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Unformatted text preview: Problems Perspective (Preceding Chapter 2) 2.1 The circuit of Fig. P2.1 has a non-linear device for which i = v . Determine v by graphical analysis. + + 12 6 3 2 + v i Figure P2.1 2.2 Repeat Problem 2.1, but let i = 2 v and reduce the 2-A source to 1 A. 2.3 The circuit of Fig. P2.3 has a non-linear device for which i = 2 v 3 / 2 (with i in mA). Determine v by graphical analysis. x + + + 12 v (mA) + v i x v 1 k 2 k 2 Figure P2.3 2.4 Repeat Problem 2.3 but let v x appear across the 2-k resistor (with positive node to the left). 2.5 A 10-V source with Thevenin resistance R t con- nects to a non-linear device for which i = 2( v- 1) 2 (with i in mA) subject to v 1 V. The device has zero current otherwise. Use a graphical procedure to determine R t such that i = 4 mA. 2.6 A current source I n with 1-k Norton resistance connects to a non-linear device for which i = v- 2 (with i in mA) subject to v 2 V. The device has zero current otherwise. Use a graphical procedure to determine I n such that i = 8 mA. 2.7 The circuit of Fig. P2.7 has a non-linear resistor for which v = ikR i iR/k i < . In this expression, k is a dimensionless constant that is subject to 0 k 1. The old-fashioned electro- mechanical ammeter measures time-averaged current < i > = 1 T Z t i ( t ) dt , where T = 2 / is the period of the ac signal. (a) Determine < i > when k = 1 (the limiting case for a linear resistor). (b) Determine < i > when k = 0 (the limiting case for an ideal diode). (c) Use graphical analysis to explain qualitatively the variation in < i > as k is varied between 0 and 1 (the diode becomes less and less ideal). (d) Determine k such that < i > = v/ 10 R . Note: The disparity of the results for parts a and b reflects diode function as a detector of ac amplitude. This is an important application (particularly for the early days of radio). + + v i R v sin t ammeter k Figure P2.7 c 2010 Edward W. Maby All Rights Reserved Section 2.1 2.8 In the study of chemistry, one learns that the number of molecules in one mole of any substance is given by Avagadros number (6 . 02 10 23 ). (a) Look up the density of gold. Then estimate the free electron concentration in gold, assuming one free electron per atom. (b) The conductivity of gold is 4 . 1 10 5 (-cm)- 1 . Estimate the electron mobility in gold. 2.9 The resistivity of copper is 1 . 7 10- 6 -cm. Determine the resistance of 100 feet of AWG #22 copper wire with 0.645-mm diameter. 2.10 In the design of a particular integrated circuit, the aluminum interconnect lines are constrained to have 1- m thickness. Any line is subject to certain failure (by becoming an open circuit) if it regularly carries a current density that exceeds 5 10 5 A / cm 2 ....
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This note was uploaded on 09/26/2010 for the course EE 457 at USC.