

A "conductor" is actually a rather vague term. If you think about it carefully, practically EVERYTHING is a conductor, even an insulator. If you have a good-enough current detector, and if you apply a high-enough voltage, even an insulator will "conducts". ..."​

I also ran across a site that discussed how to calculate the speed of an electron in a CRT:

Electron gun and cathode rays

In their example, they claim an electron propelled by a 3000 volt potential will have a speed of about 33,000,000 m/s.
That's about 1/10 the speed of light.
I know the Pacific DC Intertie operates at 500,000 volts, so I plugged that into their equation and came up with 421,000,000 m/s.
Which seems significantly above the speed of light.

My guess is, that relativity does have a limiting effect.

 

[jim hardy]

My guess is, that relativity does have a limiting effect.

Mine too. I recall looking at it long ago , noticed they gave electron's mass as "Rest mass" , so i just assumed without really understanding that was why. Wouldn't its mass become infinite at c ?

My confidence was jostled when i first heard of Cherenkov radiation. But that one resolved okay, as my practical old reactor operations instructor pointed out speed of light in water isn't c.

old jim

 

[OmCheeto]

Mine too. I recall looking at it long ago , noticed they gave electron's mass as "Rest mass" , so i just assumed without really understanding that was why. Wouldn't its mass become infinite at c ?

That's what I've heard.

My confidence was jostled when i first heard of Cherenkov radiation. But that one resolved okay, as my practical old reactor operations instructor pointed out speed of light in water isn't c.

old jim

I unsuccessfully attempted to determine the speed of electrons based on cathode voltage yesterday. I got a far a figuring out gamma, but then got stuck. I decided it was beyond the scope of this thread, so didn't ask for assistance. It just requires a couple more days of head scratching.

 

[jim hardy]

And then there's Bremsstrahlung radiation .
Is it symmetrical ? ie decelerating electrons emit it to get rid of kinetic energy. I can relate that to di/dt of a charge that experiences a change in velocity, it must make some sort of changing magnetic field..
Do accelerating electrons also emit it ?
https://www.nde-ed.org/EducationResources/HighSchool/Radiography/bremsstrahlung_popup.htm

It comes too near the question "What is the nature of the fabric of space? " for my plebian brain.

 

[analogdesign]

Relativity does have a limiting effect of course as the energy required to sustain the acceleration goes to infinity. They deal with this issue all the times in synchrotrons.

https://en.wikipedia.org/wiki/Synchrotron_radiation

The speed of light has (almost) nothing to do with the current flow in the a superconductor. Electrons in a superconductor don't physically move much faster than in copper wire.

 

[OmCheeto]

...Electrons in a superconductor don't physically move much faster than in copper wire.

Really? hmmmm...
(google google google)

Oh my god.

per wiki; "At 60 Hz alternating current, this means that within half a cycle the electrons drift less than 0.2 μm. In other words, electrons flowing across the contact point in a switch will never actually leave the switch."

The simplest things I take for granted, and never really thought about, really freak me out sometimes.

ps. This kind of reminds me of when I posted:

ps. I did do some more calculations, and discovered that a one atom wide wire of copper, one meter long, has a theoretical resistance of 326 billion ohms, and the resistance between two adjacent atoms is 92 ohms. I thought that was interesting. Not sure if it means anything.

I didn't get an infraction for the post, so I'm thinking my maths may have been somewhat correct.

 

[analogdesign]

Well the math may be correct but a one atom wire of copper acts totally different from a practical wire so the concept of "resistance" breaks down.

Resistance is a bulk effect based on mobility of charge carriers (usually in a crystal). The resistance of a one atom wide wire makes no sense.

 

[OmCheeto]

Well the math may be correct but a one atom wire of copper acts totally different from a practical wire so the concept of "resistance" breaks down.

Resistance is a bulk effect based on mobility of charge carriers (usually in a crystal). The resistance of a one atom wide wire makes no sense.

I didn't work it out the other way, so I'll take your word for it.
It made me laugh though, as it reminded me of the ultimate of an extreme parallel-series network of resistors. Similar to the "infinite plane of resistors" problem.
Fortunately, I was not willing to do the analysis, as I'm sure my head would have exploded, and I would be dead, and not posting this.

 

[analogdesign]

I remember looking at the infinite plane of resistors puzzle years ago and didn't get very far.

I'm a working chip designer now, so I guess it isn't necessary to understand that one! haha

 

[sophiecentaur]

I just read through (most of) this thread and I have to point out that Ohm's Law has absolutely nothing to do with the way free electrons and Ions behave. The ratio of V to I in a vacuum is not a constant so you cannot imply that "Ohm's Law tells us the resistance is V/I" The ratio of V and I, in a non linear conductor cannot be called Resistance. If you really have to, you can call it 'effective Resistance or Dynamic Resistance. but I have to ask why.
Edit: I re-read this and I realize that it could be judged to be a bit an extreme 'definition'. i.e. how non ohmic can a resistor be before it is allocated a resistance 'as such'. But the confusion only goes to back up my serious objection to using the term "Ohm's Law" for R=V/I. Ohm's Law is how certain substances (metals) behave at constant temperature and not just the ratio of V to I. Sloppy teaching in the first place, I think, and it's been handed down as a religion.