Answer:
Step-by-step explanation:
a) To find the current in the wire, use the formula:
I = Q / t
Where I is the current, Q is the amount of charge that passes through the wire (2.37 C), and t is the time (5.4 s).
I = 2.37 C / 5.4 s = 0.44 A
So the current in the wire is 0.44 A.
b) To find the cross-sectional area of the wire, use the formula:
A = π * r^2
Where A is the cross-sectional area, r is the radius of the wire (1.0 mm = 0.001 m), and π is Pi (3.14).
A = π * (0.001 m)^2 = 3.14 * 10^-6 m^2
So the cross-sectional area of the wire is 3.14 * 10^-6 m^2.
c) To find the charge of the charge carriers in the wire, use the formula:
Q = n * e
Where Q is the charge, n is the number of charge carriers, and e is the elementary charge (1.60 × 10^-19 C).
The wire has a charge carrier density of 7.5 × 10^26 /3, so the number of charge carriers can be calculated as:
n = (charge carrier density * cross-sectional area of the wire)
n = (7.5 × 10^26 / 3) * (3.14 * 10^-6 m^2)
n = 7.5 × 10^26 * 3.14 * 10^-6 / 3
n = 2.35 × 10^20
So the charge of the charge carriers in the wire is:
Q = n * e = 2.35 × 10^20 * 1.60 × 10^-19 C = 3.72 × 10^-19 C
d) To find the drift speed of the electrons in the wire, use the formula:
v = I / (n * e * A)
Where v is the drift speed, I is the current (0.44 A), n is the number of charge carriers (2.35 × 10^20), e is the elementary charge (1.60 × 10^-19 C), and A is the cross-sectional area of the wire (3.14 * 10^-6 m^2).
v = 0.44 A / (2.35 × 10^20 * 1.60 × 10^-19 C * 3.14 * 10^-6 m^2)
v = 0.44 / (2.35 × 10^20 * 1.60 × 10^-19 * 3.14 * 10^-6)
v = 0.44 / (3.74 × 10^-5)
v = 11766 m/s
So the drift speed of the electrons in this wire is 11766 m/s.