Define electric current as the charge passing a point per unit time; recall and use the equation I = Q / t
4.2.2 Electric Current
Definition
Electric current is the rate at which electric charge passes a given point in a circuit.
Formula: \( I = \dfrac{Q}{t} \)
- \(I\) – electric current (ampere, A)
- \(Q\) – charge transferred (coulomb, C)
- \(t\) – time taken (second, s)
Scalar nature of current
Current is a scalar quantity – it has magnitude only. The direction of flow is indicated by the convention that positive charge moves from the positive terminal to the negative terminal of a source.
Symbol and SI unit
The symbol for electric current is I. The SI unit is the ampere.
Definition of the ampere: 1 A = 1 C s⁻¹ (one coulomb of charge passing a point each second)
Using the equation \(I = Q/t\)
The relationship can be rearranged to find any of the three quantities:
- Current: \( I = \dfrac{Q}{t} \)
- Charge: \( Q = I \times t \)
- Time: \( t = \dfrac{Q}{I} \)
Conventional current vs. electron flow
- Conventional current – direction a positive charge would move (positive → negative terminal).
- Electron flow – actual charge carriers in metals are electrons, which move opposite to the conventional direction (negative → positive).
Electrical conduction in metals (optional detail)
Metals contain a “sea” of free electrons. When an electric field is applied, these electrons acquire a small average drift velocity \(v_d\). The current can be expressed as
\( I = n\,e\,A\,v_d \)
where
- \(n\) – number of free electrons per unit volume (m⁻³)
- \(e = 1.6\times10^{-19}\,\text{C}\) – elementary charge
- \(A\) – cross‑sectional area of the conductor (m²)
- \(v_d\) – drift velocity (m s⁻¹)
Direct current (d.c.) and alternating current (a.c.)
| Aspect | Direct Current (d.c.) | Alternating Current (a.c.) |
|---|---|---|
| Direction of flow | Constant (one direction) | Periodically reverses direction |
| Waveform | Straight line (constant magnitude) | Sinusoidal (or other periodic shape) |
| Typical sources | Batteries, solar cells, DC power supplies (e.g., a torch) | Generators, mains supply, inverters (e.g., household 240 V supply, 50 Hz/60 Hz) |
| Frequency | 0 Hz (steady) | Typically 50 Hz (Europe) or 60 Hz (USA) |
Ammeter use
- An ammeter measures the current flowing through a circuit and must be connected in series with the component whose current is to be measured.
- Analogue ammeters have a moving‑coil needle; the scale is fixed, so the user selects a range that comfortably encloses the expected current.
- Digital ammeters display the reading numerically; many have an auto‑range function, but manual range selection is still useful.
- Range‑selection advice: choose a range that is slightly higher than the expected current (e.g., if you expect ≈2 A, select the 2 A or 3 A range). This maximises resolution while protecting the instrument from overload.
Example calculations
1. Simple charge‑time problem
Find the current when a charge of 12 C passes a point in 3 s.
\( I = \dfrac{12\ \text{C}}{3\ \text{s}} = 4\ \text{A} \)
2. Real‑world appliance example (d.c.)
A 60 W lamp is powered from a 240 V mains supply (a.c.). The current drawn is
\( I = \dfrac{P}{V} = \dfrac{60\ \text{W}}{240\ \text{V}} = 0.25\ \text{A} \)
3. Charge‑time conversion
If a current of 0.5 A flows for 6 s, the charge transferred is
\( Q = I \times t = 0.5\ \text{A} \times 6\ \text{s} = 3\ \text{C} \)
Common misconceptions
- Current is not the same as charge; it is the *rate* of charge flow.
- Current is a scalar quantity – it has magnitude but no intrinsic direction (direction is indicated by the convention).
- Electron flow is opposite to the direction of conventional current.
Quick‑check questions
- If a current of 2 A flows for 5 s, how much charge passes the point?
- A circuit carries a charge of 30 C in 10 s. What is the current?
- How long will it take for a current of 0.5 A to transfer 9 C of charge?
- A 120 V mains supply powers a 24 W fan. Calculate the current drawn by the fan.
Unit conversion table
| Quantity | Symbol | SI Unit | Equivalent expressions |
|---|---|---|---|
| Charge | Q | Coulomb (C) | 1 C = 1 A·s |
| Current | I | Ampere (A) | 1 A = 1 C s⁻¹ |
| Time | t | Second (s) | – |
Suggested diagram
