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26 August, 03:59

Determine the sinusoidal time functions corresponding to each of the following phasors: (a) 5∠25° V,?=1000 rad/s (?) - ?5 A,?=100 Hz

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  1. 26 August, 06:17
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    The question is incomplete. the complete question is giving below

    "Determine the sinusoidal time functions corresponding to each of the following phasors: (a) 5<25°V, w = 1000 rad/s (b) - j5 A, f = 100 Hz

    answer

    a. V (t) = 5√ (2) sin (1000t+25⁰) v

    b. - 5√ (2) cos200πt A

    Explanation:

    note that the sinusoidal time function is express as

    y (t) = yₙsin (wt+α)

    where w is the angular frequency in rad/s, and α is the angle.

    a. to represent 5<25°V, w = 1000 rad/s. first we express it in polar form i. e

    V (t) = 5eⁱ²⁵

    in sinusoidal time function we have

    V (t) = Vₙsin (wt+α)

    Vₙ=5√ (2) v, the √ (2) convert the amplitude into effective or RMS value

    w=1000rad/secs

    α=25⁰

    Hence if we substitute, we arrive at

    V (t) = 5sin (1000t+25⁰) v

    b. for - j5 A, f = 100 Hz

    in polar form we have

    i (t) = 5eⁱ⁹⁰

    and w=2πf=2*π*100=200π

    hence we have

    i (t) = 5√ (2) sin (200πt+90) = (-5sin200πt) A
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