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HW11 Soln-1 - Problem 13.2 J F Shackelford Introduction to...

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13.2 A lightbulb operates with a line voltage of 110 V. If the filament resistance is 200 Ω , calcu- late the number of electrons per second traveling through the filament. SOLUTION This problem requires only a simple application of Ohm's law, Equation 13.1 on page 427 of the text, and some unit conversion. Beginning with Ohm's law, the current is given by I = V/R Substituting for the given voltage ( V ) and resistance ( R ), the current is found I = [110 V] / [200 Ω ] = 0.55 A Next, some unit conversion is required, using the conversion factors on the inside cover of the text, also found in Appendix 3, page A-7, I = 0.55 A = {(0.55 C / s) × (1 e / 0.16 × 10 –18 C)} = 3.44 × 10 18 e / s which gives the number of electrons per second traveling through the filament, 3.44 × 10 18 e / s Problem 13.2 J. F. Shackelford, Introduction to Materials Science for Engineers , 7 th Edition, Prentice Hall, New Jersey (2009) Problem 13.2 Solution Professor R. Gronsky page 1 of 1
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13.12 At what temperature will diamond have the same probability for an electron's being pro- moted to the conduction band as silicon has at 25°C? (The answer to this question indi- cates the temperature range in which diamond can be properly thought of as a semiconduc- tor rather than as an insulator.) SOLUTION The Fermi function, Equation 13.7 of the text (p. 434) establishes the probabilistic energy ( E ) distribution of carriers in a material as a function of temperature where E f is its Fermi Energy (energy of highest occupied orbital at absolute zero), k is Boltz- man's constant, and T is its absolute temperature.
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