In a full wave rectifier circuit operating from 50 Hz mains frequency, the fundamental frequency in

Q: Why does the frequency double in a full-wave rectifier?

In a standard AC wave, a full cycle consists of one positive and one negative half. A full-wave rectifier flips the negative half to positive. Now, the wave consists of identical positive pulses. Because the pattern repeats after every single pulse instead of every two pulses, the time period is halved, which means the frequency is doubled.

Q: What exactly is 'ripple frequency'?

Even though a rectifier converts AC to DC, the output isn't a perfectly flat line; it pulsates. These pulsations are called 'ripples'. The ripple frequency is simply the frequency at which these pulsations repeat.

Q: What would the answer be if it was a half-wave rectifier?

For a half-wave rectifier, the negative half-cycles are completely blocked (they become zero). The wave only pulses once per full input cycle. Therefore, the time period remains the same, and the ripple frequency equals the input frequency ($50\text{ Hz}$).

Q: Does the amplitude (voltage) of the wave affect the ripple frequency?

No. Frequency is purely a measure of time—how often a pattern repeats. The height (amplitude) of the wave has no effect on its frequency.

Q: Why is it called the 'fundamental' frequency in the ripple?

Because the pulsating DC output is not a perfect sine wave, it is actually made up of multiple frequencies added together (according to Fourier analysis). The 'fundamental' frequency is the lowest and most dominant frequency component, which corresponds to the basic repetition rate of the pulses.

Question

In a full wave rectifier circuit operating from $50	ext{ Hz}$ mains frequency, the fundamental frequency in the ripple would be

Options:

(A) $50	ext{ Hz}$

(B) $25	ext{ Hz}$

(C) $100	ext{ Hz}$

(D) $70.7	ext{ Hz}$

Sigma Percentile · Accepted Answer

### The AC Mains: Our Starting Point

Imagine the electricity flowing from the wall socket into your devices. This is Alternating Current (AC), and it behaves like a perfect mathematical sine wave. In this problem, we are given that the mains frequency is $50	ext{ Hz}$.

What does this mean physically? It means the voltage wave completes $50$ full cycles every single second. It goes from zero, up to a positive peak, back through zero, down to a negative peak, and back to zero. The time it takes to complete just one of these cycles is called the time period, denoted by $T$.

### The Magic of Full-Wave Rectification

Electronic devices usually need Direct Current (DC) to operate, not AC. To convert AC to DC, we use a circuit called a **rectifier**. Specifically, the problem mentions a **full-wave rectifier**.

A full-wave rectifier is clever. Instead of just blocking the negative half of the AC wave, it actively flips it upside down, making it positive. If you look at the output waveform, it looks like a series of continuous positive bumps—like a bouncing ball that never goes below the ground.

### The Frequency Shift

Now, let's look at the rhythm of these bumps. The original AC wave took a full time period $T$ to repeat its exact pattern (one positive bump and one negative bump).

However, because the full-wave rectifier flipped the negative bump upwards, the output wave now consists of identical positive bumps right next to each other. The pattern now repeats itself after every single bump! This means the new time period of the output wave is exactly half of the original time period:

$$T_{out} = \frac{T_{in}}{2}$$

Frequency and time period are inversely related ($f = \frac{1}{T}$). If the time period is cut in half, the frequency must double. The output wave is pulsating twice as fast as the input wave. Therefore, the fundamental frequency of these ripples is:

$$f_{out} = 2 	imes f_{in}$$

Substituting our given value:

$$f_{out} = 2 	imes 50	ext{ Hz} = 100	ext{ Hz}$$

And there we have it! The fundamental ripple frequency is **$100	ext{ Hz}$**.

Animated Solution for Physics - Semiconductors: In a full wave rectifier circuit operating from $50 Hz$ mains frequency, the fundamental frequency in the ripple would be

Select Answer:

Visualized Solution

Visualizing the Input Signal

Full-Wave Rectification

Comparing Time Periods

Frequency Relationship

Final Calculation

What about Half-Wave Rectifiers?

The Sigma Insight: P-N Junction Diode

The AC Mains

The Magic of Full-Wave Rectification

The Frequency Shift

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Animated Solution for Physics - Semiconductors: .math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } In a full wave rectifier circuit operating from 50 Hz mains frequency, the fundamental frequency in the ripple would be