We have a 3 ft long. 3 mm diameter copper wire that carries a 12 A current. Calc

Question

We have a 3 ft long. 3 mm diameter copper wire that carries a 12 A current. Calculate the resistance of the wire from the resistivity at 20 degree C. Calculate the voltage drop along the wire using Ohm's law. Calculate the current density in the wire. From the voltage, calculate the electric field inside the wire, (In electrostatics, the electric field inside conductors is zero, but with a current, that is no longer true, although the electric field is small.) Calculate the electric field from the current density. Compare with result from part d. Copper has 8.4 times10^28 conduction electrons per cubic meter. Calculate their average drift speed. Give answer in pm/s and mm h. What is the resistance of this wire if its temperature increases to 60 degree C? A 100 W light bulb has a resistance of 12 ohm at 20 degree C. When plugged in to 120 V AC. the bulb draws 100 W after the filament reaches a temperature of 3000 degree F. Estimate the average temperature coefficient of the filament of the light bulb. A 2-slice toaster with a heating element made out of Nichrome wire is designed to reaches a operating temperature of 1500 degree F. drawing 1 kW when plugged into 120 V AC. The toasting slots are 6 inches long and each have 10 heater wires on each side for a total length of 40 times 6 inches. Determine the diameter of the Nichrome wire used.

Explanation / Answer

Here

a) resistivity , p = 1.68 *10^-8 m

current , I = 12 A

resistance of wire = p * L/A

resistance of wire = 1.68 *10^-8 * 3 * 0.3048/(pi * (0.003/2)^2)

resistance of wire = 2.17 *10^-3 Ohm

b)

Voltage drop across wire = Resistance of wire * I

Voltage drop across wire = 2.17 *10^-3 * 12

Voltage drop across wire = 0.02604 V

c)

Current density of wire = Current/area

Current density of wire = 12/(pi * (0.003/2)^2)

Current density of wire = 1.697 *10^6 A/m^2

d)

electric field inside the wire = V/L

electric field inside the wire = 0.02604/(3 * 0.3048)

electric field inside the wire = 0.0285 V/m

the electric field inside the wire is 0.0285 V/m

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