How Does Resistance Vary with Wire Cross-Sectional Area Changes?

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SUMMARY

The discussion centers on how resistance per unit length varies in a current-carrying ohmic metal wire as its cross-sectional area decreases. It is established that while the current remains constant, the current density increases as the cross-sectional area (A) decreases, leading to a corresponding increase in the electric field. This results in a higher voltage across the wire, indicating that resistance does not remain constant but instead varies with changes in cross-sectional area.

PREREQUISITES
  • Understanding of Ohm's Law and its components (voltage, current, resistance).
  • Familiarity with the concept of current density (J = I/A).
  • Knowledge of electric fields and their relationship with current density.
  • Basic principles of conductive materials and their behavior under electrical stress.
NEXT STEPS
  • Study the relationship between current density and electric field in conductive materials.
  • Explore the mathematical derivation of resistance in varying cross-sectional areas.
  • Learn about the implications of resistance changes in practical applications, such as electrical wiring.
  • Investigate the effects of temperature on resistance in conductive materials.
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Students studying electrical engineering, physics enthusiasts, and professionals involved in electrical circuit design and analysis.

Sheneron
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Homework Statement



A current-carrying ohmic metal wire has a cross-sectional area that gradually becomes smaller. The current has the same value for each section of the wire. How does the resistance per unit length vary? Increase, decrease or constant?

Here is what I think: Since the wire is a conductor then the potential at one point will be the same as another point, so the voltage will be constant. And since the current is constant then the resistance is constant. Is that wrong?
 
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Or wait is this it:

Since the current density is proportional to the electric field and current density is defined as I/A then the as A decreases the current density will increase, which will increase the electric field which will increase the voltage.
 

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