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.
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