Question

A device 'X' is connected to an ac source $V=V_{0}sin\omega t$. 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 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) The device X is a capacitor.
(b) The curves A,B and C represents power consumption, voltage and current respectively.
Since, it is given that $V=V_{0}sin\omega t$
This sinusoidal variation is represented by the curve B. In case of capacitor, current (I) ,leads the voltage by 90° which is being represented by curve C Now. we know power is given by
P= V $\times$ I
So, the power would be positive for those cycles where both V and I are either positive or negative. Power would be negative when one of the two voltage or current, is negative. This illustration is followed by the curve A.
(c) Capacitive reactance, Xc = $\frac{1}{\omega C}=\frac{1}{2\pi fC}$
This shows that capacitive reactance vary inversely with the frequency.

(d)
In the given figure,
$V=V_{0}sin\omega tQ=CV=C{V}_{0}sin\omega tI=\frac{dq}{dt}=\omega C{V}_{0}cos\omega t=I_{0}sin(\omega t+\pi /2)$
Current leads the voltage by a phase angle of ${90}^{\circ }$