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**

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