Laplace Circuit Analysis Solution

# Laplace Circuit Analysis Solution - EE 2011 Practice...

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Unformatted text preview: EE 2011 Practice Problems Laplace Circuit Analysis Q1 This circuit has been in the steady state for a long time before the switch closes at t = 0. 1. Draw the s-domain circuit for t > 0. 2. Calculate I L (s). 3. Calculate i L (t) for t > 0. I L (s) = 24/s – 96,000/(s(s + 1000)(s + 4000)) = 24(s + 5000)/((s + 1000)(s + 4000)) = A/(s + 1000) + B/(s + 4000) A = 32, B = -8 i L (t) = 32 exp(-1000 t) – 8 exp(-4000 t) 16V TCLOSE = 0 24A 125uF 2mH 3.333 i L Q2 This circuit has been in the steady state for a long time before the switch closes at t = 0. a) Draw the s-domain circuit for t > 0. a) Find I L (s) b) i L (t) for t > 0. 1. Draw the circuit in the Laplace domain, with the switch closed, and with the DC currents and voltages tagged with 1/s. Remember to include sources for the initial inductor current and capacitor voltage. 2. Replace the 24 A source and the two 2 ohm resistors with their Thevenin equivalent (48/s volts and 4 ohms) 3. Write a single KCL equation for VL to solve the circuit. (VL – 48/s)/4 + 24/s + VL s/8000 + VL 500/s = 0 Solve for VL VL = -96,000/(s^2 + 2000 s + 4*10^6) IL = 24/s + VL 500/s = (24 s^2 + 48000 s + 144*10^6)/(s(s^2 + 2000 s + 4*10^6)) = A/s + (Bs + C)/(s^2 + 2000 s + 4*10^6) A = 36 B = -12 C = -24000 IL = 36/s + (-12s - 24000)/(s^2 + 2000 s + 4*10^6) IL = 36/s -12(s + 1000)/((s + 1000)^2 + 1732^2) – 6.93(1732)/((s + 1000)^2 + 1732^2) iL(t) = (36 – 12 exp(-1000 t) cos(1732 t) – 6.93 exp(-1000 t) sin(1732 t)) u(t) 2 Ω 2 Ω 125 ufd 2 mH 16 V 24 A t = 0 i L v C Q3 The circuit below had been running for a long lime when at time t = 0 the leftmost capacitor, C 1 , failed. Surprisingly, the capacitor failed short, that is, it became a short circuit. All the energy in C 1 was dissipated in the destruction of the capacitor and we are not interested in it. Using Laplace techniques, calculate v O (t) and i g (t) for positive time. Draw two circuits, the first with vg and L1 and the second with L2, C2, and Rload (along with initial inductor currents and capacitor voltages)....
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## This note was uploaded on 04/09/2008 for the course EE 2011 taught by Professor Imbertson during the Spring '08 term at Minnesota.

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Laplace Circuit Analysis Solution - EE 2011 Practice...

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