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°
