The resistance of an ohmic conductor

In summary, the resistance of an ohmic conductor increases with length due to more collisions, while decreasing the cross-sectional area increases resistance because it decreases current (using the formula R=V/I). Alternatively, adding length to a resistive wire is similar to adding resistors in series.
  • #1
Viona
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I know that the resistance of an ohmic conductor increases with length because the electrons going through the conductor must undergo more collisions in a longer conductor. But why decreasing the cross-sectional area of the conductor also increases the resistance of a conductor?
 
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  • #2
Think of increasing the area as having many conductors in parallel. Decreasing is the opposite.
 
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  • #3
I am not sure that your intuitive model, according to which you conclude more resistance means more collisions is entirely correct.
Formally resistance is defined as ##R=\frac{V}{I}##. Decreasing the cross sectional area decreases I and that's why R is increasing. (it is ##I=nSve## where ##S## the cross sectional area, ##n## the density of free electrons, ##v## the average drift velocity and ##e## the charge of electron.)
 
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  • #4
If you like an intuitive model, adding length to a resistive wire is the same as adding resistors in series.
 
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  • #5
Thank you, that was helpful and nice.
 
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1. What is an ohmic conductor?

An ohmic conductor is a material that follows Ohm's law, which states that the current through a conductor is directly proportional to the voltage applied across it. This means that the resistance of an ohmic conductor remains constant regardless of the voltage applied.

2. How is the resistance of an ohmic conductor calculated?

The resistance of an ohmic conductor can be calculated by dividing the voltage applied across the conductor by the current flowing through it. This is represented by the equation R = V/I, where R is resistance, V is voltage, and I is current.

3. What factors affect the resistance of an ohmic conductor?

The resistance of an ohmic conductor is affected by its length, cross-sectional area, and the material it is made of. Longer conductors have higher resistance, while wider conductors have lower resistance. Additionally, materials with higher resistivity have higher resistance.

4. Can the resistance of an ohmic conductor change?

Yes, the resistance of an ohmic conductor can change if the temperature or physical properties of the conductor change. For example, if the temperature of the conductor increases, its resistance will also increase.

5. What is the unit of measurement for resistance?

The unit of measurement for resistance is the ohm (Ω), named after the German physicist Georg Ohm. It is represented by the symbol Ω and is equal to one volt per ampere (V/A).

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