A device X is connected across an ac source of voltage $V= V_{0}\sin \cot \omega t$ The current through X is given as $I= I_{0}\sin \left ( \omega t +\frac{\pi }{2} \right )\cdot$ (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 frequency of the ac? Show this variation graphically. (d) Draw the phasor diagram for the device X.

a) The device X is capacitor From the values of voltage and current if is clearly seen that currently leads voltage by a phase angle $\frac{\pi }{2}$

capacitive reactance,

$X_{c}= \frac{1}{wc}= \frac{1}{2\pi fc}$
b)

this graph shows the variation of voltage and current with time over one cycle of ac.
c) Capacitive reactance

$X_{c}= \frac{1}{wc}= \frac{1}{2\pi fc}$
The capacitive reactance is inversely proportional to the frequency

therefore, the graph becomes,

d)

This shows the phaser diagram of the capacitor

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