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Solved: Copper has 8.5 X 1028 free electrons per cubic
Chapter 25, Problem 5E(choose chapter or problem)
Problem 5E
Copper has 8.5 X 1028 free electrons per cubic meter. A 71.0-cm length of 12-gauge copper wire that is 2.05 mm in diameter carries 4.85 A of current. (a) How much time does it take for an electron to travel the length of the wire? (b) Repeat part (a) for 6-gauge copper wire (diameter 4.12 mm) of the same length that carries the same current. (c) Generally speaking, how does changing the diameter of a wire that carries a given amount of current affect the drift velocity of the electrons in the wire?
Questions & Answers
QUESTION:
Problem 5E
Copper has 8.5 X 1028 free electrons per cubic meter. A 71.0-cm length of 12-gauge copper wire that is 2.05 mm in diameter carries 4.85 A of current. (a) How much time does it take for an electron to travel the length of the wire? (b) Repeat part (a) for 6-gauge copper wire (diameter 4.12 mm) of the same length that carries the same current. (c) Generally speaking, how does changing the diameter of a wire that carries a given amount of current affect the drift velocity of the electrons in the wire?
ANSWER:
Solution 5E
Step 1 of 2:
Introduction:
The electrons will move under the influence of electric field. The electrons will move with a drift velocity throughout the length of wire. We need to find the time it takes for electrons to move the length of the wire for a 12-gauge and 6-gauge wire.
Given data,
Number of electrons per cubic meter in copper wire=8.5x1028
Length of wire=71cm
Diameter of 12-gauge wire=2.05mm
Diameter of 6-gauge wire=4.12mm
Amount of current flowing=4.85A