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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**

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