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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"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