Question

How to do these two problems

3. -1 points OSColPhys2016 20.1.WA.008 My Notes Consider a copper wire with a diameter of 2.51 mm. (a) What is the drift speed of the electrons in the copper wire when a current of 11.0 A flows through it? Assume that each copper atom contributes one free electron to the metal. The density of copper is 8.92 g/cm3 m/s (b) How does this drift speed compare to the random rms speed of an electron at 20.0 C? To make this comparison, determine the random rms speed of an electron at 20.0°C using the ideal gas model and find the ratio of the two speeds. Additional Materials Reading 4. -1 points OSColPhys2016 20.3.WA.017.Tutorial My Notes As part of a class project you are given 0.900 g of nichrome and asked to fabricate a wire with uniform cross-section. You use up 95% of the nichrome and make a wire with a resistance of 0.693 Ω. The resistivity of nichrome is 00 x 10-6。·㎡ and its density is 8.31 × 103 kg/m3. (a) What length of wire do you end up with? (b) What is the diameter of the wire?

Answer 1

a )

density = 8.92 g/cm³ = 8920 kg/m³

mass of Cu atom = 63.5 g = 63.5 X 10^-3 kg

noof moles /m³ = 8920 / 63.5 X 10^-3

= 1.4 X 10⁵ moles

n = 6.02 X 10²³ X 1.4 X 10⁵ = 8.43 X 10²⁸

V = 11 / 8.43 X 10²⁸ X 1..6 X 10^-19 X ( 3.14/4 ) X 2.51 X 10^-6

V = 4.13 X 10^-4 m/s

b )

V_rms = ( 3 R T / m )^1/2

= ( 3 X 8.4 X 293 / 5.84 X 10^-7 )^1/2

V_rms = 112441.76 m/s

the ratio = 112441.76 / 4.13 X 10^-4 = 2.722 X 10⁸

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a )

using m = dV

= d ( AL )

A = m / dL

$\rho$ = R A / L

R = $\rho$ L / A

R = $\rho$ L /(m / dL)

L = ( Rm / $\rho$ d )^1/2

L = ( 0.693 X 0.9 X 10^-3 X 0.95 / 1 X 10^-6 X 8.31 X 10³ )^1/2

L = 0.267 m

b )

using r = ( m / 3.14 X d L )^1/2

r = ( 0.9 X 10^-3 X 0.95 / 3.14 X 8.31 X 10³ X 0.267 )^1/2

r = 3.5 X 10^-4 m

or

r = 0.35 X 10^-3 m

r = 0.35 mm