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Difficulty: EasyResistance and Resistivity

Which of the following factors causes an increase in the electrical resistance of a solid metallic wire?

  1. A
    Increasing the cross-sectional area of the wire
  2. B
    Decreasing the overall length of the wire
  3. Increasing the operating temperature of the wireAnswer
  4. D
    Using a wire material with higher electrical conductivity

Answer

Increasing the operating temperature of the wire causes an increase in its electrical resistance.
In metallic conductors, electrical resistance increases as temperature rises. The added thermal energy causes the atoms in the metal lattice to vibrate more vigorously, resulting in more frequent collisions with moving free electrons and hindering the flow of electric current.

Step-by-Step Solution

1
Identify the relationship between temperature and electrical resistance in metallic conductors.
Standard metals have a positive temperature coefficient of resistance, meaning resistance rises as temperature increases.
Thermal energy causes atoms in the metal lattice to vibrate more intensely, increasing collisions with flowing electrons.
2
Evaluate the effects of wire geometry and material properties using the resistance formula.
Electrical resistance is given by R=ρLAR = \rho \frac{L}{A}. Resistance increases with greater length (LL) and higher resistivity (ρ\rho), but decreases with larger cross-sectional area (AA) or higher conductivity.
Analyzing all choices confirms that among the options provided, only increasing the temperature results in higher resistance.

Key Concept

Physical factors governing conductor resistance (temperature coefficient, geometry, and material resistivity)
Estimated Time:45s
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Topics

Resistance and Resistivity

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