Answer:
1st Harmonic:
[tex]v(t) = 50\cos(2000\pi t)[/tex]
3rd Harmonic:
[tex]v(t) = 9\cos(6000\pi t)[/tex]
5th Harmonic:
[tex]v(t) = 6\cos(10000\pi t)[/tex]
7th Harmonic:
[tex]v(t) = 2\cos(14000\pi t)[/tex]
Explanation:
The general form to represent a complex sinusoidal waveform is given by
[tex]v(t) = A\cos(2\pi f t + \phi)[/tex]
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 [tex]\phi[/tex] is the phase angle in radians of the sinusoidal waveform.
1st Harmonic:
We have A = 50, f = 1000 and φ = 0
[tex]v(t) = 50\cos(2\pi 1000 t + 0) \\\\v(t) = 50\cos(2000\pi t)[/tex]
3rd Harmonic:
We have A = 9, f = 3000 and φ = 0
[tex]v(t) = 9\cos(2\pi 3000 t + 0) \\\\v(t) = 9\cos(6000\pi t)[/tex]
5th Harmonic:
We have A = 6, f = 5000 and φ = 0
[tex]v(t) = 6\cos(2\pi 5000 t + 0) \\\\v(t) = 6\cos(10000\pi t)[/tex]
7th Harmonic:
We have A = 2, f = 7000 and φ = 0
[tex]v(t) = 2\cos(2\pi 7000 t + 0) \\\\v(t) = 2\cos(14000\pi t)[/tex]
Note: The even-numbered harmonics have 0 amplitude that is why they are not shown here.
