Hello all,

i'm doing some impedance calculations, and what was going to be prove of concept has failed . The diagrams are pretty self-explanatory:

The circuit, simulated in multisim. What i'm interested in is the output RMS voltage at probe 1 (with no load).

My calculations:

Xc = 1/(2*pi*f*c) = 1/(2*pi*100hz*1e-6) = 1591.5ohm
R = 1k ohm

for completeness:

Z1 is just the real part of Z1 which is R = 1k
Z2 is just the imaginary part of Z2 which is Xc= 1591.5 ohm

which gives me, using voltage divider formula ==> vout = 20*(Z2/(Z1+Z2)) = 20*(1591.5/(2591.5)) = 12.28v RMS

Multisim gives however 16,9 volts. I must be doing some fundimental error here. This is not homework, but seemed the best section to fit this in.

I appreciate all comments in advance! Thanks

 

I got the same answer you did.

 

Your calculation are wrong. The correct one looks like this

\(Vout=Vin*\frac{Xc}{\sqrt{R^2+Xc^2}}=20*\frac{1.59}{\sqrt{1^2+1.59^2}}=16.9V\)

 

Yep, we both forgot the j=sqrt(-1) for the capacitive reactance. Xc=-j/(2piC) which will give a phase shift and magnitude 16.9V

 

Yep, we both forgot the j=sqrt(-1) for the capacitive reactance. Xc=-j/(2piC) which will give a phase shift and magnitude 16.9V

The sqrt(-1) is not part of the reactance.

Z = R + j X

where R is the resistance and X is the reactance.

In this case, X = -1/(2piC)

 

Yes, sorry for my miswording. I'm rusty on this topic.