Question

A complex single phase ac power source is connected to a non-linear load. The voltage of the power source and the current flowing through the load are represented by the following time domain expressions. vs=125sin(120πt)+80sin(360πt−10°)+8sin(600πt+45°)ViL=5sin(120πt−30°)+0.4sin(360πt+10°)+0.02sin(600πt−40°)A

a) Calculate the root means square value of the voltage source.

Answer 1

The root mean square (rms) value of the voltage source is 138.03 V.

Step-by-step explanation:

The root mean square (rms) value of the voltage source can be calculated using the given expression for the voltage vs = 125sin(120πt) + 80sin(360πt−10°) + 8sin(600πt+45°). The rms value is calculated by taking the square root of the average of the square of the voltage over a period of time.

To calculate the rms value, we square the voltage expression, take the average over one full period, and then take the square root. Using trigonometric identities and simplifying the expression, we get rms = √(125² + 80² + 8²) = 138.03 V.