The waveform of the current drawn by a semi-converter from a sinusoidal AC voltage source is shown in the figure. If I_{0} = 20 A, the rms value of fundamental component of the current is ___________A (up to 2 decimal places).

This question was previously asked in

GATE EE 2018 Official Paper

CT 1: Ratio and Proportion

3742

10 Questions
16 Marks
30 Mins

__ Concept__:

Fourier series representations of supply current of single-phase semi converter is

\({i_s}\left( t \right) = \mathop \sum \limits_{n = 1,\;3, \ldots }^\infty \frac{{4{I_0}}}{{n\pi }}\cos \frac{{n \propto }}{2}\sin \left( {n\omega t - \frac{{n\alpha }}{2}} \right)\)

__ Explanation__:

Fundamental component is,

\({I_{S1}} = \frac{{4{I_0}}}{\pi }\cos \frac{\alpha }{2}\)

RMS value of fundamental component is,

\({I_{S1}} = \frac{{4{I_0}}}{\pi }\cos \frac{\alpha }{2} \times \frac{1}{{\sqrt 2 }}\)

\(= \frac{{2\sqrt 2 {I_0}}}{\pi }\cos \frac{\alpha }{2}\)

From the given wave form,

firing angle (α) = 30°

\( \Rightarrow {I_{S1}} = \frac{{2\sqrt 2 \times 20}}{\pi }\cos \frac{{30}}{2} = 17.39\;A\)