# Calculating Capacitance of LC Circuit

## 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.

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.*0.00
0=0 --> as anything multiplied by 0 is equal to 0

Capacitance = 5.404 Farards

Last edited:

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gneill
Mentor

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

gneill
Mentor
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.

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.*0.001=V.*0
0=0

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

Yes, that looks good 