Question

A device X is connected across an ac source of voltage $V=V_{0}sin\omega T.$ The current through X is given as $I=I_{0}sin(\omega t+\frac{\pi }{2})$
(a) Identify the device X and write the expression for its reactance.
(b) Draw graphs showing variation of voltage and current with time over one cycle of ac, for X.
(c) How does the reactance of the device X vary with freqency of the ac ? Show this variation graphically.
(d) Draw the phasor diagram for the device X.

Answer 1

$V=V_{0}sin\omega t;I=I_{0}sin(\omega t+\frac{\pi }{2}).$

(a) Cleary, X is a capacitor as current leads the voltage by $\frac{\pi }{2}$ radians, .

Capacitive reactance, $X_C=\frac{1}{\omega C}$

where $\omega$ = angular velocity, C = capacitance.
(b)
(c) Capacitive reactance varies inversely with frequency as

$X_C=\frac{1}{\omega C}=\frac{1}{2\pi fC}$
(d)