Concept:The total RMS voltage is the root-sum-square of the DC component and the AC ripple components: \( V_{\text{rms}}^2 = V_{\text{dc}}^2 + V_{\text{ac,rms}}^2 \). Dividing by \( V_{\text{dc}}^2 \) relates the ripple factor directly to the Form Factor.
Formula:$$\left(\frac{V_{\text{rms}}}{V_{\text{dc}}}\right)^2 = 1 + \left(\frac{V_{\text{ac,rms}}}{V_{\text{dc}}}\right)^2 \implies \text{FF}^2 = 1 + r^2 \implies r = \sqrt{\text{FF}^2 - 1}$$
Solution:- Using \( \text{FF} = V_{\text{rms}} / V_{\text{dc}} \) and \( r = V_{\text{ac,rms}} / V_{\text{dc}} \):
- Rearranging gives \( r = \sqrt{\text{FF}^2 - 1} \).
- For a half-wave rectifier: \( r = \sqrt{1.57^2 - 1} = 1.21 \).
- For a full-wave rectifier: \( r = \sqrt{1.11^2 - 1} = 0.482 \).
Why other options are incorrect:- Option A: The relationship is quadratic, not a linear addition.
- Option B: \( r \) is not simply half the Form Factor.
- Option D: \( 1/\text{FF} \) is the rectification ratio \( V_{\text{dc}}/V_{\text{rms}} \), not the ripple factor.
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