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 7 Due 4 12 06 Problem 1 The fuse element is a resistor of resistance Rf which is destroyed when the current through it exceeds a certain value The circuit below has such a fuse in it The switch in the circuit has been in the closed position for a long time At time t 0 the switch is opened If the maximum current that can flow through the fuse is Im calculate the minimum resistance of the fuse Rf as a function of Im and the other circuit parameters R2 t 0 R1 Vs L Rf Problem 2 For the circuit below determine the values for resistors R1 and R2 so that vR2 t 0 12V and vR 2 t 2ms 6V vR2 R1 2A 6 071 22 071 Spring 2006 HW7 t 0 R2 47mH Problem 3 For the following circuit the switch S has been opened for a long time At time t 0 the switch is closed and it is opened again at time t 1 sec Sketch vc t for all t Indicate all relevant values in your sketch S 5k 50k 12 V vc 10uF Problem 4 The capacitors in the following circuit are independent They can not be combined into an equivalent capacitance A Derive the equations for the node voltages v1 and v2 B Assume a solution of the form Ae st and show that this circuit can not exhibit undedamped oscillatory behavior Note that you are not given any initial conditions since you do not need them to solve this problem v1 v2 R1 C1 R2 C2 R3 Problem 5 The switch S1 has been in position A for a very long time At t 0 the switch is moved from position A to position B Sketch the voltage vc t and the current i t Use Vs 10V R 100 L 2H C 0 1F Label all relevant values R L A B Vs 6 071 22 071 Spring 2006 HW7 i t C vc t
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