Question

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

Answer 1

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°