Question

show the variation of emf and current with respect to wt in capacitive circuit with the help of graph? ​

Answer 1

Variation of EMF and current in Alternating Current with a capacitor:

$\setlength{\unitlength}{1cm}\begin{picture}(6, 6)\put(2,4 ){\vector(0, -1){3}}\put(1, 3){\vector(1, 0){3} (I_{c}) }\put(2,1){\rm (V_{c}) }\put(4,1){\rm(V-I\: Waveform)}\put(3,2){ {90}^{\circ} }\end{picture}$

Let voltage variation be :

$V = V_{0} \sin( \omega t)$

Let current through the circuit be i ;

$\therefore \: i = C \dfrac{dV}{dt}$

$= > \: i = C \dfrac{d \{V_{0} \sin( \omega t) \} }{dt}$

$= > \: i = CV_{0} \dfrac{d\sin( \omega t)}{dt}$

$= > \: i = CV_{0} \omega \cos( \omega t)$

$= > \: i = CV_{0} \omega \sin( {90}^{ \circ} + \omega t)$

So , current leads voltage by 90°.

Refer to the attached diagram.