Phasor transformation

[Joe Bachi]

Hey guys,
I attempted to solve the following exercise but i'm pretty sure i messed up somewhere because my answers just don't seem to add up
Can you please check my work?
Hope the pictures are clear enough



1) Express L, using R, C, and w so that R(equivalent) of AC is a pure resistor
2) Knowing that E(0)=180V, Find the amplitude of the main current I(0)
3) Find the amplitudes of U(AB) and U(BC)

Thank you in advance for your help

 

[Harald Kapp]

Your error is in the first line of computing the parallel circuit of R and C.
Two impedances in parallel are calculated as

1/Ztotal = 1/Z1 + 1/Z2 where Z1, Z2 are the impedances of the resistor and the capacitor.

The impedance of a capacitor is Zc = 1/jwC

Therefore:
1/Ztotal = 1/R + jwC

With that in mind, do your calculations again. If they still don't add up, show us the new results.

 

[Joe Bachi]

Zc=1/jwC which is the equivalent to Zc=-j/Cw (by multiplying by j)

 

[Laplace]

I arrived at the same expression for L as you did so you seem to be on the right track.

 

[Joe Bachi]

I did the Fresnel representation of the circuit and my answers turned out to be the same, so i think it was right all along
Thank you all for taking the time to help