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

[Viona]

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

 

[Delta2]

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.

 

[phinds]

@Viona, just fyi, a simple Google search would have given you the answer immediately

 

[Delta2]

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).

 

[Viona]

@Viona, just fyi, a simple Google search would have given you the answer immediately

I tried but the results did not convince me!

 

[Delta2]

I tried but the results did not convince me!

What sort of explanation you would find convincing? What is your intuition behind this?

 

[Delta2]

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.

 

[phinds]

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.