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A device X is connected across an ac sou...

A device X is connected across an ac source of voltage `V = V_(0) sin omegat`. The current throught X is given as `I= I_(0)sin(omegat + (pi)/(2))`
(a) Identify the device X and write the expression for its reactance.
(b) Draw graph showing variation of voltage and current with time over one cycle of ac, for X.
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.

Text Solution

Verified by Experts

(a) `V = sin O(omegat)`
Applying kirchoff's law
`V_(0) sin (omegat) = q//c`
`V_(0)c sin omegat = q`
`V_(0)c (d)/(dt) sin(omegat) = (dq)/(dt) " "V_(0)c sin (omegat) = (dq)/(dt)`
`(V_(0))/(1//wc) cos(omegat) = i" "(V_(0))/(X_(c)) cos omegat =i`
`i_(0)sin((pi)/(2) + omegat)= i`

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