# Homework Help: Overdamped Series RLC Circuit Transient Response

1. Jun 7, 2009

### lvjudge

1. The problem statement, all variables and given/known data
Find the voltage across each component is an overdamped RLC circuit. The circuit is powered by a square wave of peak voltage 2 V. The square wave is used to model a DC source.

2. Relevant equations

Vs(0)=-2 (Everywhere else in the transient response, Vs=2)
i(t)=Ae^(s1t)+Be^(s2t)
i(0)=0
Vr(t)=i*R
Vr(0)=0
Vl(t)=L*(di/dt)=L*(As1e^(s1t)+Bs2e^(s2t))
Vl(0)=0
Vc(0)=1/C *∫i dt =1/C *(A/s1 e^(s1t)+B/s2 e^(s2t))
Vc(0)=-2

3. The attempt at a solution

Using the above equations, A=-B and B=(-2*C*s1*s2)/(s1-s2)

As part of my assignment, I created a simulation of the circuit in MultiSim. For some reason that I cannot figure out, at every point in time, Vr and Vl calculated using the above equations are half the voltage that I found in the simulation! Meanwhile the calulated and simulations value for Vc are off by varying amounts at each time interval! Needless to say, I am very confused. A screen shot of the MultiSim circuit is attached for evalution. In the simulation, I used the oscilloscope to measure the voltages at different times. It would be very very helpful if someone could tell me whether my math is wrong or my circuit is wrong.

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