ColorGrayscale Jeffrey Schiano 2014. All rights reserved. Rec 1. EE 350Continuous-Time Linear SystemsRecitation 11 Jeffrey Schiano 2014. All rights reserved. Rec 1. Recitation 1 Topics• EE 210 Review– Branch Relationships for Inductors and Capacitors– Switched RC Circuits– Switched RLC Circuits– Sinusoidal Steady-State Analysis2 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 1(A)• Consider the capacitor shown below1. What is i(t) in terms of v(t)?2. What is the energy stored in the capacitor?3. What is v(t) in terms of i(t)?4. Can v(t) change instantaneously? Why?5. Can i(t) change instantaneously?6. What is the phasor representation of the capacitor branch relationship?7. Derive the result in part 6.3C()vti( )t Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 1(A) Solution4 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 1(A) Solution5 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 1(A) Solution6 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 1(B)• Consider the inductor shown below1. What is v(t) in terms of i(t)?2. What is the energy stored in the inductor?3. What is i(t) in terms of v(t)?4. Can i(t) change instantaneously? Why?5. Can v(t) change instantaneously?6. What is the phasor representation of the inductor branch relationship?7. Derive the result in part 6.7L()vti( )t Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 1(B) Solution8 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 1(B) Solution9 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 1(B) Solution10 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 2• Consider the RC circuit below, where the switched has been opened a long time before it is closed at time t = 0.1. Determine v(0) and i(0) 2. Determine v(0+) and i(0+) 3. Determine v() and i() 4. Obtain an ODE that describes the response of v(t) for t 01160V5k10k0t10ki( )t 250 F()vt Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 2 Solution12 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 2 Solution13 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 2 Solution14 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 2 Solution15 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 3• Consider the RLC circuit below, where the switched has been closed a long time before it is opened at time t = 0.1. Obtain an ODE that describes the response of i(t) for t 0.2. Determine the initial conditions, i(t) and di/dt at time t = 0+. 3. Determine i(t) after the switch has been opened a long time.16i( )t2F2V11H10t Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 3 Solution17 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 3 Solution18 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 3 Solution19 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 3 Solution20 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 4• Consider the network below with input f(t) and output y(t)1. Determine an expression that relates the phasorrepresentations of the input and output signals.2. Determine the sinusoidal steady-state response y(t) for3. What type of filter does the network realize?21()ftR = 1k()ytL = 1mH68( ) 10cos 10 90 100cos 10 45ft t t Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 4 Solution22 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 4 Solution23 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 4 Solution24 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 4 Solution25 Jeffrey Schiano 2014. All rights reserved. Rec 1. EE 350Continuous-Time Linear SystemsRecitation 11 Jeffrey Schiano 2014. All rights reserved. Rec 1. Recitation 1 Topics• EE 210 Review– Branch Relationships for Inductors and Capacitors– Switched RC Circuits– Switched RLC Circuits– Sinusoidal Steady-State Analysis2 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 1(A)• Consider the capacitor shown below1. What is i(t) in terms of v(t)?2. What is the energy stored in the capacitor?3. What is v(t) in terms of i(t)?4. Can v(t) change instantaneously? Why?5. Can i(t) change instantaneously?6. What is the phasor representation of the capacitor branch relationship?7. Derive the result in part 6.3 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 1(A) Solution4 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 1(A) Solution5 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 1(A) Solution6 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 1(B)• Consider the inductor shown below1. What is v(t) in terms of i(t)?2. What is the energy stored in the inductor?3. What is i(t) in terms of v(t)?4. Can i(t) change instantaneously? Why?5. Can v(t) change instantaneously?6. What is the phasor representation of the inductor branch relationship?7. Derive the result in part 6.7 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 1(B) Solution8 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 1(B) Solution9 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 1(B) Solution10 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 2• Consider the RC circuit below, where the switched has been opened a long time before it is closed at time t = 0.1. Determine v(0) and i(0) 2. Determine v(0+) and i(0+) 3. Determine v() and i() 4. Obtain an ODE that describes the response of v(t) for t 011 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 2 Solution12 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 2 Solution13 Jeffrey Schiano 2014. All rights reserved. Rec 1. Problem 2 Solution14 Jeffrey Schiano 2014. All rights reserved.
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