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 ≠≠ 0
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 ≠≠ 0
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, the length L1 = 2 cm and the radius r1 = 1 mm = 0.1 cm. The cross-sectional area A1 = πr1^2 = π(0.1 cm)^2 = 0.01π cm^2.
For Wire 2, the length L2 = 4 cm and the radius r2 = 2 mm = 0.2 cm. The cross-sectional area A2 = πr2^2 = π(0.2 cm)^2 = 0.04π cm^2.
The resistivity ρ is the same for both wires since they are made of the same material (copper).
Therefore, the resistance of Wire 1 is R1 = ρL1/A1 and the resistance of Wire 2 is R2 = ρL2/A2.
To compare the resistances, we can form the ratio R1/R2 = (ρL1/A1) / (ρL2/A2) = (L1/A1) / (L2/A2) = (2 cm / 0.01π cm^2) / (4 cm / 0.04π cm^2) = 1/2.
Therefore, the resistance of Wire 1 is half the resistance of Wire 2, so 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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