What must be the diameter of a cylindrical 120-m long metal wire if its resistance is to be 6.0 Ω? The resistivity of this metal is 1.68 × 10^-8 Ω ∙ m. A)0.065 mm B)0.65 mm C)0.65 cm D)0.325 mm E)0.0325 mm

Question

Quizplus · Accepted Answer

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, L is the length of the wire, and A is the cross-sectional area of the wire.

Rearranging this equation for A, we get:

A = (ρL)/R

Substituting the given values, we get:

A = (1.68 × 10^-8 Ω ∙ m × 120 m)/6.0 Ω
A = 336 × 10^-8 m^2
A = 3.36 × 10^-6 cm^2

The cross-sectional area of a cylinder is given by the formula:

A = πr^2

where r is the radius of the cylinder. Substituting this into the previous equation, we get:

πr^2 = 3.36 × 10^-6 cm^2

Solving for r, we get:

r = sqrt(3.36 × 10^-6 cm^2/π)
r = 0.000651 cm
r = 0.0651 mm

Therefore, the diameter of the wire is twice the radius, or:

d = 0.1302 mm, which is closest to choice B (0.65 mm).

What Must Be the Diameter of a Cylindrical 120-M Long