Homework Help: Complex Circuit Analysis Simplification

1. Feb 9, 2012

jonlg_uk

I have the following circuit....

I have managed to derive an equation for U2:

Now I want to substitute U2 into U1, in order to derive equation for U1

I have defined U1 as:

Now I substitute U2 into the above equation. This is how far I get.....I am stuck...

My circuit simulator is saying that U1 is equal to:

However I cannot simplify to get this equation. Can someone please help I have spent hours trying to get U1 to look like the U1 that the simulator produces.

2. Feb 9, 2012

Jony130

Have you try to replace R1, R2 and E2 with his Thevenine equivalent circuit ?
Eth = R2/ ( R1 + R2 ) * E1 and Rth = R1||R2

V3 = I * R3

$$I = \frac{Eth}{\sqrt{(Rth + R3)^2 + Xc^2)}} = \frac{E1*\frac{R2}{R1+R2}}{\sqrt{(R1||R2 + R3)^2 + Xc^2)}}$$

And

$$V3 = \frac{E1*R2*R3}{(R1+R2)\sqrt{(R1||R2 + R3)^2 + Xc^2)}}$$

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Last edited: Feb 9, 2012
3. Feb 9, 2012

jonlg_uk

No I haven't tried this before, but I did just try it and I still can't derive U1. Perhaps I am being stupid...

4. Feb 9, 2012

Jony130

A made a small error instead of V3 I should write U1

What is the name of your simulation program?

5. Feb 9, 2012

jonlg_uk

Thanks for your help Jony, the simulator is giving me this equation:

I haven't derived that myself^. When I expand out the equation you derived:

$$V3 = \frac{E1*R2*R3}{(R1+R2)\sqrt{(R1||R2 + R3)^2 + Xc^2)}}$$

I still not can get a the equation looking like the simulator one.