Question

Currents up to 30 A can be carried by 10 gauge copper wire.

1)

What is the resistance of 110 m of 10 gauge copper wire?
?

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2)

What is the electric field in the wire when the current is 30 A?
mV/m

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3)

How long does it take for an electron to travel 110 m in the wire when the current is 30 A?
s

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Answer 1

diameter of 10 gauge,

d = 19.7 mm

= 19.7*10^-3 m

I = 30 A
L = 110 m
for copper resistivity, rho = 1.72*10^-8 ohm.m

1) R = rho*L/A

= rho*L/(pi*d^2/4)

= 1.72*10^-8*110/(pi*(19.7*10^-3)^2/4)

= 6.21*10^-3 ohm

2) V = I*R

= 30*6.21*10^-3

= 0.1863 V

E = V/L

= 0.1863/110

= 1.69*10^-3 V/m

= 1.69 mV/m

3) in copper no of charge electrons per unit volume, n = 8.45*10^28

drift speed, vd = I/(A*n*q)

= 30/(pi*(19.3*10^-3)^2/4*8.45*10^28*1.6*10^-19)

= 7.58*10^-6 m/s

time taken for the electrons to cross the wire, t = L/vd

= 110/(7.58*10^-6)

= 1.45*10^7 s