Understanding Fundamental Concepts

[Raybert]

If we have a circuit with one resistor in series with a voltage source like given in the link then at all points before the resistor the voltage is the same, and after the resistor the voltage at all points along the wire is the same, as there is no potential difference between two points before the resistor how does current flow?

http://imageshack.us/photo/my-images/683/capturecsg.jpg/

Two contradictory statements are confusing me in answering my question may be helpful in explaining the concepts to me.

In a short circuit (no potential difference anywhere along the wire current flows)
To have current flow we must first have a potential difference

 

[phyzguy]

It's not true that the potential at all points along the wire is the same, otherwise no current would flow, as you said. However, the wire is such a good conductor that the potential difference between different points along the wire is extremely small, so we usually make the approximation that all points along the wire are at the same potential. Let's put in some numbers. Say we have a a 1.5V battery and a 100 Ohm resistor. A typical wire has a resistance of say 10 micro-ohms. So the total resistance of the circuit is 100 ohms + 20 micro-ohms, which is very close to 100 ohms. So the current in the circuit is approximately 1.5V/100 ohms = 15 mA. So the voltage drop across the wire is 15 mA * 10 micro-ohms = 150 nanovolts = 1.5E-7 V. This is so close to zero that we usually just ignore it.

 

[Jiggy-Ninja]

From a mathematical modelling perspective, there is no issue. The wire is usually assumed to be 0 ohms of resistance. This means it will have 0 V dropped across it. according to Ohm's law (I = V/R), Current = 0/0.

One of the odd things in calculus is that 0/0 is called an indeterminate form, meaning that it actually can give you a correct, finite answer.

If the terminals are shorted, practical wires have a very small resistance, so a very, very large current will be drawn, if the battery can handle it.

In an ideal model, where the short is considered 0 ohms, it would draw infinite current. infinity * 0 is another one of those indeterminate forms.

 

[Jiggy-Ninja]

From a mathematical modelling perspective, there is no issue. The wire is usually assumed to be 0 ohms of resistance. This means it will have 0 V dropped across it. according to Ohm's law (I = V/R), Current = 0/0.

One of the odd things in calculus is that 0/0 is called an indeterminate form, meaning that it actually can give you a correct, finite answer.

If the terminals are shorted, practical wires have a very small resistance, so a very, very large current will be drawn, if the battery can handle it.

In an ideal model, where the short is considered 0 ohms, it would draw infinite current. infinity * 0 is another one of those indeterminate forms.

 

[Raybert]

No potential difference - no current flow. However in a short circuit the potential should be the same at all points however due to the finite resistance of the wire there is a potential difference and hence current flow, on the other hand if we tied to points in a circuit down to the same potential (say tying both the inputs of an op-amp togother), then as there is no potential difference no current flow. Am I right?

 

[cabraham]

If we have a circuit with one resistor in series with a voltage source like given in the link then at all points before the resistor the voltage is the same, and after the resistor the voltage at all points along the wire is the same, as there is no potential difference between two points before the resistor how does current flow?

http://imageshack.us/photo/my-images/683/capturecsg.jpg/

Two contradictory statements are confusing me in answering my question may be helpful in explaining the concepts to me.

In a short circuit (no potential difference anywhere along the wire current flows)
To have current flow we must first have a potential difference

No. In a superconductor, sc, large currents can flow w/o a potential difference across the ends of the sc. Somewhere in the circuit, there's a battery or generator producing current & voltage, but a perfect conductor passes current w/ zero voltage drop. Did this help?

Claude

 

[Raybert]

No. In a superconductor, sc, large currents can flow w/o a potential difference across the ends of the sc. Somewhere in the circuit, there's a battery or generator producing current & voltage, but a perfect conductor passes current w/ zero voltage drop. Did this help?

Claude

Wasn't really thinking that far into it, was just thinking about a basic circuit I could build without going into the effects of Quantam Mechanics but thanks away.

So say the current comes out of the end of the resistor as the voltage is the same at all points after there (say it is 0V) why does the current continue to flow? Is it because there is a potential difference but its too small to worry about.

 

[Jiggy-Ninja]

Potential difference is necessary to start the current flowing. It is not strictly necessary to keep it going, at least in ideal conditions (or superconductors).

To draw an analogy with Newtonian mechanics: An object at rest will remain at rest unless acted on by an unbalanced force. An object in motion will maintain constant velocity unless acted on by an unbalanced force.

In the practical world, nothing follows Newton's laws exactly. You need to keep pushing something in order to keep it moving, because friction will slow it down. If there was no friction though, you would only need force to get the object moving, and it would coast on its own.

Moving to electric circuits: velocity is analogous to current, voltage is analogous to force, inertia (mass) is analogous the the self-inductance of the wire, and force of friction is analogous to resistance.

Take a wire with absolutely no resistance. If you apply a constant voltage across it, the current will rise in a linear ramp, the "acceleration" of the ramp being proportional to the voltage an inversely proportional to the self-inductance (just like Newton's 2nd law). Most wires have very small inductance, so the ramp will be quite sharp.

Remove the voltage source, and as long as the loop stays closed, without resistance to dissipate any energy, the current will "coast" at its current level, just like an object will coast at constant speed without friction.

Add resistance to the wire, even just a small amount, and the current will not be able to remain constant on its own; it will slow down due to the resistance's "friction". You will need to apply a constant voltage in order to keep the current constant.

Does that help any?

 

[es1]

The definition of short circuit given, "no potential difference anywhere along the wire current flows," is not correct.

I would use Wikipedia's. Seems pretty good to me.

http://en.wikipedia.org/wiki/Short_circuit
"A short circuit is an abnormal low-resistance connection between two nodes of an electrical circuit that are meant to be at different voltages."

abnormal low-resistance connection, but not zero ohm.

So say the current comes out of the end of the resistor as the voltage is the same at all points after there (say it is 0V) why does the current continue to flow? Is it because there is a potential difference but its too small to worry about.

Yes, this is right. Another way to phrase it is there is an intrinsic resistance in the wire, but it's to small to worry about. On the off chance that you are worried about it (say for example you are trying to size the wire for the current so it doesn't burn out) there are ways to determine it.

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

 

[cabraham]

Potential difference is necessary to start the current flowing. It is not strictly necessary to keep it going, at least in ideal conditions (or superconductors).

To draw an analogy with Newtonian mechanics: An object at rest will remain at rest unless acted on by an unbalanced force. An object in motion will maintain constant velocity unless acted on by an unbalanced force.

In the practical world, nothing follows Newton's laws exactly. You need to keep pushing something in order to keep it moving, because friction will slow it down. If there was no friction though, you would only need force to get the object moving, and it would coast on its own.

Moving to electric circuits: velocity is analogous to current, voltage is analogous to force, inertia (mass) is analogous the the self-inductance of the wire, and force of friction is analogous to resistance.

Take a wire with absolutely no resistance. If you apply a constant voltage across it, the current will rise in a linear ramp, the "acceleration" of the ramp being proportional to the voltage an inversely proportional to the self-inductance (just like Newton's 2nd law). Most wires have very small inductance, so the ramp will be quite sharp.

Remove the voltage source, and as long as the loop stays closed, without resistance to dissipate any energy, the current will "coast" at its current level, just like an object will coast at constant speed without friction.

Add resistance to the wire, even just a small amount, and the current will not be able to remain constant on its own; it will slow down due to the resistance's "friction". You will need to apply a constant voltage in order to keep the current constant.

Does that help any?

Actually, current can start w/o a potential difference. Take a photodiode illuminated w/ light. Photons incident on the surface impart energy to valence electrons, & they transition into the conduction band. Then a depletion layer forms & a voltage develops across the junction. In this case light energy gave rise to a current followed by a voltage. There are other examples as well.

If you reread the OP, they asked that how current can exist w/o a potential difference, PD. They were implying steady state conditions, not start up. I explained that a SC can sustain current indefinitely w/o a PD. My answer was aimed towards the OP specific conditions stated.

In many cases, some type of power source must be connected to a closed loop in order for current to start. But not always. Optical excitation is very common today. Photodiodes, phototransistors, & opto-couplers are everywhere.

I believe I answered the OP question correctly. One can always add more, but the OP stated the conditions of the problem, & I addressed those specific conditions.

Claude

 

[Jiggy-Ninja]

Actually, current can start w/o a potential difference. Take a photodiode illuminated w/ light. Photons incident on the surface impart energy to valence electrons, & they transition into the conduction band. Then a depletion layer forms & a voltage develops across the junction. In this case light energy gave rise to a current followed by a voltage. There are other examples as well.

There's still power entering the circuit from somewhere. I can't quite see how that's supposed to refute my example. However, I don't know all that much about the Photoelectric effect though.

If you reread the OP, they asked that how current can exist w/o a potential difference, PD. They were implying steady state conditions, not start up. I explained that a SC can sustain current indefinitely w/o a PD. My answer was aimed towards the OP specific conditions stated.

I know what the OP says. He wasn't asking about start-up, but I was making an analogy, and used start-up conditions to help explain that analogy.

In many cases, some type of power source must be connected to a closed loop in order for current to start. But not always. Optical excitation is very common today. Photodiodes, phototransistors, & opto-couplers are everywhere.

Photoelectric effect is a power source. Again, I don't see how that's supposed to refute my example.

I believe I answered the OP question correctly. One can always add more, but the OP stated the conditions of the problem, & I addressed those specific conditions.

You answered, the question, but didn't explain it at all.

 

[cabraham]

If we have a circuit with one resistor in series with a voltage source like given in the link then at all points before the resistor the voltage is the same, and after the resistor the voltage at all points along the wire is the same, as there is no potential difference between two points before the resistor how does current flow?

http://imageshack.us/photo/my-images/683/capturecsg.jpg/

Two contradictory statements are confusing me in answering my question may be helpful in explaining the concepts to me.

In a short circuit (no potential difference anywhere along the wire current flows)
To have current flow we must first have a potential difference

There is a PD across the resistor. To have current in the non-zero resistor cannot happen w/o non-zero PD. But again, current in the short does not produce a voltage drop if the resistance is zero. No contradiction here.

The current in the superconductor incurs no losses due to inelastic collisions. Electrons in the wire tranfer energy w/o loss. But when they reach the resistor, electrons incur inelastic collisions w/ lattice ions, resulting in energy loss. The lost energy is radiated in the form of photons in the infrared range. Heat is emitted from the resistor.

In addition at the boundary between the super-conductor & resistor there is a charge distribution. An electron reaching the resistor encounters an E field due to these charges. Inside the SC however, there is no E field since J = sigma*E, & sigma is infinite. Ohm's law covers this problem well.

When materials of differing resistances ae connected across a source, the PD across each element varies w/ resistance. In the case of SC wires & a single resistor, all the source PD appears across the resistance, & none across the SC wires.

Claude