Problem 1: Consider the leaky capacitor shown in the figure above. Speci- fications are as follows: The plate area is A =3.0 cm², and the gap distance is L =20 jam. The density of free electrons is ne = 5 x 1026 particles/m, and the density of free holes n = 5 x 1026 particles/m is the same. Suppose that the holes are immobile, so only the electrons are free to move. (a) For a current I = 5 mA , what is the rate (in particles per second) at which electrons pass by the imaginary boundary? (b) What drift velocity (in meters/sec) would give rise to this current? (c) Drift velocities in conductors tend to be small, but small as compared to what? Consider the RMS thermal velocity? How many orders of magnitude smaller is the average drift velocity in this device than the RMS thermal velocity of an electron moving in free space at room temperature? (Use the law of equipartition to find the RMS thermal velocity of a free electron.)
Problem 1: Consider the leaky capacitor shown in the figure above. Speci- fications are as follows: The plate area is A =3.0 cm², and the gap distance is L =20 jam. The density of free electrons is ne = 5 x 1026 particles/m, and the density of free holes n = 5 x 1026 particles/m is the same. Suppose that the holes are immobile, so only the electrons are free to move. (a) For a current I = 5 mA , what is the rate (in particles per second) at which electrons pass by the imaginary boundary? (b) What drift velocity (in meters/sec) would give rise to this current? (c) Drift velocities in conductors tend to be small, but small as compared to what? Consider the RMS thermal velocity? How many orders of magnitude smaller is the average drift velocity in this device than the RMS thermal velocity of an electron moving in free space at room temperature? (Use the law of equipartition to find the RMS thermal velocity of a free electron.)
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Leaky capactor is a resistor.
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Transcribed Image Text:Problem 1: Consider the leaky capacitor shown in the figure above. Speci-
fications are as follows: The plate area is A =3.0 cm?, and the gap distance is
L =20 µm. The density of free electrons is ne = 5 x 1026 particles/m', and the
density of free holes n, = 5 x 1026 particles/m³ is the same. Suppose that the
holes are immobile, so only the electrons are free to move. (a) For a current
I = 5 mA , what is the rate (in particles per second) at which electrons pass
by the imaginary boundary? (b) What drift velocity (in meters/sec) would give
rise to this current? (c) Drift velocities in conductors tend to be small, but small
as compared to what? Consider the RMS thermal velocity? How many orders
of magnitude smaller is the average drift velocity in this device than the RMS
thermal velocity of an electron moving in free space at room temperature? (Use
the law of equipartition to find the RMS thermal velocity of a free electron.)
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