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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