Question

Using the charts below, if you knew that a 1 mm diameter copper-nickel alloy wire can withstand a maximum load (before plastic deformation) of 78.54 N, and possesses an electrical resistance of 0.5 Ohms, then what is its length

Answer 1

L = 10.32 m

Step-by-step explanation:

The resistance of a copper-nickel alloy wire is given by the following formula:

`R = (\rho L)/(A)`

where,

R = Resistance = 0.5 Ω

ρ = resistivity of copper-nickel alloy = 3.8 x 10⁻⁸ Ωm

L = Length of wire = ?

A = cross-sectional area of wire =
`(\pi d^2)/(4) = (\pi(1\ x\ 10^(-3)\ m)^2)/(4)` = 7.85 x 10⁻⁷ m²

Therefore,

`0.5\ \Omega = ((3.8\ x\ 10^(-8)\ \Omega.m)L)/(7.85\ x\ 10^(-7)\ m^2)`

L = 10.32 m