Answer to Question #302558 in Electric Circuits for Lia

Question

1. Calculate the drift velocity of the electrons in a 12-gauge copper wire which has a diameter of 2. 5 mm carrying    an 18.0 A , given that there is one free electron per copper atom. The density of copper is 8.80x10³ kg/m³_.

    atomic mass of copper = 63.54 g/mol; Avogadros number = 6.02 x 10 ²³ atoms/mol

2. Calculate the total DC resistance of a 100 meter roll of 2.0mm² copper wire if the resistivity of copper at 20⁰  C is 1.72 x 10^-8 ohm meter.

Answer 1

Explanations &Calculations

1.

$\qquad\qquad \begin{aligned} \small A.M.U_{Cu}&=\small 0.06354\,kg\,mol^{-1}\\ \small L&=\small 6.02\times10^{23}\,atoms\,mol^{-1}\\ \small L/A.M.U&=\small 92.7\times10^{23}\,atoms/kg^{-1}\\ \\ \small \# of \,en&=\small 92.7\times10^{23}\,atoms\,kg^{-1}\times8.80\times10^3\,kgm^{-3}\times1\,en\,atom^{-1}\\ &=\small 8.16\times10^{28}\,en\,m^{-3}\\ \\ \small I&=\small v.A.n.e\\ \small 18.0\,Cs^{-1}&=\small v.[\pi.0.25.(2.5\times10^{-3}\,m)^2]. (8.16\times10^{28}\,en\,m^{-3}).(1.6\times10^{-19}C\,en^{-1}) \end{aligned}$

• Now you can simplify and get the answer.

2.

• Just use the formula for resistance which is $\small R= \large\rho\frac{L}{Area}$
• Input all the given values in their SI forms and get the answer for resistance; so the square millimetre needs to be in square metres.