A long wire contains more metal ions for electrons to collide with compared to a short wire, so its resistance is... what?higherlowerthe same

Understanding Resistance in Wires

1. Break Down the Problem
   To determine how the length of a wire affects its resistance, it's important to understand the relationship between resistance, length, and the number of metal ions available for electrons to collide with.

2. Relevant Concepts
   The resistance $R$ of a conductor can be described by the formula: $R = \frac{\rho L}{A}$ where:

   • $R$ = resistance,
   • $\rho$ = resistivity of the material (a constant for each material),
   • $L$ = length of the conductor,
   • $A$ = cross-sectional area of the conductor.

3. Analysis and Detail
   In a long wire, the length $L$ is greater than in a short wire. Holding resistivity and cross-sectional area constant, an increase in length leads to an increase in resistance since resistance is directly proportional to length. As for the density of metal ions, a longer wire means that electrons will have more opportunities to collide with obstacles (metal ions), causing more resistance to the flow of electric current.

4. Verify and Summarize
   Therefore, as the length of the wire increases (i.e., in the long wire scenario), its resistance also increases compared to a short wire. Consequently, more metal ions in a long wire contribute to a higher chance of collision with electrons, increasing resistance.

Final Answer

The resistance of a long wire is higher compared to that of a short wire.