Alternating current (AC) is a current that repeatedly reverses direction, unlike direct current (DC) which always flows one way. In the UK, the mains supply is AC at 230 V (peak approximately 325 V) and 50 Hz. An oscilloscope displays a voltage–time trace as a sine wave, letting you read off the peak voltage, period and frequency directly.
What is the difference between AC and DC?
| Feature | Alternating current (AC) | Direct current (DC) |
|---|---|---|
| Direction of flow | Reverses repeatedly | Always flows in one direction |
| Voltage with time | Sinusoidal (sine wave) | Constant (flat line) |
| Typical source | Mains supply, generators | Batteries, solar cells, rectified AC |
| Oscilloscope trace | Regular sine wave | Horizontal straight line |
| Transmissible over long distances? | Yes — easily transformed to high voltage | No — high losses without transformation |
AC is used for the National Grid because transformers can change AC voltage — stepping it up for efficient long-distance transmission and stepping it down for safe home use. Transformers do not work with DC.
What are the key quantities in an AC supply?
Frequency (f): the number of complete cycles per second, measured in hertz (Hz). The UK mains supply is 50 Hz — 50 complete cycles (reversals) per second.
Period (T): the time for one complete cycle, measured in seconds. $$T = \frac{1}{f}$$
For the UK mains: T = 1/50 = 0.02 s (20 milliseconds per cycle).
Peak voltage (V₀): the maximum voltage reached in one cycle. For the UK mains, the stated voltage is 230 V — but this is the root mean square (r.m.s.) voltage, which is the equivalent DC voltage that would deliver the same power. The actual peak voltage is higher: $$V_0 = V_{\text{rms}} \times \sqrt{2} \approx 230 \times 1.41 \approx 325 \text{ V}$$
At GCSE, you are not required to calculate r.m.s. values, but you must know that the 230 V stated for UK mains is not the peak voltage — it is a lower, equivalent value.
How do you read an oscilloscope trace?
An oscilloscope screen is divided into a grid. Two settings control the scale:
- Timebase (time/division): how many milliseconds or seconds each horizontal grid square represents.
- Voltage gain (volts/division): how many volts each vertical grid square represents.
To find peak voltage:
- Measure the number of vertical grid squares from the centreline to the highest point of the trace.
- Multiply by the voltage gain setting.
To find the period:
- Measure the number of horizontal grid squares for one complete cycle (from one peak to the next identical peak).
- Multiply by the timebase setting.
To find frequency: Use f = 1/T, where T is the period in seconds.
Worked example:
An oscilloscope has timebase = 5 ms/div and voltage gain = 2 V/div. The trace shows:
- Peak height = 3 divisions above centre.
- One complete cycle spans 4 divisions.
Calculations:
- Peak voltage = 3 × 2 = 6 V
- Period = 4 × 5 ms = 20 ms = 0.020 s
- Frequency = 1 / 0.020 = 50 Hz
How does an AC trace compare to a DC trace on an oscilloscope?
| Supply | Oscilloscope trace |
|---|---|
| AC (sinusoidal) | Regular sine wave — rises and falls symmetrically about the zero voltage line |
| DC (constant) | Horizontal straight line above the centreline (positive voltage) |
| DC with higher voltage | Horizontal line higher above the centreline |
| AC with higher frequency | More complete waves visible in the same screen width (peaks closer together) |
| AC with higher amplitude | Peaks extend further above and below the centreline |
Why does the UK use 50 Hz and 230 V for its mains supply?
These values represent a compromise among efficiency, safety and practicality:
- 50 Hz: low enough to avoid flicker in older fluorescent lights (which would be visible above ~40 Hz in early designs) and efficient for motors; high enough that transformer cores can be reasonably sized. The USA uses 60 Hz.
- 230 V: higher voltage means lower current for the same power (P = VI), reducing energy loss in wiring. But higher voltage increases shock hazard. Europe standardised at 230 V; the USA uses 120 V.
These are engineering decisions, not fundamental physics constants — different countries made different choices when their grids were first built.
Frequently asked questions
Why is the UK mains voltage given as 230 V when the peak voltage is about 325 V?
The 230 V figure is the root mean square (r.m.s.) voltage — the equivalent DC voltage that delivers the same average power over a complete cycle. An AC supply with a peak voltage of 325 V delivers the same heating power to a resistor as a 230 V DC supply would. Because power depends on voltage squared (P = V²/R), the r.m.s. voltage is the peak divided by √2, not divided by 2. Stating r.m.s. voltage makes it easy to calculate power without needing to account for the sinusoidal waveform.
How does an oscilloscope differ from a voltmeter?
A voltmeter gives a single numerical reading of voltage — useful for DC circuits where voltage is constant. An oscilloscope displays voltage as a continuous graph against time, which is essential for AC circuits where voltage changes every millisecond. An oscilloscope shows the shape of the waveform (sinusoidal, square, triangular), the peak voltage, the period, and the frequency simultaneously. A voltmeter measuring AC gives only the r.m.s. value and cannot show any information about the waveform's shape or timing.
What does a higher frequency look like on an oscilloscope?
A higher frequency means more complete cycles fit into the same time window. On the oscilloscope screen, the peaks and troughs appear closer together — the wave is more compressed horizontally. The amplitude (peak height) is unaffected by frequency alone. For example, at 50 Hz with a timebase of 10 ms/div, two complete cycles fit across a 10-division screen (each cycle = 20 ms = 2 divisions). At 100 Hz, four complete cycles would fit across the same screen.
Why can transformers only work with AC?
A transformer works by electromagnetic induction: a changing magnetic flux in the primary coil induces a voltage in the secondary coil. Alternating current constantly changes direction and magnitude, so it creates a continuously changing magnetic field — this is what induces a voltage in the secondary coil. Direct current creates a constant magnetic field (once established) with no change in flux, so no voltage is induced in the secondary coil. Only the moment DC is switched on or off — when current changes — induces any brief voltage. For sustained voltage transformation, AC is required.
For Socratic GCSE physics with Professor Newton — predicting AC quantities from first principles and reading oscilloscope traces systematically — visit aitutors.me.