Question

A conducting wire has a 1.00 mm diameter, a 2.9 meter length, and its resistivity is 1.9×10 ^−7Ω⋅m, the resistance of the conducting wire is Ω. Use normal format with 3SF.

Answer 1

To find the value of resistance, we first need to convert the units of the diameter from mm to meter. We do this by dividing 1mm by 1000, giving us 0.001m

Next, we need to find the cross-sectional area of the wire. The formula for the cross-sectional area is:

Area = πr²

Where r represents the radius of the wire. We can calculate the radius as half of the diameter. Therefore, the radius of the wire is 0.001/2 = 0.0005m.

Substituting the radius into the area formula, we get:

Area = π* 0.0005² ≈ 7.8539816339745e-07m²

Now, we have all the values to use in the formula for finding the resistance of a wire which is,

Resistance(R) = Resistivity(ρ) * Length(l) / Cross-sectional Area(A)


Substituting all the values into the resistance formula, we have:

Resistance = 1.9 *10^-7 * 2.9 / 7.8539816339745e-07

Solving for Resistance, we get approximately 0.702 Ω, rounded to three significant figures.