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## Homework Statement

Analyze a series RLC circuit and determine the voltage across each element due to the transient response. The circuit is powered by a square wave voltage source with a peak-to-peak voltage of 4V and frequency of 1kHz.

R=50 kohms

L=33mH

C=1 nF

## Homework Equations

Since this circuit turns out to be overdamped:

I(t)=A

_{1}e

^{s1*t}+A

_{2}e

^{s2*t}

Alpha=R/(2L)

Omega_0=1/(sqrt(L*C))

S1=-alpha+sqrt((alpha^2)-(omega_0^2))

S2=-alpha-sqrt((alpha^2)-(omega_0^2))

I=V/Z

X_L=2*pi*f*L

X_C=1/(2*pi*f*C)

## The Attempt at a Solution

I have tried to solve this the best I can, but the results do not seem to come out right. I did an experiment using the circuit, so I'm comparing the calculated results to the experimental values and I am fairly confident in the experiment. I've summarized my work below, please let me know where I am going wrong.

V(0)=-2V

I(0)=-2/Z=-2/sqrt(((X_L-X_C)^2)+(R^2))=-1.20029E-5

since I(0)=A1+A2, A1=I(0)-A2

at T=0, di/dt=0

di/dt=s1A1+s2A2==>s2A2+s1(I(0)-A2)

A2=-(S1*I0))/(S2-S1)

solving for A1 and A2 give

I(t)=1.2169E-5e^(s1t)-1.65E-7e^(s2t)

Vr(t)=I(t)*R

Vc(t)=I(t)*X_C

Vl(t)=I(t)*X_L