Time left 0:08:13Question 4Tries remaining: 2Marked out of 1.00Flag questionTipsQuestion textYou have two circular wires made out of copper. Wire 1 has length 2cm and radius 1mm. Wire 2 has length 4cm and radius 2mm. How do the resistances of the two wires compare?Question 4Answera.Both are zero because copper is a conductor.b.Rwire 1 = 4 Rwire 2c.Rwire 1 = 2 Rwire 2d.Rwire 1 = 0.25 Rwire 2e.Rwire 1 = 0.5 Rwire 2f.Rwire 1 = Rwire 2 ≠≠ 0
Question
Time left 0:08:13Question 4Tries remaining: 2Marked out of 1.00Flag questionTipsQuestion textYou have two circular wires made out of copper. Wire 1 has length 2cm and radius 1mm. Wire 2 has length 4cm and radius 2mm. How do the resistances of the two wires compare?Question 4Answera.Both are zero because copper is a conductor.b.Rwire 1 = 4 Rwire 2c.Rwire 1 = 2 Rwire 2d.Rwire 1 = 0.25 Rwire 2e.Rwire 1 = 0.5 Rwire 2f.Rwire 1 = Rwire 2 ≠≠ 0
Solution
The resistance (R) of a wire can be calculated using the formula R = ρL/A, where ρ is the resistivity of the material (in this case, copper), L is the length of the wire, and A is the cross-sectional area of the wire. The cross-sectional area of a wire can be calculated using the formula A = πr², where r is the radius of the wire.
For Wire 1: Length (L1) = 2 cm = 0.02 m Radius (r1) = 1 mm = 0.001 m So, Area (A1) = π(0.001 m)² = 0.00000314 m²
For Wire 2: Length (L2) = 4 cm = 0.04 m Radius (r2) = 2 mm = 0.002 m So, Area (A2) = π(0.002 m)² = 0.00001256 m²
Assuming the resistivity (ρ) of copper is constant, we can compare the resistances of the two wires by substituting the values into the resistance formula:
R1 = ρ(0.02 m) / 0.00000314 m² = 0.006366 ρ R2 = ρ(0.04 m) / 0.00001256 m² = 0.003183 ρ
Therefore, R1 = 2R2, which corresponds to option c. Rwire 1 = 2 Rwire 2.
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