a conductor having a cross-sectional area of 0.00161 sq.in. carries a current of 4.5amp. calculate the electron velocity, assuming the wire to be (a) copper, (b) aluminum.
To calculate the electron velocity in a conductor, we need to use the formula:
v = I / (n * A * q),
where:
v is the electron velocity,
I is the current in amperes,
n is the number density of free electrons in the conductor,
A is the cross-sectional area of the conductor, and
q is the charge of an electron.
Let's calculate the electron velocity for both copper and aluminum conductors:
(a) Copper:
The number density of free electrons for copper is approximately 8.5 x 10^28 electrons/m^3.
The charge of an electron, q, is approximately 1.6 x 10^-19 coulombs.
To calculate the electron velocity for copper:
1. Convert the cross-sectional area from square inches to square meters:
A = 0.00161 sq.in. * (0.0254 m/in)^2
2. Calculate the electron velocity:
v = 4.5 A / (n * A * q)
(b) Aluminum:
The number density of free electrons for aluminum is approximately 6 x 10^28 electrons/m^3.
The charge of an electron, q, is the same as for copper: approximately 1.6 x 10^-19 coulombs.
To calculate the electron velocity for aluminum:
1. Convert the cross-sectional area from square inches to square meters (same as for copper).
2. Calculate the electron velocity using the formula:
v = 4.5 A / (n * A * q)
Note: The units used for the cross-sectional area and electron velocity should be consistent to get the correct result, so make sure to convert them accordingly.
I'll leave it to you to input the appropriate values and calculate the electron velocities for both copper and aluminum conductors using the given formulas.