Find the circuit Response using Laplace Find the response (output) for t > 0 for

Question

Find the circuit Response using Laplace

Find the response (output) for t > 0 for each of the following using Laplace transform and determine the response type: V = 5V,R1 = 625 Ohm, C1 = 1 mu F, L1 = 1 mH, i L1(0) = 0, vc(0) = 0 and the output is the voltage across the inductor L1. L1 = 4 mH, L2 = 6 mH, R1 = 5k Ohm, iL1(0) = 0.8 mA, iL2(0) = 1.2 mA and the output is the current passing through R1. (The currents in the inductors are going up while the current in R1 (the output) is going down). The output is the voltage across the 48Ohm Resistor. Given: I2(s) = 168/s(s+2)(s+12)

Explanation / Answer

a) parrallel combination of C1 and L1 is Z=sL/(s^2*LC+1)

by voltage divider voltage across LC combination is Vout=v*Z/(Z+R1)

on solving voltage across L1C1 combination is Vout=v*sL/(s^2*RLC+sL+R)

on putting respective values Vout= 5s/(s^2*.000625+s+0.625)

on taking partial fractions Vout=5s/((s+0.625)*(s+1599.37))

Take the inverse Laplace of the above equation to get the output voltage in time domain

c)

Vout(s)=48*I2(s)

Vout(s)=8064/(s*(s+2)*(s+12))

Taking Partial fractions Vout(s)=336/s-403.2/(s+2)+67.2/(s+12)

Taking Inverse Laplace Vout(t)=(336-403.2*e^-2t+67.2*e^-12t)*u(t)

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