High-pass filter output voltage calculation

[Guest Sherial]

Hello,

I have a question that is on a study guide for a final exam.

In a high-pass filter, Xc = 500 Ω and R=2.2kΩ. What is the output voltage (Vout) when the input voltage (Vin)=10 V.

The given answer is 9.75 /_ 12.8 degrees. I cannot get this answer from my calculations below.

I have calculated it two different ways and come up with two different answers that don't match the given one.

Z= √(500^2+2200^2)=2256.1Ω

10V/2256.1Ω= 4.4 mA

Vr =.0044*2200=9.68 V
VXc=.0044*500= 2.2 V

Tan^-1 (2.2/9.68)=12.80

When I plug the numbers into my TI-89 to get the polar coordinates I get 9.92/_12.8 degrees

Second try

10V/2700Ω= 3.7 mA

Vr=.0037*2200=8.14 V
VXc=.0037*500= 1.85 V

Tan^-1 (1.85/8.14)=12.80

When I plug the numbers into my TI-89 to get the polar coordinates I get 8.34/_12.8 degrees

I have been pulling my hair out for the last couple days trying to figure this one out.

Thanks for the help

[Lyker]

You are just chopping off to many digits on the current.
Your current is 4.432mA not just 4.4mA

So....
4.432mA * R(2k2) = 9.75V
4.4mA  * R(2k2) = 9.68V