Is There Really No Voltage Across an Ideal Wire According to Ohm's Law?

In summary, the textbook says that by Ohm's law, there is no voltage across an ideal wire, regardless of the current flowing through it. However, if you connect an ideal battery to the wire, you will draw an infinite current because the battery's internal resistance will drop all of the voltage.
  • #1
cepheid
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Now, this question may be incredibly stupid, but it has been bothering me nonetheless. I figure you guys can set me straight really easily. Say you have a basic circuit loop as shown in the picture.

Ohm's law:

[tex] V = RI [/tex]

Now, according to a textbook I'm reading right now, "By Ohm's law, there is no voltage across an ideal (i.e. zero-resistance) wire regardless of the current flowing through it."

I'm just wondering what the meaning of that statement is. Yeah, sure, obviously:

[tex] V = 0I = 0 [/tex]

But when I look at that picture, here's how I see it: there is definitely a potential difference between points A and B, because they are at either end of the battery. But these points are also the two ends of the wire that makes up the loop! So how could there possibly not be a potential difference across the wire?! And if there weren't, why would there be any current at all? Aren't the electrons moving from a point of high potential to low potential, gaining KE along the way? So there must be a voltage across the wire.
 

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  • #2
Have you taken into account the internal resistance of the source?
 
  • #3
Ummm. Not everything is as cut and dried as you assume. Yes, ohms law always works, but the real life components we have do things you may not expect when used outside their specs. Your drawing is somewhat of an undefined or non-permitted schematic. Kinda like dividing by zero. The wire has a near zero resistance so an IDEAL voltage source will push a very large amount of current through it. Depending on how small the wire is and how much current the voltage source can supply it can get VERY hot. Wire heats up and it's resistance goes up. Resistance goes up and the current goes down. Things will sort of stabilize. But with the average 9 volt battery you will only get a hot battery. What happens is the battery's internal resistance ends up dropping all of the voltage and you see nothing on the output terminals. Do what you have drawn with a 9 volt battery and what will happen is what I described. Do it with a car battery and you will have a glowing red hot wire in a split second. DON'T do it, take my word. The car battery has a lower internal resistance so it will supply more current. Enough current to get the wire red hot. Make sense? If not, shoot more questions out.
 
  • #4
If you connect an ideal battery (which is a perfect voltage source with no series resistance) to an ideal wire (which is a perfect conductor and has zero resistance), you'll draw an infinite current. Obviously Ohm's law is singular there, and really no longer applies. In reality, you can't have a perfect battery whose voltage never sags under load. As BoulderHead says, every real battery has some small, finite resistance effectively built into it by the nature of the chemical reactions it uses and the conductors from which they are constructed.

- Warren
 
  • #5
Understood...

Thanks for the insights. Really it's only this statement that doesn't make sense to me:

"there is no voltage across an ideal...wire"

How can there be a current in that case, let alone an infinite one?
 
  • #6
You are getting current and voltage confused. Current is a rate. It is a given number of electrons past a certain point in a given amount of time. Voltage is thought of as a type of pressure.
 
  • #7
I know the difference between current and voltage. What I'm saying is, in order for there to be a current through a wire, whether ideal or not, doesn't there have to be a potential difference between the two ends of the wire (that connect to each terminal). Wouldn't that qualify as "a voltage across the wire"?
 
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  • #8
The whole point of neglecting the voltage drop across a wire is to simplify circuit analysis. You are completely losing track of what you need to learn by obsessing on this point. When you leave the resistance out of a simple DC circuit you have nothing instructive to gain. Why not put a resistor into your circuit and get on with it.

Why are you surprised at an apparent contradiction when you incorrectly use a simplifying factor. If the wire is the only thing in the circuit you cannot neglect the wires resistance. A voltage drop across a wire can only be neglected when it is SMALL IN COMPARISON to other voltage drops in the circuit. This is NOT the case when it is the ONLY voltage drop in the circuit.
 
  • #9
Averagesupernova,
I like you explanation; as clear and simple as it is.
 

What is Ohm's Law?

Ohm's Law is a fundamental principle in physics that describes the relationship between voltage, current, and resistance in an electrical circuit. It states that the voltage across a resistor is directly proportional to the current passing through it, and the constant of proportionality is known as resistance.

How is Ohm's Law useful in circuit analysis?

Ohm's Law is useful in circuit analysis because it allows us to calculate the voltage, current, or resistance of a circuit component if we know the other two values. This helps us understand how different components affect the flow of electricity in a circuit and can be used to design and troubleshoot circuits.

What is a circuit loop?

A circuit loop, also known as a closed circuit, is a complete path for electricity to flow through in a circuit. It includes a power source, such as a battery, wires for conducting the electricity, and one or more circuit components, such as resistors, capacitors, or diodes.

How does Ohm's Law apply to a circuit loop?

Ohm's Law applies to a circuit loop by determining the voltage, current, or resistance at any point in the loop. The voltage across any component in the loop can be calculated by multiplying the current flowing through it by its resistance, according to Ohm's Law. This allows us to analyze and predict the behavior of a circuit.

What are some practical applications of Ohm's Law and a circuit loop?

Some practical applications of Ohm's Law and a circuit loop include designing and troubleshooting electronic devices, such as computers and smartphones, as well as electrical systems like power grids and lighting systems. Ohm's Law is also used in the design of electrical safety systems, such as fuses and circuit breakers, to protect against excessive currents.

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