PROBLEMS Circuit Basics As a review of the basics of circuit analysis and in order for the readers to gauge their preparedness for the study of electronic circuits, this section presents a number of relevant circuit analysis problems. For a summary of Th´evenin’s and Norton’s theorems, refer to Appendix D. The problems are grouped in appropriate categories. Resistors and Ohm’s Law 1.1 Ohm’s law relates V, I, and R for a resistor.

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For each of the situations following, find the missing item: (a) (b) (c) (d) R = 1 k, V = 5 V V = 5 V, I = 1 mA R = 10 k, I = 0.1 mA R = 100 , V = 1 V Note: Volts, milliamps, and kilohms constitute a consistent set of units. 1.2 Measurements taken on various resistors are shown below. For each, calculate the power dissipated in the resistor and the power rating necessary for safe operation using standard components with power ratings of 1/8 W, 1/4 W, 1/2 W, 1 W, or 2 W: (a) (b) (c) (d) (e) (f) 1 k conducting 20 mA 1 k conducting 40 mA 100 k conducting 1 mA 10 k conducting 4 mA 1 k dropping 20 V 1 k dropping 11 V 1.3 Ohm’s law and the power law for a resistor relate V, I, R, and P, making only two variables independent. For each pair identified below, find the other two: (a) (b) (c) (d) (e) R = 1 k, I = 5 mA V = 5 V, I = 1 mA V = 10 V, P = 100 mW I = 0.1 mA, P = 1 mW R = 1 k, P = 1 W Combining Resistors 1.4 You are given three resistors whose values are 10 k, 20 k, and 40 k. How many different resistances can you create using series and parallel combinations of these three? List them in value order, lowest first. Be thorough and organized.

(Hint: In your search, first consider all parallel combinations, then consider series combinations, and then consider series-parallel combinations, of which there are two kinds.) 1.5 In the analysis and test of electronic circuits, it is often useful to connect one resistor in parallel with another to obtain a nonstandard value, one which is smaller than the smaller of the two resistors. Often, particularly during circuit testing, one resistor is already installed, in which case the second, when connected in parallel, is said to “shunt” the first. If the original resistor is 10 k, what is the value of the shunting resistor needed to reduce the combined value by 1%, 5%, 10%, and 50%? What is the result of shunting a 10-k resistor by 1 M? Voltage Dividers 1.6 Figure P1.6(a) shows a two-resistor voltage divider. Its function is to generate a voltage VO (smaller than the power-supply voltage VDD ) at its output node X.

The circuit looking back at node X is equivalent to that shown in Fig. Observe that this is the Th´evenin equivalent of the voltage-divider circuit. Find expressions for VO and RO.

Joe crackers mendino. VDD R1 RO X X VO R2 VO RO (a) (b) Figure P1.6 1.7 A two-resistor voltage divider employing a 2-k and a 3-k resistor is connected to a 5-V ground-referenced power supply to provide a 2-V voltage. Sketch the circuit. Assuming exact-valued resistors, what output voltage (measured to ground) and equivalent output resistance result? If the resistors used are not ideal but have a ±5% manufacturing tolerance, what are the extreme output voltages and resistances that can result?

= Multisim/PSpice; * = difficult problem; ** = more difficult; *** = very challenging; D = design problem PROBLEMS D 1.8 You are given three resistors, each of 10 k, and a 9-V battery whose negative terminal is connected to ground. With a voltage divider using some or all of your resistors, how many positive-voltage sources of magnitude less than 9 V can you design? List them in order, smallest first. What is the output resistance (i.e., the Th´evenin resistance) of each? CHAPTER 1 46 Chapter 1 Signals and Amplifiers D *1.9 Two resistors, with nominal values of 4.7 k and 10 k, are used in a voltage divider with a +15-V supply to create a nominal +5-V output. Assuming the resistor values to be exact, what is the actual output voltage produced? Which resistor must be shunted (paralleled) by what third resistor to create a voltage-divider output of 5.00 V?