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Solved Problems-9

Problems-9
Determine the Fourier series of repetitive waveform of figure up to 5th harmonic, when time of repetition, T = 20 ms.
 
Calculate the fundamental frequency current in the circuit of the figure, where R = 10 ohm and L = 0.0318H with voltage transform of the waveform.
 
Description: 1225.pngDescription: 1232.png
 
Solution
The wave is having half wave symmetry.
 
an = bn = 0 ; for n even ; and
 
For n odd,
Description: 3388.png
 
Description: 3394.png
 
and a0 = 0
 
Now, v(t) = Description: 3400.png
 
∴ Description: 3410.png
 
Description: 3419.png
 
Description: 3425.png
 
Description: 3431.png
 
Description: 3437.png
 
Description: 3443.png
 
Description: 3449.png
 
∴ Description: 3456.png

The fundamental frequency voltage is
Description: 3462.png 
 
Impedance, Z = (R + L) = 10 + (0.318)
 
Current due to fundamental frequency,
 
Description: 3478.png
 
or Description: 3489.png

Here, Description: 3498.png rad/s

Patting this value,
 
∴ Description: 3504.png
 
∴ Description: 3513.png
 





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