Question

The phasor technique is not valid if the frequencies of the sinusoids in the time domain are different. Part F - Use phasors to combine sinusoids The phasor technique makes it pretty easy to combine several sinusoidal functions into a single sinusoidal expression without using trigonometric identities. However, you cannot use the phasor technique in all cases. Select the expressions below for which the phasor technique cannot be used to combine the sinusoids into a single expression.

a. 45 sin(2500t – 50°) + 20 cos(1500t +20°)
b. 25 cos(50t + 160°) + 15 cos(50t +70°)
c. 100 cos(500t +40°) + 50 sin(500t – 120°) – 120 cos(500t + 60°) -100 sin(10,000t +90°) + 40 sin(10, 100t – 80°) + 80 cos(10,000t)
d. 75 cos(8t+40°) + 75 sin(8t+10°) – 75 cos(8t + 160°)

Answer 1

A and C

• By which the phaser technique cannot be used to combine the sinusoidal into a single expression.

Answer 2

a, c

Step-by-step explanation:

As the problem statement tells you, the phasor technique cannot be used when the frequencies are different. The frequencies are different when the coefficients of t are different. The different ones are highlighted.

a. 45 sin(2500t – 50°) + 20 cos(1500t +20°)

b. 25 cos(50t + 160°) + 15 cos(50t +70°)

c. 100 cos(500t +40°) + 50 sin(500t – 120°) – 120 cos(500t + 60°) -100 sin(10,000t +90°) + 40 sin(10, 100t – 80°) + 80 cos(10,000t)

d. 75 cos(8t+40°) + 75 sin(8t+10°) – 75 cos(8t + 160°)