State that conventional current is from positive to negative and that the flow of free electrons is from negative to positive
4.2.2 Electric Current
Objective
State that conventional current is defined as flowing from the positive terminal to the negative terminal of a source, whereas the actual flow of free electrons in a metallic conductor is in the opposite direction (from negative to positive).
Key Concepts
- Conventional current is a historical convention established before the electron was discovered.
- In metals the mobile charge carriers are free electrons, each carrying a charge e = 1.60 × 10⁻¹⁹ C (negative).
- Conduction in metals occurs because these free electrons are mobile and can drift under an electric field.
- The drift velocity of electrons is extremely small (≈10⁻⁴ m s⁻¹), but the electric field propagates through the circuit at close to the speed of light, giving the impression of instantaneous current.
Definition of Electric Current (AO1)
In the Cambridge IGCSE syllabus electric current is defined as the rate of flow of charge. Mathematically
\$I = \frac{\Delta Q}{\Delta t}\$
where I is the current (A), ΔQ the charge transferred (C) and Δt the time interval (s).
Why the Convention?
When the concept of current was first introduced the nature of the charge carriers was unknown, so scientists chose the direction from positive to negative as the reference. Later experiments showed that, in most conductors, the carriers are electrons, which move opposite to the chosen direction. The convention was retained for consistency in circuit analysis and diagramming.
Direction of Charge Flow in a Simple Circuit
- The positive terminal of the battery is taken as the source of conventional current.
- Conventional current leaves the positive terminal, passes through the external circuit, and returns to the negative terminal.
- Free electrons in the metallic wires move from the negative terminal toward the positive terminal, opposite to the conventional current.
Comparison of Directions
| Aspect | Conventional Current | Electron Flow |
|---|---|---|
| Direction | Positive → Negative | Negative → Positive |
| Charge carriers | Positive charge (hypothetical) | Free electrons (negative) |
| Symbol in circuit diagrams | Arrow pointing from + to – | Arrow pointing from – to + (often omitted) |
| Historical origin | Established before discovery of electrons | Result of later experimental evidence |
Mathematical Relationships (AO1)
- Current in a metal can be related to the drift of electrons:
\$I = n\,e\,A\,v_d\$
where n = number of free electrons per m³, e = elementary charge, A = cross‑sectional area of the conductor, and vd = drift speed.
- The magnitude of the current is the same whichever direction is chosen; only the sign changes. When conventional‑current is taken as positive, the electron‑flow sign is negative.
Measuring Current with an Ammeter (AO1)
- Series connection: An ammeter must be placed in series with the component whose current is to be measured so that the same charge passes through both.
- Range selection: Choose a range that is higher than the expected current. If the reading is close to the upper limit, switch to a higher range.
- Polarity:
- Analogue ammeters have a (+) and (–) terminal; the needle moves in the direction of conventional current.
- Digital ammeters display a numeric value; the (+) terminal should be connected towards the positive side of the circuit.
Direct Current (DC) versus Alternating Current (AC) (AO1)
- Direct current (DC): Current flows continuously in one direction (positive → negative). The magnitude may be constant or vary with time, but the direction never reverses.
- Alternating current (AC): The direction of flow reverses periodically, usually in a sinusoidal (or approximately sinusoidal) waveform. The syllabus requires recognition that AC changes direction, not the detailed mathematics.
Example Problems (AO2)
Problem 1 – Drift Speed
Statement: A copper wire of cross‑section \$2.0 \times 10^{-6}\,\text{m}^2\$ carries a current of \$3.0\,\$A. The free‑electron density in copper is \$8.5 \times 10^{28}\,\text{m}^{-3}\$. Determine the average drift speed of the electrons.
- Use \$I = n e A vd\$ and solve for \$vd\$:
\$v_d = \frac{I}{n e A}\$
- Substitute the values:
\$v_d = \frac{3.0}{(8.5 \times 10^{28})(1.60 \times 10^{-19})(2.0 \times 10^{-6})}\$
- Calculate:
\$v_d \approx 1.1 \times 10^{-4}\,\text{m s}^{-1}\$
The electrons drift very slowly (≈0.1 mm s⁻¹) opposite to the conventional current direction.
Problem 2 – Using an Ammeter
Statement: A digital ammeter set to the 2 A range reads \$0.45\,\$A when a resistor is connected to a 6 V battery.
- (a) Charge transferred in 5.0 s:
\$Q = I t = (0.45\ \text{A})(5.0\ \text{s}) = 2.25\ \text{C}\$
- (b) Effect of adding an identical resistor in series:
Two identical resistors double the total resistance, so the current halves (Ohm’s law \$I = V/R\$).
\$I_{\text{new}} = \frac{0.45\ \text{A}}{2} = 0.225\ \text{A}\$
The ammeter will therefore display approximately \$0.23\,\$A (to two significant figures).
This problem demonstrates how to read a measuring instrument, calculate transferred charge, and apply the relationship between resistance and current.
Summary
- Electric current is the rate of flow of charge.
- Conventional current flows from positive to negative; free electrons flow from negative to positive.
- In metals, conduction occurs because free electrons are mobile; the drift‑speed formula \$I = n e A v_d\$ links microscopic motion to macroscopic current.
- To measure current, connect an ammeter in series, select an appropriate range, and observe polarity.
- DC maintains a single direction; AC reverses direction periodically and is usually sinusoidal.