# Electric current

> Physics · CIE A-Level
> Source: https://www.owlsprep.com/study/cie-9702-u9-electric-current/

This subtopic introduces the fundamental concept of electric current, defines it in terms of charge flow, distinguishes between conventional current and electron flow, and covers core calculations for current and charge.

**Prerequisites:** [Basic properties of electric charge](https://www.owlsprep.com/study/cie-9702-pre-alevel-electric-charge/)

## Learning objectives

- Define electric current as the rate of flow of charge
- Distinguish between conventional current and electron flow
- Calculate current, charge and number of charge carriers
- Apply the core current formula to solve basic problems

## Definition of Electric Current

**Electric Current** — Electric current is defined as the rate of flow of net charge through a cross-section of a conductor. The SI unit of current is the ampere (A), equal to $1\ \text{C s}^{-1}$.

*Notation:* $I$

$$I = \frac{\Delta Q}{\Delta t}$$

Where $\Delta Q$ is the net charge passing through the cross-section in time interval $\Delta t$. This formula is the foundation for all current calculations.

**Worked example:** A total charge of 48 C passes through a filament bulb in 20 s. Calculate the current in the bulb.

1. Recall the core formula for current:
2. $$I = \frac{\Delta Q}{\Delta t}$$
3. Substitute the given values for charge and time:
4. $$I = \frac{48\ \text{C}}{20\ \text{s}} = 2.4\ \text{A}$$

> **Exam tip:** Always include units for all numerical answers; CIE examiners award marks for correct units.

## Conventional Current vs Electron Flow

Early scientists established the convention for current direction before the discovery of electrons. In metallic conductors, the moving charge carriers are negatively charged electrons, so their flow is opposite to the defined conventional current direction.

**Conventional Current** — Conventional current is defined as flow of positive charge, moving from the positive terminal of a power source to the negative terminal. This convention is still used universally in circuit analysis.

> **info**
>
> This opposite direction does not change any circuit calculations, because the net flow of charge is the same regardless of the sign of the charge carrier.

**Worked example:** In a copper wire connected to a cell, electrons flow from the negative terminal to the positive terminal. State the direction of conventional current.

1. Conventional current is always opposite to the direction of electron flow in metallic conductors.
2. Since electrons flow from negative to positive, conventional current flows from the positive terminal of the cell to the negative terminal.

> **Exam tip:** If a question does not specify which direction to give, always answer with the conventional current direction.

## Current and Number of Charge Carriers

We can extend the current formula to find the number of individual charge carriers (e.g. electrons) passing through a conductor. If each charge carrier carries charge $e$, the total charge $\Delta Q = n e$, where $n$ is the number of charge carriers.

$$I = \frac{n e}{\Delta t} \implies n = \frac{I \Delta t}{e}$$

**Worked example:** A wire carries a current of 0.5 A for 8 minutes. Calculate the number of electrons that pass through a point in the wire. Take elementary charge $e = 1.6 \times 10^{-19}$ C.

1. Convert time to SI units (seconds):
2. $$\Delta t = 8 \times 60 = 480\ \text{s}$$
3. Calculate total charge that passes through the wire:
4. $$\Delta Q = I \Delta t = 0.5 \times 480 = 240\ \text{C}$$
5. Divide total charge by the charge of one electron to find the number of electrons:
6. $$n = \frac{\Delta Q}{e} = \frac{240}{1.6 \times 10^{-19}} = 1.5 \times 10^{21}$$

**Check your understanding**

Test your understanding:

1. How many electrons pass through a resistor per second if the current is 1.6 A?

   - 1
   - 1 × 10¹⁹
   - 1.6 × 10¹⁹
   - 1 × 10¹⁸

   *Why:* For $\Delta t = 1$ s, $\Delta Q = I \Delta t = 1.6 \times 1 = 1.6$ C. Then $n = \frac{1.6}{1.6 \times 10^{-19}} = 1 × 10^{19}$.

*Calculator:* allowed

## Common pitfalls

- **Wrong:** Forgetting to convert time to seconds before substituting into the current formula
  - Why it fails: Current is defined as coulombs per second, so using minutes or hours gives an incorrect answer that is off by orders of magnitude
  - Correct: Always convert any time measurement to seconds first, before any calculation
- **Wrong:** Assuming current direction matches electron flow direction in metals
  - Why it fails: Conventional current, the standard convention, is defined as positive charge flow opposite to electron flow
  - Correct: Use conventional current direction unless the question explicitly asks for electron flow direction
- **Wrong:** Misremembering the exponent for elementary charge, writing $1.6 × 10^{-9}$ C instead of $1.6 × 10^{-19}$ C
  - Why it fails: This common mistake leads to large order of magnitude errors in calculations
  - Correct: Memorize that elementary charge is $1.6 × 10^{-19}$ C, and double check the exponent in all calculations
- **Wrong:** Treating current as a vector quantity because it has direction
  - Why it fails: Current does not follow the rules of vector addition, so it is classified as a scalar quantity
  - Correct: Remember that current is a scalar, only direction along the conductor is specified

## Cheatsheet

| Quantity/Concept | Formula/Rule | Key Note |
| --- | --- | --- |
| Electric current | $I = \frac{\Delta Q}{\Delta t}$ | Rate of charge flow, unit: A |
| Total charge | $\Delta Q = I \Delta t$ | Unit: C |
| Number of electrons | $n = \frac{I \Delta t}{e}$ | $e = 1.6 × 10^{-19}$ C |
| Conventional current direction | Positive → Negative | Opposite to electron flow in metals |
| Current classification | Scalar quantity | Does not obey vector addition |

## What's next

Electric current is the fundamental foundation for all topics in current of electricity, and underpins all of electromagnetism and circuit analysis in CIE A-Level Physics. Mastering the basic definitions and calculations here prevents common mistakes in all future electricity problems, which make up a large fraction of exam marks. This subtopic leads directly into learning about potential difference, resistance, and Ohm's law, and the relationship between current and charge carriers extends to drift velocity, which explains current behavior in different conductors.

- [Charge carriers and drift velocity](https://www.owlsprep.com/study/cie-9702-u9-charge-carriers-and-drift-velocity/)
- [Potential difference and e.m.f.](https://www.owlsprep.com/study/cie-9702-u9-potential-difference-and-e-m/)
- [Resistance and resistivity](https://www.owlsprep.com/study/cie-9702-u9-resistance-and-resistivity/)

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