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1. A wire of radius 0.15 mm is made of an unknown metal and carries a current of

ID: 1420628 • Letter: 1

Question

1. A wire of radius 0.15 mm is made of an unknown metal and carries a current of 8.4 mA. The drift velocity for electrons in the wire is measured to be 36 x 10-6m/s. What is the carrier density of the metal from which the wire is made?

a. 2.06 x 1028 m-3

b. 1.3 x 1029 m-3

c. 4.2 x 1030 m-3

d. need more information to do this calculation.

2. Aluminum has a resistivity of 2.65 × 108 m. What is the resistance of 15 m of aluminum wire of cross-sectional area 1.0 mm2?

a. 1.6

b. 0.40

c. 0.13

d. 1.3 × 102

e. 56

Explanation / Answer

1.   Given   radius r=0.15 mm = 0.15*10^-3 m

                   current I = 8.4 mA = 8.4*10^-3A

         Drift velocity vd = 36*10^-6 m/s.

cross-sectional arrea of the wire, A = pi * r^2 = 3.14*(0.15*10^-3)2= 7.065*10-8 m2

drift velocity is given as , vd = I / (n*e*A)   where   n is the carrier

=> n = I/(vd*e*A) = 8.4*10^-3 /(36*10-6 * 1.6*10-19* 7.065*10-8)=2.06*1028 m-3

Hence option (a) is correct option

(2) . We have   R = p*L/A = 2.65*10^-8* 15 / (1.0*10^-6) = 0.4 ohm

Hence option (b) be the correct option.