Current through a conductor of zero resistance

In summary: What is the equivalent resistance between A and B in this case...Since the left end of R1 is shorted to the right end of R2, just rotate R1 up and over clockwise 180 degrees to put it in parallel with R2. Then do a similar thing with R3 -- rotate it clockwise 180 degrees to put in in parallel with R2. What does the diagram look like now?It was not suggested that the current was infinite !
  • #1
swap1996
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0
If a resistor shares common junctions to a conductor with no resistance in a circuit, will current flow through the resistor? Also, what is the equivalent resistance between A and B as in the figure...
 

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  • #2
If the wires were really perfect conductors with zero resistance, then there would be no voltage difference between the two ends of the resistor and therefore no current flow through the resistor.

In practice, no wire is a perfect conductor so there's always some tiny resistance and therefore some tiny voltage difference across the resistors to drive some tiny current flow through the resistor. However this current will be well and thoroughly negligible compared with the current through the wires (which will very quickly melt, burn, catch on fire, or explode if there's no fuse, internal resistance in the power supply, or some other current-limiting device).
 
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  • #3
if by the equivalent resistance you mean the total resistance it has with the junctions at both ends then the only resistance in your schematic is the one through "r2"
 
  • #4
What is the equivalent resistance between A and B in this case...
 

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  • #5
swap1996 said:
What is the equivalent resistance between A and B in this case...

Try redrawing that picture so that the resistors are side by side on your sheet of paper... You'll find that this makes the problem much easier.
 
  • #6
Nugatory said:
If the wires were really perfect conductors with zero resistance, then there would be no voltage difference between the two ends of the resistor and therefore no current flow through the resistor.

In practice, no wire is a perfect conductor so there's always some tiny resistance and therefore some tiny voltage difference across the resistors to drive some tiny current flow through the resistor. However this current will be well and thoroughly negligible compared with the current through the wires (which will very quickly melt, burn, catch on fire, or explode if there's no fuse, internal resistance in the power supply, or some other current-limiting device).

Where does superconductivity fit in this explanation? I understand that superconductors have zero resistance and currents do flow in suoerconductors
 
  • #7
Nugatory said:
Try redrawing that picture so that the resistors are side by side on your sheet of paper... You'll find that this makes the problem much easier.

Can you explain it properly, perhaps upload the diagram you are referring to...
 
  • #8
technician said:
Where does superconductivity fit in this explanation? I understand that superconductors have zero resistance and currents do flow in suoerconductors

There is always some current-limiting device in such a setup, so infinite currents are not observed. But you are right that a superconductor can behave a lot more like an ideal wire than anything you're going to be able buy in a roll and solder together.
 
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  • #9
swap1996 said:
Can you explain it properly, perhaps upload the diagram you are referring to...

Not until we've given you a few more hints... This problem is much easier than it looks... The end of every resistor in your diagram is connected directly to either point A or point B.
 
  • #10
swap1996 said:
Can you explain it properly, perhaps upload the diagram you are referring to...

Even though this is not directly homework, you still need to show some effort here...

Since the left end of R1 is shorted to the right end of R2, just rotate R1 up and over clockwise 180 degrees to put it in parallel with R2. Then do a similar thing with R3 -- rotate it clockwise 180 degrees to put in in parallel with R2. What does the diagram look like now?
 
  • #11
Nugatory said:
There is always some current-limiting device in such a setup, so infinite currents are not observed. But you are right that a superconductor can behave a lot more like an ideal wire than anything you're going to be able buy in a roll and solder together.

It was not suggested that the current was infinite !
What 'current-limiting device'do you have in mind?
 
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  • #12
technician said:
Where does superconductivity fit in this explanation? I understand that superconductors have zero resistance and currents do flow in suoerconductors

technician said:
It was not suggested that the current was infinite !
What 'current-limiting device'do you have in mind?

The maximum current that can be supported by a superconductor is limited either by the current density, or by the magnetic field generated by the current. Above those limits, the superconductor stops being a superconductor, develops some loss, and all hell breaks loose.

This paper from arxiv has some good info: http://www.google.com/url?sa=t&rct=...YReN1mhykYSVQvK0lVOkTmA&bvm=bv.46471029,d.cGE

.
 
  • #13
swap1996 said:
What is the equivalent resistance between A and B in this case...
As Crazymechanic already pointed out, the equivalent resistance between A and B is R2 .

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For the parallel portions of the circuit:

You can't use ##\displaystyle \ \frac{1}{R_\text{Parallel}}=\frac{1}{R_A}+\frac{1}{R_B} \,,\
## because one of the resistances is zero.

Instead, use ##\displaystyle \ R_\text{Parallel}=\frac{R_A\,R_B}{R_A+R_B} \ .##
 

1. What is "Current through a conductor of zero resistance"?

Current through a conductor of zero resistance refers to the flow of electricity through a material with no resistance, meaning there is no opposition to the flow of electrons.

2. Is it possible for a conductor to have zero resistance?

Yes, certain materials such as superconductors have the ability to conduct electricity with zero resistance when cooled to extremely low temperatures.

3. What are the advantages of using a conductor with zero resistance?

Conductors with zero resistance allow for a more efficient flow of electricity, resulting in less energy loss and lower operating costs. They also have the potential for faster data transmission and can be used to create powerful electromagnets.

4. What is the relationship between current and voltage in a conductor with zero resistance?

According to Ohm's law, in a conductor with zero resistance, the current and voltage are directly proportional. This means that as the voltage increases, so does the current, resulting in a constant ratio between the two.

5. Can a conductor with zero resistance overheat or catch fire?

No, since there is no resistance, there is no energy dissipated in the form of heat. This means that a conductor with zero resistance will not overheat or catch fire, making it a safer option for high-power applications.

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