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jools111
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Homework Statement
For a series circuit with the following components:
1. Vin(t)
2. 1K resistor
3. 100 mH Inductor
4. 1 uF capacitor
1. Write down the differential eqn. for Vc in the circuit.
2. Solve the DE, calculate the natural and forced response with the following initial conditions: Vc(0) = 0 and dVc(t)/dy = 0
3. Explain the difference between theoretical and experimental results.
Homework Equations
This was the signal we applied in the lab:
Vin(t) = (1V)sin(2∏(2 kHz)t)u(t)
The Attempt at a Solution
This is what I have for the DE:
dv(t)/dt + (1/RL)Vl(t) + (C/R)d^2Vc(t)/dt^2 = 0
This is for a lab where we have to compare theoretical value to measured value, and apparently they are supposed to be different.
I think it's right... but I'm not positive. I'm a little confused because there are 4 different voltages in the circuit (Vl, Vc, Vr, and Vtot), and I'm getting tripped up as to which one I'm solving for. I know that I should take the DE and set it equal to the initial conditions in order to solve for the forced and natural responses, but I really need a little push here to get started. Any help would be appreciated. Thanks.