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Difficulty: EasyResistance and Resistivity

An electrical technician wants to reduce the electrical resistance of a standard copper wire run without changing the metal type or operating temperature. Which of the following modifications will decrease the resistance of the wire?

  1. A
    Increasing the total length of the wire
  2. Increasing the cross-sectional area of the wireAnswer
  3. C
    Operating the wire at a significantly elevated temperature
  4. D
    Selecting a wire with a smaller circular diameter

Answer

Increasing the cross-sectional area of the wire decreases its electrical resistance.
Electrical resistance in a conductor is inversely proportional to its cross-sectional area (R=ρLAR = \rho \frac{L}{A}). Increasing the thickness or cross-sectional area provides more conductive pathways for free electrons, thereby lowering the total resistance.

Step-by-Step Solution

1
Recall the fundamental physical relationship between conductor dimensions and electrical resistance
R=ρLAR = \rho \frac{L}{A}, where RR is resistance, ρ\rho is material resistivity, LL is conductor length, and AA is cross-sectional area
This formula defines how physical geometry directly influences opposition to electron flow.
2
Analyze how changing the cross-sectional area (AA) impacts resistance (RR)
Because cross-sectional area (AA) is in the denominator, resistance is inversely proportional to area (R∝1AR \propto \frac{1}{A})
Increasing the area (AA) reduces the calculated resistance (RR), allowing electrons to flow more easily.

Key Concept

Physical factors governing conductor resistance
Estimated Time:45s
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Topics

Resistance and Resistivity

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