Resistance in a Wire
How material, length, area, and temperature affect electrical resistance
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Is resistance in a wire always bad?
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The Physics
2) The resistance in a wire depends on:
a) resistivity - ρ a metals structural resistance to electron flow p. 4 Reference
b) Length (L) of the wire
c) Thickness (Cross Sectional Area) of the wire (A)
Ex) R, A relationship?
Inverse relationship 4
3) Resistance and Temperature
(Double Click on Picture above to start video) Full Size Video
Scientific Advisors: Dr. Saul Dushman; Dr. Roman
Smoluchowski; Dr. David Harker
Metals
T down, R down
T up, R up
(many electrical devices
Nonmetals – When temperature increases, resistance decreases
Superconductor - conductor with no resistance
Achieved only at very low temperatures
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Task
Check Your Understanding
5 quick questions — pick an answer to see if you’re right.
1. A wire's length is doubled while its material and thickness stay the same. Its resistance:
2. Why do powerful speakers need thick speaker wire?
3. A uniform 10 Ω wire is cut into two pieces, one 20% and one 80% of the length. What are their resistances?
4. As a metal wire gets hotter, its resistance:
5. A superconductor is a material that:
Designing a Wire
The resistance of a wire depends on its material, length, cross-sectional area, and temperature, as modeled by R = ρL ÷ A. Copper has a resistivity of 1.72 × 10−8 Ω·m at 20 °C.
Table 1: Four Copper Wires at 20 °C
| Wire | Length (m) | Cross-Sectional Area (m²) |
|---|---|---|
| A | 1.0 | 1.0 × 10−6 |
| B | 2.0 | 1.0 × 10−6 |
| C | 1.0 | 2.0 × 10−6 |
| D | 2.0 | 0.50 × 10−6 |
Which wire has the least resistance?
▶ Want a challenge? Open 6 more Regents-style questions (harder · mixed formats)
Challenge score: 0 / 6
C1. Substitute numerical values into a mathematical representation that can be used to determine the resistance of wire D. Then calculate the resistance.
C2. A student makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.
C3. How does the resistance of wire D compare with wire A?
C4. An engineer needs a copper wire with the same cross-sectional area as wire A but a resistance of 1.0 Ω. Determine the length of wire needed.
C5. If a wire’s diameter is doubled (same length), how does its resistance change?
C6. MRI machines use coils made of superconducting wire that has zero resistance when cooled with liquid helium to about −269 °C. Identify one benefit and one drawback of using superconducting wire instead of ordinary copper wire.