Ripple factor vs. form factor in rectifiers In rectifier circuits, the ripple factor RF and the form factor FF are related by which expression?

Introduction / Context:
Ripple factor (RF) measures the AC ripple content relative to the DC component at a rectifier output, while form factor (FF) is the ratio of RMS value to average value of the output waveform. Their relationship is frequently tested in exams.

Given Data / Assumptions:

• V_rms denotes RMS value of output.
• V_dc denotes average (DC) value of output.
• AC component RMS is V_ac_rms where V_ac_rms^2 = V_rms^2 − V_dc^2.

Concept / Approach:

By definition, RF = V_ac_rms / V_dc and FF = V_rms / V_dc. Substituting V_ac_rms in terms of V_rms and V_dc yields a direct algebraic relation between RF and FF.

Step-by-Step Solution:

Verification / Alternative check:

For pure DC (no ripple), FF = 1 and RF = 0, which satisfies RF = sqrt(1 − 1) = 0.

Why Other Options Are Wrong:

Other options contradict the squared relationship derived from RMS-DC decomposition.

Common Pitfalls:

Confusing average and RMS definitions or forgetting that the AC component is orthogonal to the DC component in power calculation.

Final Answer:

RF = (FF^2 − 1)^0.5