Find the natural frequency of a circuit containing inductance of `100 mu` H and a capacity of 0.01 mu F`. To which wavlength, its response will be maxmum ? For how long will the oscillations continue ?

Explanation

Here, E = 100 sin 314 t. In a capacitor. Current leads the applied e.m.f. by a phase angle of `90^(@)`
`:. I = I_(0) sin (314 t + 90^(@)) = (E_(0))/(1//omega C) cos 314 t`
` = 100 xx 314 t xx 637 xx 10^(-6) cos 314 t`
`= 20 cos 314 t` Instantaneous power = EI
`= 10 sin 314 t xx 20 cos 314 t`
`= 1000 (2 sin 314 t cos 314 t)`
`= 1000 (sin 628 t)` watt
Max. energy stored ` = (1)/(2) CE_(0)^(2)`
` = (1)/(2) xx 637 xx 10^(-6) (100)^(2) = 3.185 J`