An emf `E=100 sin 314 t V` is applied across a pure capacitor of `637muF`. Find
(a) the instantaneous current `I`
(b) the instantaneous power `P`
(c ) the frequency of power
(d) the maximum energy stored in the capacitor.

Explanation

(a) Current leads over applied emf by `pi/2` in a capacitance .
`therefore I_0 = (epsi_0)/(X_C) = epsi_0 xx omega C` where `epsi_0 = 100V`
`I_0 = (100) xx (314) xx (500 xx 10^(-6))`
`I_0 = 314 xx 5 xx 10^(-2) = 15.70A`
`therefore I = I_0 sin (omega t + pi/2)` where `omega = 314 rad s^(-1)`
`I = (15.70) cos omega t A = 15.70 cos 314t A`
(b) Instantaneous power
`P = EI`
`P = (100 sin 314 t) (15.70 cos omega t)`
`= 1570 (sin 314 t) (cos 314t)`
`= 785 xx (2 sin 314 cos 314t)`
`= 785 sin 628t W`
(c ) Frequency of power
`v_P = (omega)/(2pi) = (628)/(2 xx 3.14) = 100Hz`
(d) Maximum energy stored in capacitor
`U_0 = 1/2 Cepsi_0^2`
`U_0 = 1/2 xx (500 xx 10^(-6) ) xx (100)^2`
`U_0 = 2.5J`