ECET SA Week 4

# ECET SA Week 4 - 5 milliseconds. (Hint: use the MATLAB...

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ECET-305 Supplementary Assignment 4 (version 2) Laplace Transform Applications in Electronic Circuits 1. Consider the series RLC circuit shown below. Suppose the switch has been in the position shown for a long time. Recall that capacitance is defined as where Q(t) is the charge on the capacitor at time t and V c (t) is the voltage across the capacitor at time t. Recall also that the current at a point in a circuit is . At t = 0, the switch is thrown, connecting the input side of the circuit to ground. a. What is the initial charge on the capacitor; that is, Q(0)? Solution: Vc(0) is equal to 12V as it is fully charged. Q(0) is: b. Write and solve the differential equation for the charge across the capacitor, Q(t) for . (Assume that the current is zero at t = 0.) Solution: We have: c. Using MATLAB, plot the voltage across the capacitor, V c (t), versus t from t = 0 to

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Unformatted text preview: 5 milliseconds. (Hint: use the MATLAB function ezplot . See the help file for the function and/or see the tutorial in Doc Sharing.) Solution: We have the plot: 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 10-3-10-8-6-4-2 2 4 6 8 10 t (12 (cos(500 1999 1/2 t) + (1999 1/2 sin(500 1999 1/2 t))/1999))/exp(500 t) 2. Repeat the analysis of the RLC circuit as given in the previous problem but replace the 2 ohm resistor with a 100 ohm resistor. a. Find the voltage across the capacitor, V cap (t), for t &gt; 0. Solution: We have: b. Using MATLAB, plot V c (t) versus t from t = 0 to t = 500 microseconds. Solution: We have the plot: 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 10-4 2 4 6 8 10 12 t (12 (cosh(5000 5 1/2 t) + 5 1/2 sinh(5000 5 1/2 t)))/exp(25000 t) Circuit for Problems 1, 2 L1 2mH C1 1uF R1 2 J2 Key = Space V1 12 V...
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## This note was uploaded on 01/09/2012 for the course ECET 305 taught by Professor Unknown during the Fall '11 term at DeVry Addison.

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ECET SA Week 4 - 5 milliseconds. (Hint: use the MATLAB...

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