Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6 002 Circuits and Electronics Spring 2003 Handout S03 037 Homework 7 Issued Wed Mar 19 Due Fri Apr 4 Problem 7 1 The circuits below are driven by either step functions or impulse functions In each case determine the initial t 0 and final asymptotic values of the designated voltages and or currents Label your answers clearly R A i Vu 1 t v L B Iu 1 t R i L v i C Qu0 t R v C 2R D u0 t R E v C 2R i Qu0 t R L v Problem 7 2 Pick any three of the five circuits shown in Problem 7 1 For each of your choices sketch and dimension the indicated voltages and currents for t 0 Evaluate time constants in terms of circuit elements Label your drawings clearly including the designation A B E of your choices Endeavor to do this problem without formally solving the differential equations Problem 7 3 The gray box shown below contains only linear circuit elements and satisfies the strict definition of linearity u0 t a b GRAY vI vO BOX a b When the box is initially without stored energy and is driven by a unit voltage inpulse at the terminals aa0 as shown the response of the voltage vO for t 0 is vO t 2 3 2 t vO t e 3 for t 0 0 t A Determine the response vO t when the input vI at aa0 is a step of amplitude V vI V u 1 t B The input to the box is shown below vI t V 0 T t Determine the output voltage vO t for t 0 Note that a response to a delayed input can be written as v t u 1 t T f t T where f t is the response to an excitation at t 0 and T is the time the input is delayed The multiplier u 1 t T ensures that there is no reponse for t T Hint Resolve the input into the sum of three inputs each of which is a scaled singularity function Problem 7 4 The LC circuit below is driven by an impulse i Qu0 t v C L A Determin v 0 and i 0 B At t 0 What is the sign of the first derivative of v What is the sign of the first derivative of i C Note that for t 0 the circuit is i L v C Write a differential equation for v t or i t and solve it Express both v t and i t as functions of time
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