Calculating Capacitance in Parallel Circuits with AC Generator

[phys62]

Homework Statement

Two identical capacitors are connected in parallel to an ac generator that has a frequency of 660 Hz and produces a voltage of 27 V. The current in the circuit is 0.14 A. What is the capacitance of each capacitor? Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise.

Homework Equations

Z = x of c = V/I
x of c = 1/(2pi*fc)

The Attempt at a Solution

x of c = 27V /.14A = 192.86 ohms

192.86 ohms = 1 / (2pi*fc) = 1 / (6.28*(660)c) = 1/(4144.8 x c)
c=1.25 uF

1.25uF equals the capacitance of the two identical capacitors connected in parallel.
The capacitance of each capacitor equals 1.2uF/2 = .625 uF

This answer is incorrect, but I have absolutely no idea what I'm doing wrong.. Thanks for any help!

 

[Delphi51]

Looks okay to me!

 

[phys62]

They're asking me to submit my answer in units of F, and I think I may just have my decimal point in the wrong place... (I submitted .625 F). And now I'm confusing myself a lot as to where the decimal place really should be. Should my final answer actually be 6.25x10^-13 F?

6.25x10^-7 uF x (1x10^-6 F / 1 uF) = 6.25x10^-13 F ?

 

[Delphi51]

micro means 10^-6
.625 uF = .625 x 10^-6 F = 6.25 x 10^-7 F

 

[phys62]

Whew, dumb mistake on my part. Thanks!