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Wires of different diameters connected in series, why is the number density the same?

Assume they have the same length. Since they are connected in series, the rate of flow of charges(current) will be the same. So if one wire is thinner than the other, shouldn't the number density be higher? Because there is less volume, but the same flow of charges.
All replies are most appreciated!!!!:smile:
Original post by WhatNameToUse
Assume they have the same length. Since they are connected in series, the rate of flow of charges(current) will be the same. So if one wire is thinner than the other, shouldn't the number density be higher? Because there is less volume, but the same flow of charges.
All replies are most appreciated!!!!:smile:


If the wires of different diameter are connected in series then yes, the current, I, is the same through them all.
If they are of the same material, then the number of free electrons available per unit volume, n, is the same in all of them.

The formula for the current in this case is

I = nAve

where A is the cross section area and e the charge on the electrons (assuming they are the carriers here)

v is the drift velocity of the electrons

In the wires of different cross section, it is this drift velocity which will vary depending on the diameter.

In the thinner wire, they will have to drift faster to maintain the same current. (Think of a river flowing more rapidly in a narrower section)

You can also explain this by remembering that the thinner wire has a higher resistance per unit length, and thus a higher pd across unit length, giving those electrons more 'push' to move them faster.
(edited 3 years ago)
Original post by WhatNameToUse
Assume they have the same length. Since they are connected in series, the rate of flow of charges(current) will be the same. So if one wire is thinner than the other, shouldn't the number density be higher? Because there is less volume, but the same flow of charges.
All replies are most appreciated!!!!:smile:


number density is a property of the material the wires are made of... so wires of the same material have the same number density.

it's number of 'things' per unit volume so it's comparable to ordinary density which is the amount of mass per unit volume. The density of a thin copper wire is the same as the density of a thick copper wire. If both wires were the same length they'd have different masses because they have different volumes.
Original post by Stonebridge
If the wires of different diameter are connected in series then yes, the current, I, is the same through them all.
If they are of the same material, then the number of free electrons available per unit volume, n, is the same in all of them.

The formula for the current in this case is

I = nAve

where A is the cross section area and e the charge on the electrons (assuming they are the carriers here)

v is the drift velocity of the electrons

In the wires of different cross section, it is this drift velocity which will vary depending on the diameter.

In the thinner wire, they will have to drift faster to maintain the same current. (Think of a river flowing more rapidly in a narrower section)

You can also explain this by remembering that the thinner wire has a higher resistance per unit length, and thus a higher pd across unit length, giving those electrons more 'push' to move them faster.

Ahh thank you so much!
Original post by Joinedup
number density is a property of the material the wires are made of... so wires of the same material have the same number density.

Thank you so much, I wish every textbook could just be as clear as this!!:tongue:

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