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Friday, September 27, 2019

A slice of germanium of cross-sectional area 1.0 cm2 carries a current of 56 μA. The number density of charge carriers in the germanium is 2.0 × 1013 cm-3


Question 15
A slice of germanium of cross-sectional area 1.0 cm2 carries a current of 56 μA. The number density of charge carriers in the germanium is 2.0 × 1013 cm-3. Each charge carrier has a charge equal to the charge on an electron.




What is the average drift velocity of the charge carriers in the germanium?
A 0.18 m s-1                     B 18 m s-1                         C 180 m s-1                       D 1800 m s-1





Reference: Past Exam Paper – June 2018 Paper 13 Q30





Solution:
Answer: A.

I = nqAv
Drift velocity v = I / nqA

We need to convert the quantities given into SI units.

Cross-sectional area A = 1.0 cm2 = 1.0×10-4 m2 

Number density n = 2.0×1013 cm-3
That is, in 1 cm3, there are 2.0×1013 charge carriers

1 cm3 = 1×10-6 m3

1 cm3 - - > 2.0×1013 charge carriers
1×10-6 m3 - - > 2.0×1013 charge carriers
1 m3 - - > (2.0×1013) / (1×10-6) = 2.0×1019 charge carriers

So, number density n = 2.0×1013 cm-3 = 2.0×1019 m-3

Drift velocity v = I / nqA
Drift velocity v = (56×10-6) / (2.0×1019 × 1.6×10-19 × 1.0×10-4)
Drift velocity v = 0.175 m s-1 = 0.18 m s-1

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