Question

A silver wire 2.6 mm in diameter transfers a charge of 420 C in 80 min. Silver contains 5.0 x 10^28 free electrons per cubic meter. (a) What is the current in the wire? (b) What is the magnitude of the drift velocity of the electrons in the wire?

Answer 1

Answer:

a) 0.0875A

b) 2.06*10^-6m/s

Explanation:

given

Diameter, d = 2.6mm = 0.0026m

Charge, Q = 420C

Time, t = 80mins = 80*60s = 4800s

Concentration of electrons, n = 5*10^28

To find the current, recall that q = it

Therefore, i = Q/t

Current, i = 420/4800

i = 0.0875A

To get the drift velocity, recall that I = n*q*Vd*A

A = πd²/4

A = π*0.0026²/4

A = 5.3*10^-6m²

Then, Vd = I/nqA

Vd = 0.0875/(5*10^28 * 1.6*10^-19 * 5.3*10^-6)

Vd = 0.0875/42400

Vd = 2.06*10^-6m/s

Note, low Vd causes low current.

Therefore, the current is 0.0875A and the Vd is 2.06*10^-6m/s