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Electricity is central to modern physics and technology. At A-Level, you need a thorough understanding of circuits, charge flow, and the relationship between current, voltage, and resistance. This topic covers charge carriers, drift velocity, resistance, circuit analysis using Kirchhoff's laws, and sensor circuits.
Key Definition: Electric charge (Q) is a fundamental property of matter, measured in coulombs (C). The fundamental unit of charge is the charge on an electron: e = 1.60 × 10⁻¹⁹ C.
Charge is quantised — it always comes in integer multiples of e.
Current (I) is the rate of flow of charge:
I = ΔQ/Δt
Current is measured in amperes (A). In a metal conductor, current is carried by free (delocalised) electrons, which drift from the negative terminal to the positive terminal. Conventional current flows in the opposite direction — from positive to negative.
The potential difference (p.d.) between two points is the energy transferred per unit charge:
V = W/Q
It is measured in volts (V). One volt means one joule of energy per coulomb of charge.
P = IV = I²R = V²/R E = IVt = Pt
In a conductor, the free electrons do not move in a straight line — they undergo random thermal motion and drift slowly in the direction of conventional current (opposite to electron flow).
Key Definition: Drift velocity (v) is the average velocity of charge carriers along the conductor due to the applied electric field.
The current is related to drift velocity by:
I = nAve
where:
A copper wire of cross-sectional area 1.5 × 10⁻⁶ m² carries a current of 3.0 A. The number density of free electrons in copper is 8.5 × 10²⁸ m⁻³. Calculate the drift velocity.
I = nAve → v = I/(nAe) = 3.0 / (8.5 × 10²⁸ × 1.5 × 10⁻⁶ × 1.60 × 10⁻¹⁹)
v = 3.0 / (2.04 × 10⁴) = 1.5 × 10⁻⁴ m s⁻¹ (about 0.15 mm s⁻¹)
This is extremely slow! Yet the electrical signal travels at close to the speed of light because the electric field propagates almost instantaneously through the wire, setting all electrons in motion simultaneously.
Exam Tip: The drift velocity is surprisingly slow — typically less than 1 mm s⁻¹ in metals. Do not confuse the drift velocity of electrons with the speed of the electrical signal (which is close to c).
Resistance is a measure of how difficult it is for current to flow through a component:
R = V/I (measured in ohms, Ω)
Ohm's Law states that for an ohmic conductor at constant temperature, the current through it is directly proportional to the potential difference across it.
Key Definition: An ohmic conductor is one that obeys Ohm's law: I ∝ V at constant temperature, giving a straight-line I-V graph through the origin.
Described diagram — I-V graph for an ohmic conductor (e.g. metal wire at constant temperature): A straight line passing through the origin with a constant positive gradient. The gradient equals 1/R. The line extends into the third quadrant (negative V and negative I) with the same gradient, showing symmetrical behaviour.
Described diagram — I-V graph for a filament lamp: A curve through the origin that starts steep (low resistance when cold) and gradually flattens (higher resistance as the filament heats up). The curve is symmetrical about the origin. As current increases, the filament temperature rises, increasing resistance, so the graph curves towards the V-axis.
Described diagram — I-V graph for a semiconductor diode: For positive (forward) voltages below about 0.6 V, virtually no current flows. Above the threshold voltage (~0.6 V for silicon), current increases rapidly. For negative (reverse) voltages, negligible current flows. The graph is asymmetric — the diode conducts in one direction only.
| Component | Key Feature |
|---|---|
| Ohmic conductor | Straight line through origin; constant R |
| Filament lamp | Curve; R increases with temperature |
| Diode | Conducts above ~0.6 V forward; blocks reverse |
| Thermistor (NTC) | R decreases as temperature increases |
| LDR | R decreases as light intensity increases |
Resistivity (ρ) is a property of the material itself, not the component:
R = ρL/A
where L is the length and A is the cross-sectional area of the conductor. Resistivity is measured in Ω m.
| Material | Approximate Resistivity (Ω m) |
|---|---|
| Copper | 1.7 × 10⁻⁸ |
| Aluminium | 2.8 × 10⁻⁸ |
| Constantan | 4.9 × 10⁻⁷ |
| Silicon | ~10³ (varies with doping) |
| Glass | ~10¹⁰ |
Key Definition: A superconductor is a material that has zero resistivity below a critical temperature (T_c).
When a material becomes superconducting:
Applications of superconductors:
The main limitation is that current superconductors require cooling to extremely low temperatures (e.g. liquid nitrogen at 77 K or liquid helium at 4 K), which is expensive and impractical for many applications.
A cell or battery has an electromotive force (EMF, ε), which is the total energy transferred per unit charge by the source.
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