Calculating Equivalent Impedance in a Simple AC Circuit - Step-by-Step Guide

[tabsquare]

hello I have a problem in calculating the equivalent impedance of a simple AC circuit, where the impedances are:

Z1 = 5+i20
Z2 = 5+i20
Z3 = 10-i2,5
Z4 = -i10
Z5 = 5

and I need to find:


Z_eq = Z3 // [(Z1 // Z4) + (Z2 // Z5)]

where the + indicates 2 components in serie and the // indicates 2 components in parallel.


My calculations always bring me to
Z_eq=6,25-i3,75


but my book says Z_eq=28,33.


Which is the correct eqv impedance?


Thank you
PS-I used the formula Za//Zb = (Za*Zb)/(Za+Zb)
to calculate equivalent impedances of two components in parallel, and the sum for components in serie.

 

[The Electrician]

Well, there's a mistake somewhere.

If I use the values you gave for Z1 to Z5, I get the same result you did.

However, if you set Z3 = 5 + i20, then you will get the result in the book.

 

[tabsquare]

Ok then there probably is a mistake in the book because Z3 is in fact equal to 10-i2,5 as I calculated and as the book reports. Lost some time on this stupid mistake...

Thank you very much for taking the time to verify this! :)

Riccardo