In an electrical circuit, how does a $\pi$-filter (composed of two parallel capacitors and a series inductor, $C_1$- · Electronics MDCAT Past Paper MCQ

Physics Electronics PMDC Conceptual Practice

PMDC Verified Question 53 of 494

In an electrical circuit, how does a $\pi$-filter (composed of two parallel capacitors and a series inductor, $C_1$-$L$-$C_2$) achieve superior DC smoothing compared to a simple shunt capacitor filter?

It completely blocks all DC current while doubling AC voltage amplitude

It provides two low-impedance shunt paths for AC ripple and a high-impedance series path that blocks AC harmonics while passing DC

It eliminates the need for rectifier diodes by generating DC electrochemically

It steps up the line frequency so ripple becomes invisible to the human eye

Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:

Option B: It provides two low-impedance shunt paths for AC ripple and a high-impedance series path that blocks AC harmonics while passing DC

Concept:

A $\pi$-filter combines capacitive bypassing and inductive choking: the first shunt capacitor ($C_1$) bypasses the majority of the AC ripple to ground; the series choke inductor ($L$) offers high inductive reactance ($X_L$) to block remaining AC ripple; and the second capacitor ($C_2$) further smooths residual ripple before the load.

Formula:

$$\text{Ripple Factor (}\pi\text{-filter): } r \approx \frac{\sqrt{2}}{8\omega^3 L C_1 C_2 R_L}$$

Solution:

Shunt capacitors $C_1$ and $C_2$ have low capacitive reactance ($X_C = \frac{1}{2\pi f C}$) to AC ripple, shorting ripple to ground.

Series choke $L$ has high inductive reactance ($X_L = 2\pi f L$) to AC ripple, blocking ripple from reaching the load.

For DC ($f = 0$), $X_C = \infty$ (open) and $X_L = 0$ (short), allowing DC to pass without attenuation.

Why other options are incorrect:

Option A: The primary goal of a power supply filter is to pass DC, not block it.
Option C: A filter smooths existing rectified waveforms; it does not generate DC electrochemically.
Option D: Filters attenuate ripple amplitude; they do not alter the fundamental ripple frequency.

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