A device X is connected across an ac source of voltage V = V₀sinωt. The current through X is given as I = I₀sin(ωt + π/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 frequency of the ac?

(a) Here V = V₀sinωt
I = I₀sin(ωt + π/2)
Since current is leading the voltage by π/2, hence the circuit must be capacitive and the element "X" must be a capacitor.
Its reactance is given by Xc = 1/ωC
(b) Graph of voltage and current w.r.t time in fig(b)
(c) Graph showing the variation of XC with frequency f in fig(c)
Since Xc = 1/(2πfC)
Xc ∝ 1/f
Hence, reactance is inversely proportional to the frequency
(d) Phase diagram for device X is shown in fig (d)