Calculation of Length of Copper Wire

To calculate the length of a copper wire with a given diameter that will have a resistance of 34 ohms, we can use the formula:

R = ρ * (L / A)

Where:
R is the resistance,
ρ (rho) is the resistivity of copper,
L is the length of the wire, and
A is the cross-sectional area of the wire.

Resistivity of Copper
The resistivity of copper is given as 1.7 * 10^-8 ohm metre.

Conversion of Diameter to Radius and Area
Given that the diameter of the wire is 0.1 mm, we can calculate the radius and the cross-sectional area of the wire.

The radius (r) is half of the diameter, so:
r = 0.1 mm / 2 = 0.05 mm = 0.05 * 10^-3 m

The cross-sectional area (A) of the wire is given by the formula:
A = π * r^2

Substituting the value of the radius, we get:
A = π * (0.05 * 10^-3)^2

Calculating the Length
Now, we can rearrange the resistance formula to solve for length:

L = (R * A) / ρ

Substituting the given values:
L = (34 * π * (0.05 * 10^-3)^2) / (1.7 * 10^-8)

Evaluating the expression and simplifying the units:
L = (34 * π * (0.05 * 10^-3)^2) / (1.7 * 10^-8)
L = (34 * 3.14 * (0.05 * 10^-3)^2) / (1.7 * 10^-8)
L = (34 * 3.14 * 0.0025 * 10^-6) / (1.7 * 10^-8)
L = (0.0269 * 10^-6) / (1.7 * 10^-8)
L = 1.58 m

Conclusion
Therefore, a copper wire with a diameter of 0.1 mm will have a length of approximately 1.58 meters to achieve a resistance of 34 ohms, assuming the resistivity of copper is 1.7 * 10^-8 ohm metre.