Electric charge and current
Section: Electricity | Syllabus: Cambridge AS Level Physics (9702)
Electric Current
Electric current is defined as the rate of flow of electric charge past a point in a circuit.
Electric Current The rate of flow of charge: I = (Q/t) or equivalently Q = ItCurrent is measured in amperes (A). One ampere is the current when one coulomb of charge passes a point in one second.
SI DefinitionThe ampere is defined based on the fixed value of the elementary charge e = 1.602\,176\,634 × 10^-19 C.
Key Equation
Charge-Current Relationship Q = Itwhere Q = charge (C), I = current (A), t = time (s)
Charge Carriers in Different Media
Electric current requires charge carriers - particles that are free to move and carry electric charge. The type of charge carrier depends on the medium:
| Medium | Charge Carriers | Notes |
|---|---|---|
| Metals | Free (delocalised) electrons | Electrons move freely between fixed positive metal ions |
| Electrolytes | Positive and negative ions | Both types of ion contribute to current in opposite directions |
| Semiconductors | Electrons and holes | Fewer charge carriers than metals; number increases with temperature |
| Ionised gases / Vacuum | Electrons and ions | Free electrons can also travel through vacuum (e.g., cathode ray tubes) |
Show positive metal ions arranged in a regular lattice structure with free (delocalised) electrons represented as smaller particles moving randomly in the spaces between the ions.
FIG 9.2: Movement of Ions in an ElectrolyteShow a beaker containing an electrolyte solution with two electrodes connected to a battery. Positive ions (cations) move towards the cathode (negative electrode) and negative ions (anions) move towards the anode (positive electrode).
Quantisation of Charge
Electric charge is quantised, meaning it exists only in discrete amounts. The smallest unit of charge is the elementary charge, e.
Elementary Charge e = 1.60 × 10^-19 CAll observable charges are integer multiples of e:
- Charge on an electron: -e = -1.60 × 10^-19 C
- Charge on a proton: +e = +1.60 × 10^-19 C
Calculating Number of Electrons
The number of electrons in a given charge is found by:
Number of Electrons n = (Q/e)where n = number of electrons, Q = total charge (C), e = 1.60 × 10^-19 C Worked Example: Charge and Electron Count
Question: A current of 0.75 A flows through a lamp for 15 minutes. Calculate (a) the charge that flows, and (b) the number of electrons that pass through the lamp.
Solution(a) Calculate charge:
Q = It = 0.75 × (15 × 60) = 0.75 × 900 Q = 675 C(b) Calculate number of electrons:
n = (Q/e) = 6751.60 × 10^-19 n = 4.22 × 10^21 electronsConventional Current vs Electron Flow
Conventional current is defined as flowing from the positive terminal to the negative terminal of a power supply.
However, in metallic conductors, the actual charge carriers (electrons) flow in the opposite direction - from negative to positive.
FIG 9.3: Conventional Current vs Electron FlowShow a simple circuit with a battery and wire. Include arrows indicating conventional current direction (from + to −) and separate arrows showing electron flow direction (from − to +) in the opposite direction.
Historical NoteThe direction of conventional current was defined before electrons were discovered (1897). We continue to use this convention today.
Drift Velocity
In a metal, free electrons move randomly at high thermal speeds (typically 10^6 m s^-1). When a potential difference is applied, electrons also drift slowly towards the positive terminal.
FIG 9.4: Electron Drift in a Metal WireShow a conduction electron's path as it moves through a wire, colliding with metal ions. Illustrate the fast random thermal motion (zig-zag path) combined with a slow net drift towards the positive terminal of the connected battery.
Mean Drift Velocity The average velocity of charge carriers in the direction of current flow, typically very small (mm s^-1 in metals).The Current Equation
Consider a conductor of cross-sectional area A carrying current I. If the charge carriers have:
- number density n (number of charge carriers per unit volume, in m^-3)
- charge q on each carrier (in C)
- mean drift velocity v (in m s^-1)
where I = current (A), A = cross-sectional area (m^2), n = number density (m^-3), v = drift velocity (m s^-1), q = charge per carrier (C)
Derivation of I = Anvq
FIG 9.5: Wire Section for Deriving I = AnvqShow a cylindrical section of wire with length d and cross-sectional area A clearly labelled. Include the positive terminal of the battery on one side and show charge carriers (electrons) distributed throughout the volume of the wire.
Consider a wire of length d and cross-sectional area A:
- Volume of wire section: V = A × d
- Number of charge carriers in this volume: N = n × A × d
- Total charge in this section: Q = N × q = nAdq
- If electrons travel distance d in time t: drift velocity v = (d/t), so d = vt
- Substituting: Q = nA(vt)q
- Current: I = (Q/t) = (nAvtq/t) = Anvq
Question: A copper wire has cross-sectional area 1.0 mm^2 and carries a current of 4.0 mA. Given that copper has 8.49 × 10^28 free electrons per m^3, calculate the mean drift velocity.
SolutionRearrange I = Anvq for v:
v = (I/Anq)Convert units: A = 1.0 × 10^-6 m^2, I = 4.0 × 10^-3 A
v = 4.0 × 10^-3(1.0 × 10^-6) × (8.49 × 10^28) × (1.60 × 10^-19) v = 4.0 × 10^-31.36 × 10^4 v = 2.9 × 10^-7 m s^-1 (or about 0.0003 mm s^-1)Why Signals Travel Fast Despite Slow Drift
Although drift velocity is extremely small, electrical signals propagate almost instantaneously (close to the speed of light). This is because:
- Free electrons already exist throughout the entire wire
- When a switch is closed, an electric field is established almost instantly along the wire
- All electrons begin drifting simultaneously - they don't need to travel from the battery to the lamp
Think of a tube already full of balls. Push one ball in at one end, and a ball immediately emerges from the other end - even though the individual balls move slowly.
Conductors, Semiconductors and Insulators
Materials are classified by their number density of charge carriers, n:
| Material Type | Number Density (n) | Conductivity | Examples |
|---|---|---|---|
| Conductors | Very high ( 10^28 m^-3) | High | Copper, aluminium, silver |
| Semiconductors | Moderate ( 10^16 to 10^23 m^-3) | Variable (increases with temperature) | Silicon, germanium |
| Insulators | Very low ( 10^7 m^-3 or less) | Very low | Rubber, glass, plastic |
Since I = Anvq, for a given current and wire dimensions, a higher number density n means a lower drift velocity v. Metals have very high n, so drift velocities are very small.
Common Exam Mistakes
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