Calculating Capacitance in Parallel Circuits with AC Generator

AI Thread Summary
The problem involves calculating the capacitance of two identical capacitors connected in parallel to an AC generator with a frequency of 660 Hz and a voltage of 27 V, resulting in a current of 0.14 A. The impedance was calculated as 192.86 ohms, leading to a derived capacitance of 1.25 microfarads for the two capacitors combined. The confusion arose regarding the correct representation of the final capacitance value, with the initial incorrect submission of 0.625 microfarads being clarified as 6.25 x 10^-7 F. The final correct capacitance for each capacitor is confirmed to be 0.625 microfarads, or 6.25 x 10^-7 F. The discussion highlights the importance of unit conversion and careful attention to decimal placement in calculations.
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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!
 
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Looks okay to me!
 
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 ?
 
micro means 10^-6
.625 uF = .625 x 10^-6 F = 6.25 x 10^-7 F
 
Whew, dumb mistake on my part. Thanks!
 

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