Explain the term 'capacitive reactance'.Show graphically the variation of capacitive reactance with frequency of the applied alternating voltage.
An `a.c.` voltage `E=E_(0) sin omegat` is applied a across a pure capacitor `C`.Show mathematically that the current flowing through it leads the applied voltage by a phase angle of `pi//2`

Explanation

Capacitve reactance:The effective resistance offered by the capacitor `C`.It is denote by `X_(C)` its is `ohm`. The graph between frequency `(v)` and `X_(C)` is shown in Fig.
`A.C.` Source Containing a capacitor:Let a source of alternating `e.m.f V=V_(m) sin wt` be connected a capacitor of capacitance `C` only.
`V=V_(m) sin wt`...(i)
At every instant the potential `V` is given by `V=q/C rArr V_(m) sin omegat=q/C`
`q=CV_(m) sin omegat`
If it is instanteious value of current in the circuit at instant `t`, then
`i=(dg)/(dt)=d/(dt)(C V_(m) sin omegat)`
`i=C V_(m) (cos omegat) omega=V_(m)/(1//omegaC)sin (omegat+pi/2)`
The current will be maximum. When `(sin omegat+pi/2)`
`therefore i_(m)=V_(m)/(1//omegaC)xx1=V_(m)/(1//omegaC), i=i_(m)sin (omegat+pi/2)`
Therefore, alternating current `i` leads the alternating voltage by a phase angle of `pi/2`.The phasor diagram for the circuit between `vecV` and `veci` at any instant `t` is shown in fig.