Massachusetts institute of Technology Department of Nuclear Science and Engineering Department of Electrical Engineering and Computer Science 22 071 6 071 Introduction to Electronics Signals and Measurement Spring 2006 Homework 2 Due 2 22 06 Problem 1 A voltage divider is formed with resistors R1 and R2 A voltmeter is used to measure the voltage across resistor R2 The following table gives the values for the measured voltage Vo as a function of resistors R1 and R2 and the ideal voltage source VB VB Volts 5 5 5 5 R1 Ohms 1000 10000 100000 500000 R2 Ohms 1000 10000 100000 500000 Vo Volts 2 498 2 475 2 273 1 667 1 From these data develop a simple circuit model for the voltage measuring device 2 Give the parameters for an ideal voltmeter i e a device which for the above cases will always measure 2 50 Volts Problem 2 We know have an ideal voltmeter and we measure the voltage across R2 with the following results VB Volts 5 5 5 5 R1 Ohms 1000 10000 100000 500000 R2 Ohms 1000 10000 100000 500000 Vo Volts 1 667 2 381 2 488 2 498 1 Now develop a simple model for the voltage source 2 How would you design an ideal voltage source Problem 3 The hatched rectangles in the circuit below represent general two terminal elements with the polarity and voltage drop across them as indicated Use Kirchhoff s laws to determine the unknown voltages V1 V2 V3 V4 4V V1 2 V 3V V2 V4 V3 4V Problem 4 Find the equivalent resistance of the following resistor networks at the terminals A B A 30 20 Req 10 5 B 10 30 40 A 30 Req 10 B R R 20 R R R A R Req B R R R R Hint 1
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