Know the difference between direct current (d.c.) and alternating current (a.c.)

4.2.2 Electric Current – Direct vs Alternating Current

Learning objective

Explain the difference between direct current (d.c.) and alternating current (a.c.) and use this knowledge to answer exam questions on electrical quantities, measurement and safety.

1. What is electric current?

• Definition (syllabus wording): Electric current is the rate at which electric charge flows past a point in a circuit.
• Mathematically, I = Q / t, where I is the current (ampere, A), Q is charge (coulomb, C) and t is time (s).
• Current is a scalar quantity; its magnitude is given by the ampere, and its direction is indicated by the convention that current flows from the positive terminal to the negative terminal (conventional current).
• In metallic conductors the charge carriers are free electrons, which move opposite to the conventional direction.

2. Measuring current

• Ammeter (or galvanometer) – always connected in series with the component whose current is to be measured.
• Analogue ammeters have a moving‑coil pointer; digital ammeters give a numerical read‑out.
• Most ammeters provide a selector switch for several current ranges (e.g. 0–0.2 A, 0–2 A, 0–20 A). Choose the smallest range that can accommodate the expected current to minimise reading uncertainty.
• Uncertainty:

  • Analogue: ±½ scale division.
  • Digital: ±(least‑significant‑digit + % of reading).

3. Electrical conduction in metals

• Metals contain a “sea” of delocalised electrons that are free to move when an electric field is applied – the free‑electron model.
• The applied potential difference creates an electric field; electrons drift opposite to the field, giving a steady flow of charge (conventional current).
• Insulators have electrons tightly bound to atoms; very few charge carriers are available, so the current is negligible.

4. Direct current (d.c.) vs Alternating current (a.c.)

5. Mathematical description of a sinusoidal a.c.

The instantaneous current in a simple sinusoidal circuit is

\( i(t)=I_{\text{max}}\sin(2\pi ft) \)

• I_max – peak (maximum) current
• f – frequency in hertz (Hz)
• t – time in seconds (s)

6. RMS values – why they are used

RMS (root‑mean‑square) values allow an alternating quantity to be compared with a direct quantity in terms of heating effect (power). For a sinusoidal waveform:

\( I{\text{rms}} = \dfrac{I{\text{max}}}{\sqrt{2}} \qquad\text{and}\qquad V{\text{rms}} = \dfrac{V{\text{max}}}{\sqrt{2}} \)

Thus a 230 V rms a.c. supply delivers the same average heating power as a 230 V d.c. source.

7. Effect of resistance on current (link to other syllabus sections)

• Ohm’s law: V = IR. For a given voltage, a higher resistance reduces the current.
• In d.c. circuits the current is constant, so the heating in a resistor is P = I^{2}R.
• In a.c. circuits the same expression uses RMS values: P = I_{\text{rms}}^{2}R.

8. Practical implications

1. Transmission: a.c. can be stepped up or down with transformers, allowing high‑voltage, low‑current transmission and reducing \( I^{2}R \) losses.
2. Safety: Household a.c. (50/60 Hz) can cause muscle tetany, making it harder to let go of a live conductor; a d.c. shock is usually a single, less severe contraction.
3. Device design: Most electronic circuits need d.c.; therefore the mains a.c. supply is rectified (using diodes) and filtered to obtain a stable d.c. voltage.

9. Quick revision checklist

• Current = charge flow rate; I = Q/t; unit = ampere (A).
• Conventional current direction: positive → negative; electron flow opposite.
• Ammeters are connected in series; choose the smallest appropriate range.
• Key differences between d.c. and a.c. (direction, waveform, frequency, RMS conversion).
• Sinusoidal equation \( i(t)=I_{\text{max}}\sin(2\pi ft) \) and RMS factor \(1/\sqrt{2}\).
• a.c. is preferred for power transmission because it can be transformed to high voltage.
• Safety: a.c. (50/60 Hz) → tetany; d.c. → single shock.