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Difficulty: MediumResistance and Resistivity

A technician cuts a solid copper grounding rod exactly in half to create a shorter lead. How do the electrical resistance and the material resistivity of one of the shortened pieces compare to the original rod?

  1. A
    Both the electrical resistance and the resistivity are halved.
  2. The electrical resistance is halved, while the resistivity remains unchanged.Answer
  3. C
    The electrical resistance is doubled, while the resistivity is halved.
  4. D
    The electrical resistance remains unchanged, while the resistivity is halved.

Answer

The electrical resistance is halved, while the resistivity remains unchanged.
Electrical resistance (RR) depends on geometry (R=ρLAR = \rho \frac{L}{A}), so cutting the length in half directly halves the resistance. Resistivity (ρ\rho) is an intrinsic property of the material (copper) at a given temperature, so altering the rod's length does not change its resistivity.

Step-by-Step Solution

1
Analyze how physical dimensions affect total electrical resistance (RR).
R=ρLAR = \rho \frac{L}{A}, showing resistance is directly proportional to length (LL).
Electrical resistance is an extrinsic property determined by the conductor's geometry and material.
2
Calculate the new resistance after halving the length.
Rnew=ρL/2A=12RoriginalR_{\text{new}} = \rho \frac{L/2}{A} = \frac{1}{2} R_{\text{original}}.
Halving the conductor length reduces the opposition encountered by flowing electrons by half.
3
Determine the effect on resistivity (ρ\rho).
ρnew=ρoriginal\rho_{\text{new}} = \rho_{\text{original}}.
Resistivity is an intrinsic physical property of copper determined by its atomic structure, independent of size or shape.

Key Concept

Distinction between extrinsic resistance (RR) and intrinsic resistivity (ρ\rho)
Estimated Time:45s
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Topics

Resistance and Resistivity

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