Solving a Complex Circuit Equation

jonlg_uk · Feb 8, 2012

Homework Statement

I have the following circuit...

Circuit schematic with a voltage source E1 at top right, resistors R1, R2 and R3, capacitor C1, and voltmeters U1 and U2 across R3 and R2 respectively.

I have managed to derive an equation for U2:

$Equation for U2 as a fraction: numerator R2 E1 + j w C1 R2 R3 E1, denominator R1 + R2 + j w C1 (R1 R2 + R1 R3 + R2 R3).$

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

I have defined U1 as:

$Equation: U1 = R3 / (R3 - j/(omega C1)) times U2, written as a fraction with R3 in the numerator.$

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:

$Circuit solved: U1 equals R2 R3 E1 divided by (R1 R2 + R1 R3 + R2 R3 - j (R1/(w C1) + R2/(w C1))), written as a typeset fraction.$

However I cannot simply 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.

I thank you in advance.

jonlg_uk · Feb 9, 2012

Wow 380 hits and no-one can solve it. I was up until 3am last night trying to do this and still couldn't get U1 looking like the simulator produced. I would be massively grateful if someone, with better mathematical skills than me have a go at solving this, its driving me BONKERS.

Solving a Complex Circuit Equation

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