hello forum,
just a simple question about power dissipation and resistors:

If a conductor has infinite conductivity (zero resistivity) then the voltage across it is zero, so by the formula P= I^2 R, it dissipates zero power as heat. Imagine connecting wires.

but if I use the formula P=V^2/R, would I get an indeterminate form: 0/0 since V=0 and R=0 ?

In a simple circuit, if the load is meant to generate a lot of heat (for heating or cooking) , do we want the wires to be very conducting and dissipate almost no heat (small wire gauge), but do we want the load resistor to be large or small?

IF the voltage is constant, it appears that we would need a small load resistor R_L, according to the I^2 R, so more current goes out ( and current is at the 2nd power).If the resistance were too big, little current would go out, and little power dissipated.

It seems that the more the resistance, the less the ohmic loss... something wrong here..

If two resistors are in series (same current) then the bigger resistor dissipates more heat. If they are in parallel, the smaller resistor makes more heat.

In the case of a fixed voltage, I guess we want to match the heater resistor to the internal resistor of the voltage source. That gives maximum power transfer and therefore dissipation.

But what if, in some "ideal" case, I had perfectly conducting wires and a perfect battery ( no internal resistance). Would I choose a large or a small resistance for the heater in order to generate the max heat? The voltage would be all across the resistor, no matter if it is small or large. The smaller the resistor the higher the current, the more power.
But there is a threshold. How small can the resistance be ?
If there resistance is too small, then no power is dissipated across it, since there is voltage drop either...

thanks
antennaboy

 

If a conductor has infinite conductivity (zero resistivity) then the voltage across it is zero, so by the formula P= I^2 R, it dissipates zero power as heat. Imagine connecting wires.

All we can do is imagine zero resistivity conductors. If you could actually make a conductor of zero resistance that were infinitely strong one molecule in diameter, it would carry all of the electrical power in the universe with headroom to spare.

but if I use the formula P=V^2/R, would I get an indeterminate form: 0/0 since V=0 and R=0 ?

This guy managed to successfully divide by zero, but it created a time and space warp through his house:

In a simple circuit, if the load is meant to generate a lot of heat (for heating or cooking) , do we want the wires to be very conducting and dissipate almost no heat (small wire gauge), but do we want the load resistor to be large or small?

Perfect conductors to the heating element, perfectly stable voltage supply, and a load of a resistance to develop the desired amount of heat. Under these conditions, the lower the resistance, the greater the heat dissipation. It could be a very low value of resistance, which would generate an extreme amount of heat.

IF the voltage is constant, it appears that we would need a small load resistor R_L, according to the I^2 R, so more current goes out ( and current is at the 2nd power).If the resistance were too big, little current would go out, and little power dissipated.

If the resistance were large, less current would pass through the resistance and result in less power dissipation as heat.

It seems that the more the resistance, the less the ohmic loss... something wrong here..

Nothing wrong.

If two resistors are in series (same current) then the bigger resistor dissipates more heat. If they are in parallel, the smaller resistor makes more heat.

In the case of a fixed voltage, I guess we want to match the heater resistor to the internal resistor of the voltage source. That gives maximum power transfer and therefore dissipation.

If you want equal heat dissipation in the power source and the load, then I suppose so. However, power dissipation in the voltage source is generally considered an un-good thing, as it typically degrades the efficiency of the power source and results in a good deal of waste heat.

But what if, in some "ideal" case, I had perfectly conducting wires and a perfect battery ( no internal resistance). Would I choose a large or a small resistance for the heater in order to generate the max heat? The voltage would be all across the resistor, no matter if it is small or large. The smaller the resistor the higher the current, the more power.
But there is a threshold. How small can the resistance be ?
If there resistance is too small, then no power is dissipated across it, since there is voltage drop either...

If you had an imaginary power source with an internal resistance of 0 Ohms capable of producing a constant 1v output, with wires of zero resistance, connected to a load that measured 1.0e-10000 Ohms, you would have power dissipation in the load of 1.0e+10000 Watts.

However, I wouldn't want to be within a trillion miles of it when you hit the switch.

 

This reminds me of why I don't spend a whole lot of time on truly "ideal components"!!! ;o)
ALL real world devices, wires, etc. have resistance (and capacitance, inductance, too!). Superconductors come close to zero, but not quite. The 'ideal models' are to help simplify design and are don't exist in reality. If they're taken too far, you end up contorting the mind and confusing yourself.

We're fortunate things in physics are as they are....that little bit o' resistance in a wire run, etc. Keeps things in balance and prevents infinite current - it just allows enough to flow to burn the thing out and make you have to think about WHY )

 

Actually superconductors are zero ohms, it is part of the definition and is a quantum property. Their current limit is set by their magnetic tolerance, exceed a certain number of Tesla and they aren't superconducting any more. I remember a class of conductors that fits Mikes description, Low Resistance Conductors, but haven't been able to find any links for it, it was something a text book threw at us in college.

Zero ohms does exist, other variables control the amount of current it can handle. The current (no pun intended) goal is something that does it at room temperature. Right now it is only slightly above liquid nitrogen.

 

My point exactly...the practical world and theoretical world are 2 entirely different things. 1 is reality, 1 is not. There is no practical superconductor other than experimental devices in labs.....YET. There will be; then we can talk about zero ohms, and see it in action!! )

I am willing to bet that other quantum effects will be noticed once we put superconducting into practice, leading to other 'parasitics' we'll have to consider during design. Everything has ramifications! No free lunches, boys and girls! lol

 

I indulged our OP in a purely theoretical discussion, with a bit of humor thrown in.

When you're talking real-world stuff, it keeps us out of trouble (more or less) - or tells us where the problems are.

Even in theory, there are limits. You cannot have an infinitely small diameter conductor, as a molecule has to have a diameter to keep the valence electrons circling the proton mass. If you approach absolute zero, and the nucleus collapses, then you change the structure of the molecule - I am quite uncertain as to what happens at that point, as are most of us.

If superconduction ever becomes practical, things will become interesting indeed.

Anyeay, let's put this thread to bed. Purely theoretical discussions can be interesting, but we have lots of folks that need help.

 

Too broad of a subject "Quantum Physics" in another words "Neutrinos" is a very good example of energy flowing throw space (Universe). What is the perfect conductor?

 

My point exactly...the practical world and theoretical world are 2 entirely different things. 1 is reality, 1 is not. There is no practical superconductor other than experimental devices in labs.....YET. There will be; then we can talk about zero ohms, and see it in action!! )

I am willing to bet that other quantum effects will be noticed once we put superconducting into practice, leading to other 'parasitics' we'll have to consider during design. Everything has ramifications! No free lunches, boys and girls! lol

Superconductors exist, they are in use for many industrial and medical equipment thanks to the "high" temperature types using liquid nitrogen. These are not experimental applications. Not common, but practical.

You want to see it in action it is within the home budget, you can buy samples and liquid nitrogen. While not in common use, they exist.

You stated

Superconductors come close to zero, but not quite.

This is incorrect.

 

I've just found a tech article from 2001 mentioning the possibility of MRI machines using high temperature superconductors rather than low temperature.

The first commercial MRI machines were built in the early to mid 1980s.

Superconductors have been in practical real-world use for many, many years.

 

OK, OK, I give! There ARE superconductors in practical use! I'm going to build an MXR Distortion + for my guitar with one, LOL. Just as soon as I get together 5 million dollars.

I merely was pointing out that if resistance goes to zero, all of the 'normal' equations governing electronics fall apart. It's unlikely that many people will ever see 'zero resistance'; possibly EXTREMELY SMALL resistance such as short wire lengths, but not zero. Maybe quantum mechanics takes over there, I don't know. My background is not in mathematics, it's in the field, hands-on. That's why I come here; to integrate a little of the theory (to understand more). So I told the OP to disregard a zero resistance, because, unless you're going very high-level, the condition will not exist for you. And if you are, you will re-learn how to deal with zero when you get to that plateau. )

 

Thing is, room temperature superconductors could happen at any time. There is intense research on this subject, and it isn't a natural law that they have to be cold to work. It is obvious why it is such a big deal, first person/company that succeeds is Microsoft all over again.

None of the normal equations fall apart, we just have to add some new ones to cover the failure modes, such as magnetic fields being too high. I remember a company experimenting with superconducting wire, they used copper as insulation around a core of extremely thin ceramic. They had some success, but since it isn't commercially available I'm betting they ran into some snags they couldn't solve. The wire was going to be used in superconducting motors.

Other real effects that exist at really cold temperatures.

Super viscosity - materials that have 0 viscosity. They tend to climb out of the containers holding them.

Super Thermal Conductivity - Since electrical and thermal conductivity are often linked there is some hope that a room temperature superconductor might do both. Imagine a hyper efficient thermal transfer system with no moving parts.

Super conducting equivalents to MOSFETs. Josephson Junctions already exist.

This is a subject I've been following with a lot of interest.