20095ee102_1_EE102 HW-2

20095ee102_1_EE102 HW-2 - v(t) ? (Assume that the...

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EE 102 SYSTEMS & SIGNALS HOMEWORK # 2 Posted: 10.07.09 Due: 10.14.09 (in lecture) 1) For the RC circuit shown in the figure; R=1000 ohms C=1 micro Farad Calculate the response v(t) to the input; u(t) = (cos(120 π t)) 2 , t > 0 for an initial voltage across the condenser: v(0) = 5 Volts. What is the steady state response? 2) Find the output voltage at t = 1 sec. v(1) = ? For t > 1 , the input changes to zero from then on, i.e.; u(t) = (cos(120 π t)) 2 , 0 < t < 1 u(t) = 0 , t > 1 What is the response v(t) for t > 1 ? How long does it take the output voltage to become (1/100)v(1) ? What would be the effect of increasing the resistance on the output voltage
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Unformatted text preview: v(t) ? (Assume that the resistance is increased at t = 1 , comment on how the output voltage is affected for t &gt; 1 ?) 3) In MATLAB or similar program; plot the input and the output in problems 1 and 2 (in separate figures), showing the steady state part and the transient part. (For problem 2; plot for t &gt; 1 ) 4) For the same RC circuit in problem 1; assume that we only know the value of the resistor, and the input is zero, u(t) = 0 for t &gt; 0. If you observe that; v(1) / v(0) = e-2 What is the value of C in terms of R ?...
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