In an oscillating `L-C` circuit in which `C = 4.00muF`, the maximum potential difference capacitor during the oscillations is `1.50 V` and the maximum current through `50.0 mA`.
(a) What is the inductance `L`?
(b) What is the frequency of the oscillations?
(c) How much time does the charge on the capacitor take to rise from zero to its maximum value?

Answer

A

Explanation

a. `1/2Li_0^2=1/2CV_0^2`
`:. L=(CV_0^2)/i_0^2=((4xx10^-6)(0.5))/((50xx10^-3)^2)`
`=3.6 xx 10^-3H`
b. `f=1/(2pisqrtLC)=1/(2pisqrt((3.6xx10^-3)(4xx10^-6)))`
`=0.133xx10^4Hz`
`=1.33kHz`
c.`t=T/4=1/(4f)=1/(4xx1.33xx10^3)s`
`=0.188xx10^-3s`
`=0.188ms`