Question

A device 'X' is connected to an ac sources $V=V_{0}sin\omega t$. The variation of voltage, current and power in one cycle is in the following graph:
(a) Identify the device 'X'.
(b) Which of the curves A, B and C represent the voltage, current and the power consumed in the circuit? Justify your answer.
(c) How does its impedance vary with frequency of the ac source? Show graphically.
(d) Obtain an expression for the current in the circuit and its phase relation with ac voltage.

Answer 1

A) Phase difference between V and I is $\frac{\pi }{2}$. So the device can be a capacitor.
B) Curve A represents power P=VI , where the amplitude is equivalent to the multiplication of amplitudes of V and I curve. Curve B is sine curve and represents voltage and curve C is a cosine curve representing the current.
Full cycle of the graph consist of two positive and two negative symmetrical area. So the average power consumed in the circuit is zero.
C) The AC impedance of a capacitor is known as Reactance and as we are dealing with capacitor circuits, more commonly called Capacitive Reactance, $X_C$. Graph shows variation of capacitive reactance with frequency.
D) $V=V_0\sin \omega t$
$Q=CV$
Where C is capacitance.
$I=\frac{dQ}{dt}=C\frac{dV}{dt}=C{V}_0\omega \cos \omega t$
Thus there is a $\frac{\pi }{2}$ phase difference between current and voltage.