# Current in a circuit

• B
If we measure the voltage in a simple series circuit to be 5v and the resistance to be 10 ohms. The current given is .5A. Is this the amount of chage traveling from the first point to the second point per unit time, or is it the amount of charge flowing through a cross section of the conductor between those two points?

russ_watters
Mentor
Both.

This is very similar to what you asked a few days ago.

• FS98
anorlunda
Staff Emeritus
Ampere of current is defined as one coulomb of charge per second. That is what you calculated using Ohm's Law.

Current density is the electric current per unit area of cross section.

• FS98
Both.

This is very similar to what you asked a few days ago.
How can it be both? If there was a certain finite amount of charge flowing through the cross section of a wire wouldn’t the amount of charge flowing through a point on that cross section have to be nearly 0?

Also sorry for the similar post, I realized that I was still a bit confused on this topic and it felt like the earlier post was too old to revisit given the slight differences between them.

Dale
Mentor
2020 Award
If we measure the voltage in a simple series circuit to be 5v and the resistance to be 10 ohms. The current given is .5A. Is this the amount of chage traveling from the first point to the second point per unit time, or is it the amount of charge flowing through a cross section of the conductor between those two points?
I think you have a little confusion. The voltage is defined between two points, the current is defined at a single point*. The current at a point is the amount of charge that flows past that point in a unit time.

In a series circuit the current is the same at all points. But the definition of current doesn’t require looking at multiple points. There should be no “two points” here.

*technically it is at a cross section through the conductor, but the geometry is neglected in circuit theory

• sophiecentaur and FS98
I think you have a little confusion. The voltage is defined between two points, the current is defined at a single point*. The current at a point is the amount of charge that flows past that point in a unit time.

In a series circuit the current is the same at all points. But the definition of current doesn’t require looking at multiple points. There should be no “two points” here.

*technically it is at a cross section through the conductor, but the geometry is neglected in circuit theory
But if the amount of charge flowing through a given point per unit time was .5A, wouldn’t the amount of charge flowing through a cross section be infinite because there are an infinite number of points on the cross section?

russ_watters
Mentor
How can it be both? If there was a certain finite amount of charge flowing through the cross section of a wire wouldn’t the amount of charge flowing through a point on that cross section have to be nearly 0?
You didn't ask anything about a point on the cross section, unless you're not understanding the way you used the word "point".

For basic circuit analysis, a wire is one dimensional. It doesn't have a cross section, so a "point" is the entire wire at the one location. if you want the wires to be three dimensional, then the cross section is a slice, not a point. You seem to be mixing and matching, but I dont even understand what these questions are for.

anorlunda
Staff Emeritus
But if the amount of charge flowing through a given point per unit time was .5A, wouldn’t the amount of charge flowing through a cross section be infinite because there are an infinite number of points on the cross section?
You shouldn't use those meanings of point those ways. Length is Length, area is area, the description that they are made of an infinite number of points is not useful.

russ_watters
Mentor
But if the amount of charge flowing through a given point per unit time was .5A, wouldn’t the amount of charge flowing through a cross section be infinite because there are an infinite number of points on the cross section?
No. You're definitely mixing and matching two different geometries. See my above post.

sophiecentaur
Gold Member
2020 Award
But if the amount of charge flowing through a given point per unit time was .5A, wouldn’t the amount of charge flowing through a cross section be infinite because there are an infinite number of points on the cross section?
If someone tells you there are ten cars an hour passing along a section of road, you don't have to know which lane they are using. It would be a good idea for you just to go along with the notation and the definitions as they are used by millions of people. You will find that it works very well in most cases. Time enough to go into the details when you have got the basics.

• jbriggs444, berkeman and russ_watters
russ_watters
Mentor
If someone tells you there are ten cars an hour passing along a section of road, you don't have to know which lane they are using.
Good analogy. For a basic circuit analysis, you aren't given a wire size (number of lanes) because it doesn't matter.

But if the amount of charge flowing through a given point per unit time was .5A, wouldn’t the amount of charge flowing through a cross section be infinite because there are an infinite number of points on the cross section?
Current is charge per second. A point is a measure of size, area, volume, length.

The current you measure as being 0.5 amperes is the same wherever in the wire you measure it, irrespective of the dimensions of the wire conductor.

The current you measure as being 0.5 amperes is the same wherever in the wire you measure it, irrespective of the dimensions of the wire conductor.
Exactly. Spatial dimensions have nothing to do with it.

Well, actually, you're not measuring at any point. You're measuring all of the cross-section.

If we measure the voltage in a simple series circuit to be 5v and the resistance to be 10 ohms. The current given is .5A. Is this the amount of chage traveling from the first point to the second point per unit time, or is it the amount of charge flowing through a cross section of the conductor between those two points?
"If Is this the amount of chage traveling from the first point to the second point per unit time, or is it the amount of charge flowing through a cross section of the conductor between those two points"

Both are wrong.

sophiecentaur
Gold Member
2020 Award
Being too concerned about the actual route taken by the current is not advisable when you consider that Alternating Current only travels near the surface of a conductor due to the skin effect. Current distribution over the cross section of a conductor can be highly relevant but you have to get skilled at regular circuit theory before straying into that. It's a big step to get into Maxwell's Equations.

If we measure the voltage in a simple series circuit to be 5v and the resistance to be 10 ohms. The current given is .5A. Is this the amount of chage traveling from the first point to the second point per unit time, or is it the amount of charge flowing through a cross section of the conductor between those two points?
Okay, so, it is the total charge flowing through a boundary per unit time. It doesn't matter how big or small the area is. And, there is no real thing as a point. You're basically confusing math with engineering.

"First point to a second point" is an abstract mathematical concept that doesn't exist.

All wires have a cross section larger that a line. It doesn't matter how big the cross section is in measuring current. Current isn't in units of area.

Current density is in Coulomb's per second per meter squared (C/m*s). Current density is across an abstract boundary of zero area.

What is current in a stream? Is it between two points of the stream or through a cross section? It is liters per second. It doesn't matter how deep or wide the stream is. Current doesn't account for the width of the stream, only the total volume per unit time.

The language in physics is very strict. If you say "cross section", you are including area. If you say, "through a point", you are talking about current density, not current.

Current is Joules per second. That is over whatever size cross-section that the physical wire is. There are no units of area

Current density is in Joules/(s*m^2). It is dependent in how thick the wire is. It is a theoretical measure that can only be calculated. It is "in the limit" as diameter goes to zero.

In circuit analysis, the wire is taken as infinitely thin. Wire diameter only comes in when actually specifying what wire size the purchasing agent should buy. Then, the wire rating becomes important. For the identical current, a thin wire will melt. Bit that also depends on the type of material.

So, you gotta get that "current" has nothing to do with physical dimensions. It is through whatever cross section size you mean, from a theoretical point to the width of a lightning bolt.

Good analogy. For a basic circuit analysis, you aren't given a wire size (number of lanes) because it doesn't matter.
Now we're getting down to it.

• russ_watters
sophiecentaur
Gold Member
2020 Award
What is current in a stream? Is it between two points of the stream or through a cross section? It is liters per second. It doesn't matter how deep or wide the stream is. Current doesn't account for the width of the stream, only the total volume per unit time.
Terms like flux or volumetric flow or flux density come in here and they apply to many different 'flowing' quantities.

Okay, so, it is the total charge flowing through a boundary per unit time. It doesn't matter how big or small the area is. And, there is no real thing as a point. You're basically confusing math with engineering.

"First point to a second point" is an abstract mathematical concept that doesn't exist.

All wires have a cross section larger that a line. It doesn't matter how big the cross section is in measuring current. Current isn't in units of area.

Current density is in Coulomb's per second per meter squared (C/m*s). Current density is across an abstract boundary of zero area.

What is current in a stream? Is it between two points of the stream or through a cross section? It is liters per second. It doesn't matter how deep or wide the stream is. Current doesn't account for the width of the stream, only the total volume per unit time.

The language in physics is very strict. If you say "cross section", you are including area. If you say, "through a point", you are talking about current density, not current.

Current is Joules per second. That is over whatever size cross-section that the physical wire is. There are no units of area

Current density is in Joules/(s*m^2). It is dependent in how thick the wire is. It is a theoretical measure that can only be calculated. It is "in the limit" as diameter goes to zero.

In circuit analysis, the wire is taken as infinitely thin. Wire diameter only comes in when actually specifying what wire size the purchasing agent should buy. Then, the wire rating becomes important. For the identical current, a thin wire will melt. Bit that also depends on the type of material.

So, you gotta get that "current" has nothing to do with physical dimensions. It is through whatever cross section size you mean, from a theoretical point to the width of a lightning bolt.
Is voltage always measured between theoretical points?

Also, if the physical dimensions of the wire don’t matter when finding this sort of thing, why are wires treated as infinityley thin in circuit analysis? I would think that there wouldn’t be a size assigned if it was trivial.

jbriggs444
Homework Helper
Is voltage always measured between theoretical points?
Are you asking about drawings of circuits or about real circuits? In real circuits you clamp the alligator clips on a piece of wire. In drawings, you select a node. A node is not the same thing as a point, though you can call it one if you like.

Also, if the physical dimensions of the wire don’t matter when finding this sort of thing, why are wires treated as infinityley thin in circuit analysis? I would think that there wouldn’t be a size assigned if it was trivial.
In circuit analysis, wires are not treated as having a size at all, infinitely thin or otherwise. They are nothing more than connections between nodes and circuit elements.

• FS98
Are you asking about drawings of circuits or about real circuits? In real circuits you clamp the alligator clips on a piece of wire. In drawings, you select a node. A node is not the same thing as a point, though you can call it one if you like.

In circuit analysis, wires are not treated as having a size at all, infinitely thin or otherwise. They are nothing more than connections between nodes and circuit elements.
Just in general when we talk about voltage in ohms law. Can it be between points or between non-points?

What is voltage if we’re not referring to single points? I’ve understood voltage to be a difference in electrical potential between two points.

berkeman
Mentor
Just in general when we talk about voltage in ohms law. Can it be between points or between non-points?
What is voltage if we’re not referring to single points? I’ve understood voltage to be a difference in electrical potential between two points.
It's between equipotential surfaces. "Points" could only be used if you are talking about thin wires, where the surface area of the wire can be approximate by a "point" on the wire.

Why are you being so obtuse and argumentative?

• sophiecentaur
Dale
Mentor
2020 Award
But if the amount of charge flowing through a given point per unit time was .5A, wouldn’t the amount of charge flowing through a cross section be infinite because there are an infinite number of points on the cross section?
There is no geometry in circuit theory. Neither the cross section nor the length matter. All that matters is its voltage and the current through it. So when I say “point” I am not referring to a 0 dimensional geometric object, there is no geometry in circuit theory.

A “point” in this context is a connection between two circuit elements. Thus “The current at a point is the amount of charge that flows past that point in a unit time” refers to the amount of charge flowing across the connection between two circuit elements.

• FS98 and sophiecentaur