Solving A.C Circuits with complex numbers II

[mattakun]

Here is another problem that I'm not sure how to approach

A Circuit consisting of a 500 Ohm Resistor in series with a 1.2 micro F capacitor is connected to a supply at a frequency of 400Hz. Use complex numbers to determine the values of resistance R and capacitance C, that when connected in parallel will present the same value of impedance to the supply.

I'm really not very sure at all where to start here, I've drawn the circuits in series and parallel, I have the complex impedance of the series circuit:
500 - j331 but I don't know where to go from here.

Thanks.

 

[Curious3141]

You know how to calculate the reactance of a pure capacitor. When you determine the impedance of two reactances in parallel, just work it out like you would two resistances in parallel (only this time, you're using complex expressions for each reactance).

Derive an expression for the overall impedance of a parallel circuit comprising a resistance R and a capacitance C at a frequency of 400 Hz. Then compare that to the prior result and work out what R and C should be.

 

[mattakun]

This is driving me crazy, I'm using the formula Z = R(XC squared)/(R Squared) + (Xc Squared) -j (R Squared)Xc/(R Squared) + (Xc Squared)

The first section being the real number and the second being the imaginary number. By using this I can figure out the parallel impedance of an RC circuit. However the part I'm stuck on is trying to create a formula to find out what R and Xc should be to give me a specific complex number, in this case being 500 - j331.

So in otherwords I don't know how I can get the impedance 500 - j331

Thanks

 

[mattakun]

My god, after hours and hours of work trying to figure it out I've come to the conclusion that Xc = 1086 Ohms and R = 719 Ohms. in order to get the impedance 500 - j331. Not 100% sure if this is correct, but it seems to work..

All I need to do now is calculate what type of capacitor i'd need to get 1086 Xc at 400hz and hopefully this should be fine..

Thanks