A particular wire has a diameter of 1.7 mm and length of 1.3 m.If 45 $\mu$V is the potential drop measured across the wire when 3.0 mA flow in it,what is the resistivity of the metal from which it is made?

Question

Quizplus · Accepted Answer

The resistivity (denoted by ρ) of a material is given by the formula:

ρ = (RA)/L

where R is the resistance of the wire, A is its cross-sectional area, and L is its length.

We are given the diameter of the wire, so we can find its radius:

r = d/2 = 0.85 mm = 0.85 x 10^-3 m

The cross-sectional area of the wire is:

A = πr^2 = π(0.85 x 10^-3)^2 = 2.26 x 10^-6 m^2

We are also given the potential drop across the wire and the current flowing through it, so we can use Ohm's law to find the resistance of the wire:

R = V/I = 45 x 10^-6 / 3 x 10^-3 = 15 Ω

Substituting these values into the formula for resistivity, we get:

ρ = (RA)/L = (15 x 2.26 x 10^-6) / 1.3 = 2.6 x 10^-8 Ωm

Therefore, the best choice is B.

A Particular Wire Has a Diameter of 1 μ\muμ V Is the Potential Drop Measured Across the Wire When

A Particular Wire Has a Diameter of 1 $\mu$ V Is the Potential Drop Measured Across the Wire When