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  • A device ‘X’ is connected to an ac source . The variation of voltage, current and power in one cycle is shown i

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.

 

 

Answers (1)

a) The element X is a capacitor

b) A represents the power

    B represents the voltage

    C represents the current

c) impedance

z = X_{c}=\frac{1}{2\pi fc}

d) Let the voltage applied be V_{0}\; \sin (\omega t)

The instantaneous value of current in the circuit is

I=\frac{dq}{dt}=\frac{dCV}{dt}=\frac{d}{dt}\left ( C\; V_{0}\; \sin \omega t \right )

=\omega C \; V_{0} \cos \omega t=\frac{V_{0}}{1/\omega c}\sin (\omega t+\frac{\pi }{2})

I = I_{0}\sin (\omega t+\frac{\pi }{2})

\Rightarrow Current leads voltage by 90^{o}

Posted by

Safeer PP

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