The waveform is given by v(t) = 10 sin (2π100t). What will be the magnitude of the second harmonic in its Fourier series representation?

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ESE Electronics 2012 Paper 1: Official Paper
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  1. 0 V
  2. 20 V
  3. 100 V
  4. 200 V

Answer (Detailed Solution Below)

Option 1 : 0 V
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Detailed Solution

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Concept:

The exponential representation of the Fourier series is given by:

\(x\left( t \right) = \;\mathop \sum \limits_{ - \infty }^\infty {C_k}\;{e^{jk{ω _0}t}}\)

Where, Ck in the Fourier coefficient given by:

\({C_k} = \frac{1}{{{T_0}}}\smallint x\left( t \right)\;{e^{ - jk{ω _0}t}}dt\)

Given:

v(t) = 10 sin (2π100t)

ω0 = 200π 

v(t) = (10 ej200πt - 10 e-j200πt )/2j

∴ The second harmonic = 0

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