A capacitor of capacitance `54 mu F` is charged ot a potential of 25 V and then connected to a 15 mH inductor to produce oscillations. What was the energy stored in the capacitor initially and to what wavelength will the circuit respond ?

Explanation

Here, `C = 10 mu f = 100 xx 10^(-6) F = 10^(-4) F`
`V = 50 V, L = 10 mH = 10 xx 10^(-3) H = 10^(-2) H`
As `(1)/(2) LI^(2) = (1)/(2) CV^(2)`
`:. I = sqrt((C )/(V)) V = sqrt((10^(-4))/(10^(-2))) xx 50 = 5 A`
`v = (1)/(2 pi sqrt(LC)) = (1)/(2 pi sqrt(10^(2) xx 10^(-4)))`
` = (1000)/(2 pi) = (500)/(pi) Hz`
Here, `C = 54 mu F = 54 xx 10^(-6) F`
`V = 25 V, L = 15 mH = 15 xx 10^(-3) H`
Energy stored initially is
`U = (1)/(2) CV^(2) = (1)/(2) xx 54 xx 10^(-6) (25)^(2)`
` = 1.687 xx 10^(-2) J`
Frequency of oscillations produced.
`v = (1)/(2 pi sqrt(LC)) = (1)/(2 xx 3.14 sqrt(15 xx 10^(-3) xx 54 xx 10^(-6))`
`= (10^(4))/(6.28 xx 9) = 176.8 Hz`