Relationship between ripple factor (RF) and form factor (FF) in rectifier outputs Choose the correct formula linking RF and FF.

Introduction / Context:
Ripple factor and form factor are standard quality measures for rectifier outputs. Form factor quantifies the ratio of RMS value to average value, while ripple factor quantifies the AC component relative to the DC component in a rectified waveform.

Given Data / Assumptions:

• Let V_rms be total RMS of the rectified output.
• Let V_dc be the average (DC) value.
• Let V_ac,rms be the RMS value of the ripple component alone.

Concept / Approach:

By definition: FF = V_rms / V_dc and RF = V_ac,rms / V_dc. Also, V_rms^2 = V_dc^2 + V_ac,rms^2. Rearranging these gives the direct relationship between RF and FF.

Step-by-Step Solution:

Verification / Alternative check:

Plug common rectifier values (e.g., half-wave, full-wave) to confirm known RF values are recovered from the corresponding FF values.

Why Other Options Are Wrong:

Linear relationships RF = FF − 1 or RF = FF^2 − 1 ignore the Pythagorean relationship from RMS summation. The square-root of (FF − 1) is dimensionally inconsistent relative to the derivation.

Common Pitfalls:

Confusing total RMS with ripple RMS; forgetting that RMS components add in power (square) not linearly.

Final Answer:

RF = (FF^2 − 1)^(1/2)