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13 December, 10:26

You wish to use phasor notation to convert V 100 cos (100t 30°) 5 sin (100t - 40) into a single sinusoidal function. Which of the following functions are equivalent to the phasor form of V?

a. 95.3228.97 1002300+52 (-130°)

b. 83.44462 1002300 + j54 (-40)

c. 100£309-52500

d. 101.82/27.36。 90.43+j46.79

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  1. 13 December, 10:53
    0
    The given options are not typed correctly, the correct options are given below

    Options:

    a. 95.32 < 28.97°

    b. 100 < 30° + 5 < - 130°

    c. 83.4 + j46.2

    d. 100 < 30° + j5 <-40°

    e. 100 < 30° - 5 < 50°

    f. 90.43 + j46.79

    Answer:

    a. V = 95.32 < 28.97°

    b. V = 100 < 30° + 5 < - 130°

    c. V = 83.4 + j46.20

    Explanation:

    Given sinusoidal function V = 100cos (100t + 30°) + 5sin (100t - 40°)

    We have to convert it to phasor notation

    In polar form,

    100cos (100t + 30°) = 100 < 30°

    In rectangular form,

    100 < 30° = 86.6 + j50

    Covert the sine into cosine by adding phase shift of - 90° (to perform any mathematical operation, it is important to have both quantities in the same function i. e. either sine or cosine

    5sin (100t - 40° - 90°) = 5cos (100t - 130°)

    In polar form,

    5cos (100t - 130°) = 5 < - 130°

    In rectangular form,

    5 < - 130° = - 3.21 - j3.83

    Now add the two quantities

    V = 86.6 + j50 + (-3.21 - j3.83)

    V = 100 < 30° + 5 < - 130°

    In rectangular form

    V = 83.4 + j46.20

    In polar form

    V = 95.32 < 28.97°

    Therefore, the answer is

    in rectangular form V = 83.4 + j46.20

    in polar form V = 95.32 < 28.97°
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