A smaller cross-sectional area increases the resistance of a conductor?

In summary: Then you should SAY so in your post. Since you gave no indication of any research, it was a natural assumption that you didn't DO any. When you know something about a subject, tell us and then tell us what you don't understand about it. That gives us better focus on presenting an answer for you.
  • #1
Viona
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why smaller cross-sectional area increases the resistance of a conductor?
 
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  • #2
The answer to that question is basically Ohm's law, with some other things(Drude model of current in conductors).
Hold on while I expand my reply with more details.
 
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  • #3
@Viona, just fyi, a simple Google search would have given you the answer immediately
 
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  • #4
Well basically we can start with Ohm's law in differential form ##J=\sigma E##, then if ##S## is the cross section and ##l## the length of the conductor we will have have that the current is ##I=JS=\sigma ES##, while the voltage in the two points of the conductor is ##V=El##, and hence the resistance $$R=\frac{V}{I}=\frac{El}{\sigma ES}=\frac{1}{\sigma}\frac{l}{S}$$.

I don't know if you were lookin for something like an intuitive explanation, like with the water through a pipe analogy, if the pipe has smaller cross section then we need to apply bigger pressure difference (analogy Voltage) in its two ends in order to achieve the same volumetric flow rate (analogy current).
 
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  • #5
phinds said:
@Viona, just fyi, a simple Google search would have given you the answer immediately
I tried but the results did not convince me!
 
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  • #6
Viona said:
I tried but the results did not convince me!
What sort of explanation you would find convincing? What is your intuition behind this?
 
  • #7
What I said in post #3 hold for the DC or Quasi DC (low frequency AC) case, where we can consider the electric field ##E## to be uniform through out the conductor. If the wavelength is small enough (or equivalently frequency high enough) in comparison to the dimensions of the conductor, then the electric field ##E## varies in space and time as a wave and what I said in post #3 don't hold. More specifically in high frequencies what we have is the skin effect where the ohmic resistance is effectively increased because the current flows only in a thin surface layer (i.e. the "skin") of the conductor.
 
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  • #8
Viona said:
I tried but the results did not convince me!
Then you should SAY so in your post. Since you gave no indication of any research, it was a natural assumption that you didn't DO any. When you know something about a subject, tell us and then tell us what you don't understand about it. That gives us better focus on presenting an answer for you.
 
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FAQ: A smaller cross-sectional area increases the resistance of a conductor?

1. What is cross-sectional area?

Cross-sectional area refers to the measure of the area of a conductor when viewed from the end. In the case of a wire or a cylindrical conductor, it is the area of the circle formed by the diameter of the wire.

2. How does a smaller cross-sectional area increase resistance?

A smaller cross-sectional area means that there is less space for electrons to flow through the conductor. This results in a higher concentration of electrons and more collisions between them, leading to an increase in resistance.

3. Does the material of the conductor affect the resistance?

Yes, the material of the conductor plays a significant role in determining its resistance. Materials with higher resistivity, such as copper and aluminum, will have higher resistance compared to materials with lower resistivity, such as silver and gold.

4. How does temperature affect the resistance of a conductor?

Temperature has a direct impact on the resistance of a conductor. As the temperature increases, the atoms in the conductor vibrate more, causing more collisions with the electrons and increasing resistance. This is known as the temperature coefficient of resistance.

5. Can a smaller cross-sectional area be beneficial in any way?

Yes, a smaller cross-sectional area can be beneficial in certain situations. For example, in electronic circuits, smaller wires are used to increase the resistance and control the flow of current. Additionally, smaller cross-sectional areas can also reduce the weight and cost of the conductor.

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