The ripple factor in a half-wave rectifier is

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Question

(A) The ripple factor $r$ is defined as the ratio of the root mean square value of the ripple component to the direct current component of the output.

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$1.21$

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(A) The ripple factor $r$ is defined as the ratio of the root mean square value of the ripple component to the direct current component of the output.For a half-wave rectifier,the $rms$ value of the output current is $I_{rms} = I_0 / 2$ and the $dc$ value is $I_{dc} = I_0 / \pi$.The formula for the ripple factor is $r = \sqrt{\left( \frac{I_{rms}}{I_{dc}} \right)^2 - 1}$.Substituting the values: $r = \sqrt{\left( \frac{I_0 / 2}{I_0 / \pi} \right)^2 - 1} = \sqrt{\left( \frac{\pi}{2} \right)^2 - 1}$.Since $\pi \approx 3.14$,$\pi / 2 \approx 1.57$.$r = \sqrt{(1.57)^2 - 1} = \sqrt{2.46 - 1} = \sqrt{1.46} \approx 1.21$.

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