A device 'X' is connected to an ac sourde `V = V_(0) sin omegat`. The variation of voltage, current
and power in one cycle is shown in the following graph:

(a) Identify the device 'X'
(b) Which of the curves A,B and C represent the valtage , current and the power consumed
in the circuit ? Justify your answer.
(c) How does its impendence very with frequency of the source ? Show graphically.
(d) Obtain an expression for the current in the circuit and its phase relation with ac voltage.

Explanation

(a) X is a capacitor as current is leading by an angle of `pi//2`.
(b) Curve A `to` Power
Curve B ` to` Emf
Curve C `to` Current
(c) For capacitor,
Impendence,
`X_(c) = (1)/(wC)`
`rArr X_(c) = (1)/(2pi f_(c))`

(d) Let capacitor of capacotance C is connected with a source whose emf is given by :
`V = V_(0) sin omega t`
The emf across the capacitor is given by,
`V = (q)/(c) therefore (q)/(c) = CV sin omega t`
`q = CV_(0) sin omegat rArr (dq)/(dt) = CV_(0) (d(sin omegat))/(dt)`
`I = ComegaV_(0) sinomegat rArr 1 = (V_(0))/((1)/(Comega)) (sumsin (omegat + (pi)/(2))`
Here, ` (1)/(Comega)` is the resistance offered by a capacitor for A.C. called capacitive reactance
`(X_(C))` .
`therefore I = (V_(0))/(X_(0)) sin (omega + pi//2)`
Now, ` (V_(0))/(X_(c)) = I _(0) therefore I = I _(0) sin (omegat + pi//2)`
`rArr phi ` = phase `lt pi//2`. Current leads the voltage by `pi//2` .