You 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.Rwire 1 = 4 Rwire 2b.Rwire 1 = 2 Rwire 2c.Both are zero because copper is a conductor.d.Rwire 1 = 0.25 Rwire 2e.Rwire 1 = 0.5 Rwire 2f.Rwire 1 = Rwire 2 ≠≠ 0Clear my choiceCheckQuestion 4
Question
You 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.Rwire 1 = 4 Rwire 2b.Rwire 1 = 2 Rwire 2c.Both are zero because copper is a conductor.d.Rwire 1 = 0.25 Rwire 2e.Rwire 1 = 0.5 Rwire 2f.Rwire 1 = Rwire 2 ≠≠ 0Clear my choiceCheckQuestion 4
Solution
The resistance of a wire is given by the formula R = ρL/A, where R is the resistance, 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.
For Wire 1: Length, L1 = 2 cm = 0.02 m Radius, r1 = 1 mm = 0.001 m So, the cross-sectional area, A1 = πr1^2 = 3.14 * (0.001 m)^2 = 3.14 * 10^-6 m^2
For Wire 2: Length, L2 = 4 cm = 0.04 m Radius, r2 = 2 mm = 0.002 m So, the cross-sectional area, A2 = πr2^2 = 3.14 * (0.002 m)^2 = 12.56 * 10^-6 m^2
Now, let's compare the resistances of the two wires:
R1/R2 = (ρL1/A1) / (ρL2/A2) = (L1/A1) / (L2/A2) = (0.02 m / 3.14 * 10^-6 m^2) / (0.04 m / 12.56 * 10^-6 m^2) = 0.5
So, the resistance of Wire 1 is half the resistance of Wire 2. Therefore, the correct answer is e. Rwire 1 = 0.5 Rwire 2.
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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
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