# Differential equations - 2

Discussion in 'Homework Help' started by MrRockchip, May 27, 2010.

1. ### MrRockchip Thread Starter New Member

May 25, 2010
18
0
This circuit is more difficult, because E is not constant.
I know that ,
also e(0-), e(0+) and e(t).
But how to create the differential equation for Uc using all this information?

http://myimgs.net/images/izuk.jpg

2. ### MrRockchip Thread Starter New Member

May 25, 2010
18
0
Please, help me; I've tried to solve it but my results are completely wrong
This task seems to be a lot more difficult than the previous one

3. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
782
I guess your problems are arising from not knowing how to treat the time varying sinusoidal forcing function - rather than a constant forcing function.

I presume you are required to solve it using differential equations ...

A couple of suggestions on how I might firstly solve for the steady state part of the solution .....

1. Reduce the sinusoidal source and the two resistors R1 & R2 to a Thevenin equivalent. Then you have a source, a single resistor and the capacitor all in series.

2. Write down the differential equation (DE) for the equivalent circuit with the capacitor voltage Vc(t) as the variable to be solved.

3. Assume a solution of the form Vc(t)=Acos(ωt) + Bsin(ωt) and plug this into your DE. Then solve for the unknowns A & B.

4. You then have the steady-state solution.

Since the source is non zero at t=0 there will be a transient component you will have to solve for as well. You would assume a transient part solution for the capacitor voltage of the form Vc(t)=Kexp(-t/RC). It has this form since it is a first order circuit and there would be no steady state offset in the complete [transient + steady-state] final value of Vc(t).

This isn't a trivial exercise and will require some time and effort.

MrRockchip likes this.
4. ### MrRockchip Thread Starter New Member

May 25, 2010
18
0
Will I get the correct result if solve this circuit for the constant E and then (at the end)
just put in the answer that e(t)=200*sin(10000*t+45degrees) ?

5. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
782
I'm not sure where you got that answer, but it's not the answer to the problem you posted.

The input source voltage is a sinusoid with maximum value of 14.4 V. It's impossible that the output (capacitor voltage) would be a sinusoid with a maximum of 200 V.

Perhaps you should check what you posted or your source for the answer.

6. ### MrRockchip Thread Starter New Member

May 25, 2010
18
0
Is it correct to solve this circuit for constant e(t) and then make it AC to get the final answer?