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Difficulty: EasyResistance and Resistivity

An automotive technician is replacing a damaged section of wiring in a 12-volt vehicle circuit. If the replacement copper wire has the same length as the original wire but a smaller American Wire Gauge (AWG) number, what effect will this have on the wire's electrical resistance?

  1. A
    The electrical resistance will increase because a lower gauge number corresponds to a narrower wire.
  2. The electrical resistance will decrease because a lower gauge number corresponds to a larger cross-sectional area.Answer
  3. C
    The electrical resistance will remain constant because resistance depends solely on conductor length.
  4. D
    The electrical resistance will drop to zero because changing gauge eliminates all opposition to current.

Answer

The electrical resistance will decrease because a lower gauge number corresponds to a larger cross-sectional area.
In the American Wire Gauge (AWG) standard, gauge numbers are inversely related to physical wire diameter. A conductor with a smaller AWG number has a larger diameter and therefore a greater cross-sectional area. According to the formula R=ρLAR = \rho \frac{L}{A}, resistance is inversely proportional to cross-sectional area when material resistivity and length are constant. Thus, replacing a wire with one of a smaller AWG number results in lower electrical resistance.

Step-by-Step Solution

1
Identify the relationship between the American Wire Gauge (AWG) scale and conductor diameter.
In the AWG standard, smaller numerical gauge numbers designate thicker conductors with larger cross-sectional areas (AA).
The AWG numbering system is inverse; as the gauge number decreases, the physical diameter of the wire increases.
2
Apply the physical resistance formula: R=ρLAR = \rho \frac{L}{A}.
Because conductor length (LL) and material resistivity (ρ\rho) remain unchanged, increasing cross-sectional area (AA) reduces total electrical resistance (RR).
Electrical resistance is inversely proportional to the cross-sectional area of the conductor.

Key Concept

Relationship between American Wire Gauge (AWG), cross-sectional area, and electrical resistance (R=ρLAR = \rho \frac{L}{A})
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Topics

Resistance and Resistivity

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