Electricity
Current as a flow of charge carriers, quantised charge, Q = It and I = Anvq, potential difference and power, resistance and Ohm's law, I–V characteristics of a wire, diode and filament lamp, resistivity, and LDRs and thermistors.
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In 30 seconds
- Current is the rate of flow of charge: I = Q/t. In metals the charge carriers are free electrons. Charge is quantised: it comes in multiples of e = 1.60 × 10⁻¹⁹ C.
- I = Anvq links the current to the number density n of carriers and their drift speed v.
- Potential difference is energy transferred per unit charge: V = W/Q. Power P = VI = I²R = V²/R.
- Resistance R = V/I at any point. Ohm's law applies only when I ∝ V, e.g. a metal wire at constant temperature.
- Resistivity is a property of the material: R = ρL/A.
By the end you can
- Explain current as a flow of charge carriers and use Q = It and I = Anvq.
- Define potential difference and use V = W/Q and the three power equations.
- Define resistance, state Ohm's law, and sketch and explain I–V characteristics.
- Use R = ρL/A, and describe how LDR and thermistor resistances change.
1Current and charge
Definitions
Electric current — the rate of flow of charge, I = ΔQ/Δt.
The coulomb — the charge that passes a point when a current of 1 A flows for 1 s (1 C = 1 A s).
- Charge is quantised: any charge is a whole-number multiple of the elementary charge e = 1.60 × 10⁻¹⁹ C.
A current of 2.5 A flows for 3.0 minutes. Find the charge and the number of electrons.
- Q = It = 2.5 × 180 = 450 C C1 A1
- N = 450/1.60 × 10⁻¹⁹ = 2.8 × 10²¹ electrons A1
I = Anvq
- Derivation: in time t, carriers move a distance vt. The volume Avt contains nAvt carriers with total charge nAvtq. So I = Q/t = Anvq.
A copper wire of cross-sectional area 1.0 mm² carries 2.0 A. Copper has 8.5 × 10²⁸ free electrons per m³. Find the drift speed.
- v = I/(Anq) = 2.0/(1.0 × 10⁻⁶ × 8.5 × 10²⁸ × 1.60 × 10⁻¹⁹) C1
- = 1.5 × 10⁻⁴ m s⁻¹ A1 (very slow: the signal travels fast, the electrons don't)
- Same current, thinner section ⇒ faster drift (v ∝ 1/A). A semiconductor has a much smaller n, so its carriers drift much faster for the same current.
2Potential difference and power
Definitions
Potential difference — the energy transferred from electrical energy to other forms per unit charge passing between two points, V = W/Q.
The volt — one joule per coulomb.
A kettle is rated 2.0 kW at 230 V. Find the current and the resistance of its element.
- I = P/V = 2000/230 = 8.7 A A1
- R = V²/P = 230²/2000 = 26 Ω A1
3Resistance
Definitions and Ohm's law
Resistance — the ratio of the potential difference across a component to the current in it, R = V/I.
The ohm — the resistance of a component when a p.d. of 1 V drives a current of 1 A through it.
Ohm's law — the current in a metallic conductor is proportional to the potential difference across it, provided the temperature (and other physical conditions) remain constant.
I–V characteristics
| Component | I–V graph | Explanation |
|---|---|---|
| Metal wire at constant temperature | straight line through the origin | R constant: obeys Ohm's law |
| Filament lamp | curve, gradient decreasing as V increases | higher current ⇒ hotter filament ⇒ ions vibrate more ⇒ more collisions ⇒ R increases |
| Semiconductor diode | almost zero current in reverse; current rises sharply above about 0.6 V forward | very high resistance in reverse, low resistance once forward-biased |
- Resistance at a point = V/I at that point, not the gradient of the graph. The 2024 Paper 4 report also warns against confusing the inverse of the gradient with resistance.
From a lamp's I–V graph, I = 0.25 A when V = 6.0 V. Find its resistance at this point.
- R = V/I = 6.0/0.25 = 24 Ω A1
Resistivity
Resistivity — a property of a material defined by ρ = RA/L; numerically the resistance of a sample of unit length and unit cross-sectional area (Ω m).
A nichrome wire (ρ = 1.1 × 10⁻⁶ Ω m) is 0.80 m long with diameter 0.30 mm. Find its resistance.
- A = π(0.15 × 10⁻³)² = 7.07 × 10⁻⁸ m² C1
- R = 1.1 × 10⁻⁶ × 0.80/7.07 × 10⁻⁸ = 12 Ω A1
LDRs and thermistors
- Light-dependent resistor (LDR): resistance decreases as light intensity increases (more charge carriers are released).
- Thermistor (NTC): resistance decreases as temperature increases. Assume a negative temperature coefficient in this syllabus.
- They are used in potential dividers to make sensing circuits: see D.C. circuits.
Test yourself — cover the answers first
Quick check
- Define potential difference.
- State Ohm's law.
- A wire is stretched to twice its length at constant volume. By what factor does R change?
- How does the resistance of an NTC thermistor change as it warms?
- Find the energy transferred by a 3.0 Ω heater on 12 V for 5.0 minutes.
Exam-style
- Explain why the resistance of a filament lamp increases as the current increases.
- Two wires of the same material carry the same current. Wire X has twice the diameter of wire Y. Find the ratio of drift speeds v_X : v_Y.
- Show that the ohm is equivalent to kg m² s⁻³ A⁻².
Show answers
- energy transferred from electrical to other forms per unit charge
- I ∝ V for a metallic conductor at constant temperature
- ×4 (L doubles, A halves)
- it decreases
- P = 48 W; E = 14 400 J
- more current ⇒ higher temperature ⇒ lattice ions vibrate with greater amplitude ⇒ electrons collide more often ⇒ resistance rises
- A_X = 4A_Y, so v_X : v_Y = 1 : 4
- V = W/Q = kg m² s⁻²/(A s) = kg m² s⁻³ A⁻¹; Ω = V/A = kg m² s⁻³ A⁻²
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