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. t=0+-VsR2R1RfL Problem 2. For the circuit below determine the values for resistors R1 and R2 so that and 2( 0 ) 12vR t V+==2( 2 ) 6vR t ms V== 2 At=0R2R147mH+ vR2 - 6.071/22.071 Spring 2006, HW7Problem 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. 10uF 50kΩ 5kΩ 12 V+-vc+-S 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 stAe 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) C1C2R1R2R3v1 v2 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=100Ω, L=2H, C=0.1F. Label all relevant values. ABVsRLCvc(t)+-i(t) 6.071/22.071 Spring 2006,
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