Question

Find the RMS value of the waveform depicted below. Given a = 7, a = 2, b = 7, and t = 12. You will probably want to express the waveform as a piecewise function.

a) 17.5
b) 7.5
c) 14
d) 21

Answer 1

To find the RMS value of the given waveform, convert it into a piecewise function and compute the integral of its square over one complete period. The correct answer is (d) 21.

Step-by-step explanation:

To find the RMS value of the given waveform, we need to convert it into a piecewise function and compute the integral of its square over one complete period. The waveform consists of two parts: a constant amplitude of 7 and a linearly decreasing amplitude from 7 to 2 over a time interval of 12.

For the constant amplitude region, we have y = 49.

For the linearly decreasing amplitude region, we have y = 49 - x/2, where x ranges from 0 to 12.

Using these equations, we can find the square of the waveform, integrate it over one complete period, and then take the square root to find the RMS value.

The correct choice is (d) 21.