The shape of the lesson
By the end of the lesson, learners can
- Rectify, then smooth: Switch between half-wave and full-wave rectification and watch the output.
- Diodes and the capacitor: Three ideas carry most of the marks.
- Sinusoidal a.c.: i = I₀ sinωt, ω = 2πf, T = 1/f.
- R.M.S.: divide peak by √2; mean power = Iₕₘₛ²R = ½ peak power.
- Rectification: half-wave (1 diode), full-wave (4-diode bridge); smoothing capacitor in parallel with the load reduces ripple, full-wave ripple at twice the supply frequency.
One picture every idea returns to
A diode passes current one way only. A single diode gives half-wave rectification (only the positive halves pass); a bridge of four diodes gives full-wave rectification (the negative halves are flipped up). A smoothing capacitor across the load charges to the peak and discharges slowly between peaks, reducing the ripple.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, From a.c. to steady d.c.. Many devices need direct current, but the mains delivers alternating current. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 17 min | Teach and check: Rectify, then smooth | Switch between half-wave and full-wave rectification and watch the output. Project tab 2 of the lab (Rectification) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: Diodes and the capacitor | Three ideas carry most of the marks. | Jigsaw |
| 30 to 43 min | Check and plenary | The quick-check questions from the student lesson, answered on mini whiteboards one at a time; re-teach the one most get wrong, then a random call on the last. | Individual, then whole class |
| 43 to 45 min | Exit and homework | Set the worksheet below (6 questions, 51 marks) from the topic practice set. Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Diodes and the capacitor, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Jigsaw
Split the content into expert pieces. Expert groups master one piece each, then regroup so every home team has one expert per piece, and each expert teaches their piece to the team.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| The smoothing capacitor goes in parallel with the load, not in series. | A larger capacitance (or load resistance) gives less ripple, because the time constant RC is longer. The ripple of a full-wave rectifier is at twice the supply frequency (two bumps per cycle), while a half-wave output ripples at the supply frequency. |
Rectification and smoothing: topic worksheet
6 questions, 51 marks. Written in the style of the papers; no past paper question is reproduced. These questions cover the whole topic, so sibling lessons share them.
A single diode is connected in series with a resistor and a sinusoidal a.c. supply.
(a) Explain how the diode produces half-wave rectification. [2]
(b) Describe the output voltage across the resistor over one cycle. [2]
(c) State the fraction of each cycle during which current flows in the resistor. [1]
(d) Explain why the mean power delivered is less than for full-wave rectification of the same supply. [2]
(e) State one disadvantage of half-wave rectification. [1]
Fig. 6.1 shows the output of a full-wave rectifier (no smoothing) supplied from 50 Hz a.c.
(a) State the number of diodes in a bridge rectifier. [1]
(b) Explain how the bridge produces full-wave rectification. [3]
(c) State the frequency of the output shown in Fig. 6.1, and explain your answer. [2]
(d) State one advantage of full-wave over half-wave rectification. [2]
A capacitor is added to the output of a rectifier to smooth it.
(a) State how the smoothing capacitor is connected relative to the load. [1]
(b) Explain how the capacitor smooths the output. [3]
(c) State and explain the effect on the ripple of using a larger capacitance. [2]
(d) State the effect on the ripple of increasing the load resistance. [1]
(e) State what the output would be if the load were disconnected entirely. [1]
An a.c. supply of r.m.s. value 12 V and frequency 50 Hz is connected to a single-diode (half-wave) rectifier and a load. Parts (a) and (b) use the a.c. characteristics; the rest use rectification.
(a) Calculate the peak voltage of the supply. [2]
(b) Stating any assumption, give the peak output voltage across the load. [1]
(c) For how long in each cycle does the diode conduct? [2]
(d) A smoothing capacitor is now connected across the load. Describe the output. [2]
(e) State the ripple frequency of this smoothed half-wave output. [1]
A full-wave rectifier supplied from 50 Hz a.c. feeds a load of resistance 2.2 kΩ with a smoothing capacitor of 100 μF in parallel.
(a) Calculate the time constant of the load and capacitor. [2]
(b) State the frequency and period of the ripple before smoothing. [2]
(c) By comparing the time constant with the ripple period, explain whether the smoothing is effective. [2]
(d) State and explain the effect of replacing the capacitor with a 470 μF one. [2]
This question follows a power supply from end to end. A transformer secondary provides 9.0 V (r.m.s.) at 50 Hz to a bridge rectifier, whose output is smoothed and connected to a load.
(a) Calculate the peak voltage at the secondary. [2]
(b) State the type of rectification and the number of diodes used. [2]
(c) State the ripple frequency of the rectified output. [2]
(d) A smoothing capacitor is added across the load. Describe the output voltage. [2]
(e) The load is changed to draw a larger current (a smaller resistance). State and explain the effect on the ripple. [3]
Answer key and marking notes
- (a)The diode conducts only when it is forward biased ✓, so current passes during only one half of each cycle ✓
- (b)Positive half-cycles appear across the resistor; during the other half the output is zero ✓✓
- (c)One half of each cycle ✓
- (d)Energy is delivered for only half of each cycle ✓; full-wave uses both halves, so its mean power is greater ✓
- (e)Half the available power is wasted (or the output has a large ripple) ✓
- (a)Four ✓
- (b)On each half-cycle two of the four diodes are forward biased ✓; they route the current through the load in the same direction both times ✓, so both halves of every cycle are used ✓
- (c)100 Hz ✓; there are two output bumps per input cycle, so the frequency is twice the 50 Hz supply ✓
- (d)It uses both halves of each cycle, so it delivers more power ✓ and is easier to smooth (smaller ripple) ✓
- (a)In parallel with the load ✓
- (b)The capacitor charges up to the peak voltage ✓; when the rectified voltage falls, the capacitor discharges through the load ✓, holding the voltage up and filling in the dips ✓
- (c)The ripple is smaller ✓, because a larger C gives a longer time constant RC, so the capacitor discharges less between peaks ✓
- (d)The ripple is smaller (larger R also lengthens RC) ✓
- (e)The capacitor stays charged at the peak voltage, giving a constant output (no ripple) ✓
- (a)V₀ = 12 × √2 ✓ = 17 V ✓
- (b)About 17 V ✓, assuming the diode has no voltage drop (ideal diode)
- (c)One half of the 20 ms cycle, so 10 ms ✓✓
- (d)A nearly steady d.c. near the peak voltage, with a small ripple as the capacitor discharges between peaks ✓✓
- (e)50 Hz (one charging pulse per cycle for half-wave) ✓
- (a)τ = RC = 2200 × 100 × 10⁻⁶ ✓ = 0.22 s ✓
- (b)Full-wave ripple frequency = 100 Hz ✓; period = 1/100 = 10 ms ✓
- (c)τ (220 ms) is much greater than the ripple period (10 ms) ✓, so the capacitor barely discharges between peaks: the smoothing is effective and the ripple is small ✓
- (d)The ripple is smaller still ✓; a larger C gives a longer time constant, so even less discharge between peaks ✓
- (a)V₀ = 9.0 × √2 ✓ = 12.7 V ✓
- (b)Full-wave rectification ✓, using four diodes (a bridge) ✓
- (c)Twice the supply frequency = 100 Hz ✓✓
- (d)A nearly steady d.c. close to the peak (about 12.7 V) with a small ripple ✓✓
- (e)The ripple becomes larger ✓; the smaller load resistance gives a shorter time constant RC ✓, so the capacitor discharges more between peaks ✓
The lesson's own checks as a quiz
The quick-check and exam-style questions from the student lesson, printable with the key.
A single diode in series with a resistor and an a.c. supply produces:
- Ahalf-wave rectification
- Bfull-wave rectification
- Ca smoothed d.c. output
- Dan amplified a.c. output
A bridge rectifier that gives full-wave rectification contains:
- Afour diodes
- Bone diode
- Ctwo diodes
- Da capacitor only
To reduce the ripple in a rectifier output, a smoothing capacitor is connected:
- Ain parallel with the load
- Bin series with the load
- Cin series with the diode only
- Dacross the a.c. supply input
A full-wave rectifier is supplied from 50 Hz mains. The ripple in its output has a frequency of:
- A100 Hz
- B50 Hz
- C25 Hz
- D200 Hz
Quiz key
One diode conducts only on the half-cycles when it is forward biased, so only the positive halves pass: half-wave rectification.
A bridge of four diodes directs both halves of each cycle the same way through the load, giving full-wave rectification.
The capacitor is placed in parallel with the load, so it charges at the peak and discharges through the load between peaks, filling the dips.
Full-wave rectification gives two output bumps per input cycle, so the ripple frequency is twice the supply frequency: 100 Hz.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.