Wire-Resistance Questions
Applying resistance relationships to wires, circuits, and classroom problems
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Brainiac, Season 1 Episode
4. School blocks YouTube? Use the file below.
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The Physics
1) What is the resistance of .30 m length of copper wire that has a cross-sectional area of 5.0 x 10-5 m2?
R = ρL/A
L = .30 m
A = 5.0 x 10-5 m2
Page 4 Reference Table
ρ = 1.72 x 10-8 Ωm (reference)
R = 1.0 x 10-4 Ω
a) How could you alter the dimensions of this wire to reduce the resistance?
R = ρL/A
To reduce the resistance in a wire you could: L ?
Shorten
A?
Increase
2) If the length of a wire were halved, how would that change the wires resistance? R = ρL/A
R, L direct
Cross-sectional Area (A) doubled?
R = ρL/A
R, A inverse
3) Which material on your reference table would produce a wire that would allow current to flow the best?
Silver, lowest resistivity
R, L plot for resistor?
(June 1997)
Rank the wire resistance from least to greatest
June 2017
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Check Your Understanding
5 quick questions — pick an answer to see if you’re right.
1. Find the resistance of 0.30 m of copper wire (ρ = 1.72 × 10⁻⁸ Ω·m) with area 5.0 × 10⁻⁵ m².
2. To reduce the resistance of a wire, you could:
3. A wire's length is halved AND its cross-sectional area is doubled. Its new resistance is:
4. Wires of the same size are made of silver, copper, aluminum and nichrome. Which carries current best?
5. People touching an electric fence while standing on thick styrofoam did not get shocked. Why?
Choosing an Extension Cord
A contractor needs a 30.-m extension cord to run a power saw. Thin cords (cross-sectional area 1.0 × 10−6 m²) are cheaper than thick cords (2.0 × 10−6 m²). Copper’s resistivity is 1.72 × 10−8 Ω·m; aluminum’s is 2.82 × 10−8 Ω·m.
What is the resistance of one 30.-m thin copper conductor in the cord?
▶ Want a challenge? Open 6 more Regents-style questions (harder · mixed formats)
Challenge score: 0 / 6
C1. The saw draws 12 A. How much power is wasted as heat in one thin copper conductor?
C2. The saw draws 12 A. Determine the potential difference lost across one 30.-m thin copper conductor in the cord.
C3. A student makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.
C4. Substitute numerical values into a mathematical representation that can be used to determine the resistance of one 30.-m thick aluminum conductor. Then calculate the resistance.
C5. Which cord is the safest choice for the high-current saw?
C6. The contractor is deciding between the thin copper cord and the thick copper cord for the 12-A saw. Using a calculation of the power wasted in one conductor of each cord, identify one benefit and one drawback of choosing the thick cord.