Answer:
Therefore, the phasor angle of the complex number 9 + j5 is approximately 29.74°.
Explanation:
To calculate Vrms (root mean square voltage), we need to find the square root of the average of the squared values of the voltage over a complete cycle.
For the given voltage waveform Vs = 183Cos(452t+80∘), we can see that the amplitude of the cosine function is 183.
The RMS value can be calculated as follows:
Vrms = Vmax / √2
Where Vmax is the amplitude of the voltage waveform.
In this case, Vmax = 183, so we can calculate Vrms as:
Vrms = 183 / √2 ≈ 129.6 V
Therefore, the RMS voltage is approximately 129.6 V.
Moving on to the second question, given the complex number 9 + j5, we can calculate the phasor angle by using the arctan function:
Phasor angle = arctan(imaginary part / real part)
In this case, the real part is 9 and the imaginary part is 5, so:
Phasor angle = arctan(5/9)
Using a calculator or math software, we find:
Phasor angle ≈ 29.74°