Question

Using the data in the photo write the complex waveform expression​

Answer 1

Answer:

1st Harmonic:

$v(t) = 50\cos(2000\pi t)$

3rd Harmonic:

$v(t) = 9\cos(6000\pi t)$

5th Harmonic:

$v(t) = 6\cos(10000\pi t)$

7th Harmonic:

$v(t) = 2\cos(14000\pi t)$

Explanation:

The general form to represent a complex sinusoidal waveform is given by

$v(t) = A\cos(2\pi f t + \phi)$

Where A is the amplitude in volts of the sinusoidal waveform

Where f is the frequency in cycles per second (Hz) of the sinusoidal waveform

Where $\phi$ is the phase angle in radians of the sinusoidal waveform.

1st Harmonic:

We have A = 50, f = 1000 and φ = 0

$v(t) = 50\cos(2\pi 1000 t + 0) \\\\v(t) = 50\cos(2000\pi t)$

3rd Harmonic:

We have A = 9, f = 3000 and φ = 0

$v(t) = 9\cos(2\pi 3000 t + 0) \\\\v(t) = 9\cos(6000\pi t)$

5th Harmonic:

We have A = 6, f = 5000 and φ = 0

$v(t) = 6\cos(2\pi 5000 t + 0) \\\\v(t) = 6\cos(10000\pi t)$

7th Harmonic:

We have A = 2, f = 7000 and φ = 0

$v(t) = 2\cos(2\pi 7000 t + 0) \\\\v(t) = 2\cos(14000\pi t)$

Note: The even-numbered harmonics have 0 amplitude that is why they are not shown here.

Answer 2

Just to save myself the time lol, exactly what the other guy said!