Question

A 25.0-meter length of platinum wire with a cross-sectional area of 3.50 × 10^−6 meter^2 has a resistance
of 0.757 ohm at 20°C. Calculate the resistivity of the wire. [Show all work, including the equation and
substitution with units.]

Answer 1

R= (rou * L) / area
where R is the wire resistance
rou: resistivity of the wire material
L : wire length
A : cross section area of wire
by sub.
0.757= (rou*25)/ 3.5*10^-6
25*rou = 2.6495*10^-6
rou= 1.0598*10^-7 ohm.m

Answer 2

The resistivity of the plantinum wire is 1.06 × 10⁻⁷Ωm

Calculating Resistivity

From the question,

We are to determine the resistivity of the wire

Resistivity can be calculated from the formula

$\rho = \frac{RA}{l}$

Where $\rho$ is the resistivity of the wire

R is the resistance

A is the cross-sectional area

and $l$ is the length of the wire

From the given information,

R = 0.757 ohm (Ω)

A = 3.50 × 10⁻⁶ m²

$l$ = 25.0 m

Putting the parameters into the formula, we get

$\rho = \frac{0.757 \times 3.50 \times 10^{-6} }{25}$

$\rho = 0.10598 \times 10^{-6}$

$\rho = 1.0598 \times 10^{-7}$

$\rho \approx 1.06 \times 10^{-7} \ \Omega m$

Hence, the resistivity of the plantinum wire is 1.06 × 10⁻⁷Ωm

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