Two wires both carrty the same curent I. the moving Charged particles in both wi

Question

Two wires both carrty the same curent I. the moving Charged particles in both wires are electrons, but the concentation of moving electrons in wire #1 is duble the concentration of moving electrns in wire #2. Under what circumstances will the drift speed of elctrons be the same in both wires?

a. if the diameter of wire #2 is 1/sqrt2 the diameter of wie #1

b. if the diameter of wire #2 is 4 times the diameter of wire #1

c. if the diameter of wire 2 is sqrt2 times the diameter of wire #1

d. if the diameter of wire #2 is 1/4 the diameter of wire #1

e. if the diameter of wire #2 is 1/2 the diameter of wire #1

Explanation / Answer

V = I/neA = q/neAt = q/(nepi*r^2*t)

a) V2/ V1 = n1*d1^2/n2*d2^2 = n1*d1^1/(2n1*d1^2/2) = 1

V2 = V1

b) V2/ V1 = n1*d1^2/n2*d2^2 = n1*d1^1/(2n1*4*d1^2) = 1/8====> V1 = 8V2

c) V2/ V1 = n1*d1^2/n2*d2^2 = n1*d1^1/(2n1*2d1^2) = 1/4==========> V1 = 4V2

d) V2/ V1 = n1*d1^2/n2*d2^2 = n1*d1^1/(2n1*d1^2/16) = 1/16=======> v1 = 16V2

e) V2/ V1 = n1*d1^2/n2*d2^2 = n1*d1^1/(2n1*d1^2/4) = 2========> V1 = V2/2

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