Calculating Capacitance of LC Circuit

AI Thread Summary
The discussion revolves around calculating the capacitance of an LC circuit with a 30H inductor, where the voltage depletes to zero in 20 seconds. The resonant frequency was calculated as 0.0125 Hz, leading to an angular frequency of 0.0785 rad/s. The capacitance was determined to be 5.404 Farads using the formula C = 1/(ω^2 * L). A key point of confusion was the calculation of the cosine function in radians versus degrees, which was clarified during the discussion. Ultimately, the correct capacitance value was confirmed as 5.404 Farads.
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Homework Statement



Calculate capacitance of LC Circuit where:

Inductor - 30H
Capacitance voltage fully charged goes to zero in 20 seconds

Homework Equations



Main Eq: V=V. *cost(ωt) where V is final Voltage, V. = Voltage initial, ω = resonant angular frequency

ω = 1/√(LC) = 2∏f

f. = 1/2∏√(LC) --> resonance frequency

The Attempt at a Solution



Calculated f=1/80 =0.0125Hz as voltage of capacitor takes 20s to deplete 1/4 cycle
∴ ω = 2∏*0.0125=0.0785

Rearranged angular frequency equation to solve for C
∴C=1/(ω^2 * L) = 5.404F

Since Voltage = 0 after t = 20s = 1/3min,

V=V. *cost(ωt)
0=V.*cos(0.0785*(1/3))

Since the whole equation is multiplication, calculating V. would not be required since if cos equaled 0 then so would the whole right hand side of the equation. However cos equals close to 1 and therefore I'm stuck.

Please help

Thank you

Edit: Thread has been answered and I'm correcting my mistake for those reading this post as a reference on how to answer this type of question. Mistake was in the calculation of main equation:

V=V.*cost(ωt)
0=V.*cos(0.0785rad/s*20s) --> Calculate using radian mode on calculator
0=V.*0.00
0=0 --> as anything multiplied by 0 is equal to 0

Answering main question of this thread...

Capacitance = 5.404 Farards
 
Last edited:
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Check your calculator for degrees versus radians setting.
 
gneill said:
Check your calculator for degrees versus radians setting.

Hi,

I checked by calculating cos in radians and degrees but both equal a figure close to one but i need it to equal zero.

Thank you
 
omer10000 said:
Hi,

I checked by calculating cos in radians and degrees but both equal a figure close to one but i need it to equal zero.

Thank you

Your ω is in units of radians per second. Your time should be specified in seconds, not fractions of a minute.
 
gneill said:
Your ω is in units of radians per second. Your time should be specified in seconds, not fractions of a minute.

Alright I got it.

V=V.*cos(ωt)
0=V.cos(0.0785rad/s * 20s)
0=V.*0.001=V.*0
0=0

Thanks for the help gneill, I suppose the above therefore is correct.

Answering the main question of this thread;

Capacitance = 5.404 Farads

Thank you
 
Last edited:
Yes, that looks good :smile:
 
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