A 120-m long metal wire having a resistivity of 1.68 × 10^-8 Ω ∙ m has a resistance of 6.0 Ω.What is the diameter of the wire? A)0.065 mm B)0.65 mm C)0.65 cm D)0.65 m

Question

Quizplus · Accepted Answer

We can use the formula for resistance:

R = (ρL)/A

Where R is the resistance, ρ is the resistivity, L is the length of the wire, and A is the cross-sectional area of the wire.

We can rearrange this formula to solve for A:

A = (ρL)/R

Substituting the given values:

A = (1.68 × 10^-8 Ω ∙ m)(120 m)/(6.0 Ω)
A = 3.36 × 10^-7 m^2

We can calculate the diameter using the formula:

A = π/4 × d^2

Where d is the diameter.

Rearranging and substituting:

d = √(4A/π)
d = √(4(3.36 × 10^-7 m^2)/π)
d = 0.0654 m or 65.4 mm

So the answer is B, 0.65 mm (rounded to two significant figures).

A 120-M Long Metal Wire Having a Resistivity of 1