A current of 8.959 milliamps (10-3 A) is measured flowing through a tungsten wire of diameter 0.1 mm and 9 cm long when 1.7 mV is applied. What is the resistivity of tungsten? Express your answer in ohm-m.
R = resistivity*L/A
Calculate R and substitute L for length and A for cross section area and solve for resistivity. I believe L is in meters and A in square meters for resistivity to be reported in ohm-m.
To find the resistivity of tungsten, we can use Ohm's Law and the formula for resistance:
Resistance (R) = Voltage (V) / Current (I)
The resistance can also be calculated using the equation:
R = (ρ * L) / A
where:
ρ is the resistivity of the material,
L is the length of the wire, and
A is the cross-sectional area of the wire.
Given:
Current (I) = 8.959 milliamps = 8.959 * 10^(-3) A
Diameter (d) = 0.1 mm
Length (L) = 9 cm = 0.09 m
Voltage (V) = 1.7 millivolts = 1.7 * 10^(-3) V
First, let's calculate the cross-sectional area of the wire, A:
Area (A) = π * (d/2)^2
= π * (0.1 mm / 2)^2
= π * (0.05 mm)^2
= π * 0.0025 mm^2
= π * 2.5 * 10^(-6) m^2
Next, calculate the resistance (R) using Ohm's Law:
R = V / I
= (1.7 * 10^(-3) V) / (8.959 * 10^(-3) A)
Now, substitute the values of R, L, and A into the resistance formula to find the resistivity (ρ):
R = (ρ * L) / A
Rearranging the formula to solve for resistivity, ρ:
ρ = R * (A / L)
Substituting the known values:
ρ = [(1.7 * 10^(-3) V) / (8.959 * 10^(-3) A)] * [π * 2.5 * 10^(-6) m^2 / 0.09 m]
Simplifying:
ρ = 1.7 * π * 2.5 * 10^(-6) / 8.959 * 10^(-3) * 0.09
Calculating:
ρ = 1.5 × 10^(-7) ohm-m
Therefore, the resistivity of tungsten is approximately 1.5 × 10^(-7) ohm-m.