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Complete Electricity Mastery: A-Level Physics 9702 Guide
Everything you need to know for the CIE A-Level Physics Electricity topic, including exam insights and common pitfalls
9.1 Electric Current
Electric Current as Flow of Charge Carriers
An electric current is the rate of flow of electric charge. Understanding charge carriers is crucial:
Conductors (e.g., Copper)
Contain conduction electrons that are not attached to specific atoms and can drift freely through the material.
Insulators (e.g., Plastic, Glass, Rubber)
All electrons are firmly bound to atoms/molecules and cannot drift through the material.
Conventional current flows from positive to negative, opposite to actual electron flow.
Quantisation of Charge
Electric charge exists in discrete packets. The fundamental unit is the elementary charge (e):
e = 1.60 × 10⁻¹⁹ C
Any charge Q can be expressed as: Q = ne, where n is an integer.
Scale Insight: 1 ampere = 6.24 × 10¹⁸ electrons per second - that's over six million million million electrons every second!
Charge, Current and Time
Q = I × t
Where:
Q = charge in coulombs (C)
I = current in amperes (A)
t = time in seconds (s)
Worked Example
Problem: What charge is provided by a current of 15A to a cooker in one hour? How many electrons pass any point?
Solution:
Charge = 15A × 3600s = 54,000 C
Number of electrons = 54,000 C ÷ 1.6 × 10⁻¹⁹ C = 3.4 × 10²³ electrons
Current and Drift Velocity - The Complete Picture
I = A × n × v × q
Where:
I = current (A)
A = cross-sectional area (m²)
n = number density of charge carriers (m⁻³)
v = mean drift velocity (m/s)
q = charge on each carrier (C)
Understanding the Derivation:
Consider a wire of cross-sectional area A. In one second, electrons move distance v along the wire.
The number of electrons in this "shaded cylinder" volume = n × A × v
Total charge passing per second = n × A × v × e = Current I
Key Insight: A current of 10A doesn't necessarily mean carriers flow 10× faster - it could mean 10× more carriers all traveling at the same speed, or any combination that gives 10× the charge flow rate.
Drift velocity is very small (mm/s), but current is large due to enormous n (~10²⁹ m⁻³ for copper).
9.2 Potential Difference and Power
Potential Difference (p.d.) - Energy Transformation
Definition: The energy transferred per unit charge from electrical energy to other forms.
V = W / Q
Where:
V = potential difference in volts (V)
W = energy transferred in joules (J)
Q = charge in coulombs (C)
1 Volt = 1 Joule per Coulomb
Real-World Context:
Torch bulb (3V): 3 joules transformed per coulomb passing through
Mains lamp (240V): 240 joules transformed per coulomb passing through
P.D. tells you where energy is being transformed in the circuit
Electromotive Force (e.m.f.) - Energy Source
Definition: The energy transferred from other forms (chemical, mechanical) to electrical energy per unit charge.
E = W / Q
Crucial Distinction: e.m.f. is energy supplied TO the circuit; p.d. is energy transformed FROM electrical energy IN the circuit.
Electrical Power - Rate of Energy Transfer
Fundamental Definition: P = W / t
Derived Equations:
P = V × I
P = I² × R
P = V² / R
Power Strategy Guide:
Use P = I²R when current is constant/known
Use P = V²/R when voltage is constant/known
Use P = VI as the universal equation
Efficiency Calculation Example
Problem: Motor from 240V supply provides 900W output with 4.0A current for 80s.
Solution:
Energy supplied = 240V × 4.0A × 80s = 76,800J
Work done = 900W × 80s = 72,000J
Efficiency = 72,000J ÷ 76,800J = 94%
9.3 Resistance and Resistivity
Resistance and Ohm's Law
Definition: R = V / I
Ohm's Law: For a metallic conductor at constant temperature, current is directly proportional to potential difference (R is constant).
1 ohm = 1 volt per ampere
I-V Characteristics - Component Fingerprints
Metallic Conductor (constant temp)
Straight line through origin
Constant resistance
Obeys Ohm's Law
Filament Lamp
Curved line flattening as V increases
Resistance increases "almost uniformly" with temperature
Room temperature resistance is NOT zero
Semiconductor Diode
Infinite resistance until current starts
Conducts only after ~0.6V threshold in forward bias
Resistance falls rapidly once current flows
Resistivity - Material Property
R = ρL / A
Where:
R = resistance (Ω)
ρ = resistivity (Ω·m)
L = length (m)
A = cross-sectional area (m²)
Key Insight: When volume is constant (wire stretched), R ∝ L²
Sensors
Light-Dependent Resistor (LDR)
Resistance decreases as light intensity increases
Thermistor (NTC)
Resistance decreases as temperature increases
Advanced Concepts for Exam Success
Internal Resistance - The Complete Circuit Model
E = I(R + r) or V = E - Ir
Where:
E = e.m.f. of cell
V = terminal p.d.
I = current
r = internal resistance
R = external resistance
Internal Resistance Calculation
Problem: Battery of e.m.f. 9.0V, internal resistance 1.2Ω connected to 3.8Ω resistor.
Solution:
Current = 9.0V ÷ (1.2Ω + 3.8Ω) = 1.8A
Terminal p.d. = 1.8A × 3.8Ω = 6.84V
Power to resistor = 6.84V × 1.8A = 12.3W
Efficiency = 12.3W ÷ (9.0V × 1.8A) = 76%
Maximum Power Transfer Theorem
Maximum power is delivered to external load when:
R = r
This is a frequently tested concept!
Kirchhoff's Laws - Circuit Analysis Tools
First Law (Junction Rule)
ΣIin = ΣIout
Conservation of charge
Current cannot be created or destroyed
Second Law (Loop Rule)
ΣE = ΣIR
Conservation of energy
Gains and losses of energy balance around any closed loop
Teacher's Problem-Solving Framework
The "Four Changes" Strategy
1 watt
1 joule per second
1 ampere
1 coulomb per second
1 volt
1 joule per coulomb
1 ohm
1 volt per ampere
Using these conversions often gives more meaning to problems and helps identify the right approach.
Common Exam Pitfalls & How to Avoid Them
Resistivity Calculations
Error: Using diameter instead of radius for area
Solution: A = πr² = π(d/2)² - remember area wrong by factor of 4 if diameter used
Unit Conversions
Error: 1 mm² = 10⁻³ m² (WRONG!)
Solution: 1 mm² = 10⁻⁶ m² (area scales with square of length)
Multi-step Calculations
Error: Rounding too early causing accumulated error
Solution: Keep at least one extra significant figure until final answer
Physical Reasonableness
Error: Not checking if answers make sense
Solution: AA cells: mA to ~1A, 9V max. Car battery: tens of A, 12V. Mains: ~30A max, 240V/110V
Exam Strategy Checklist
✓ Instantly recall and apply all key formulas
✓ Sketch and interpret I-V graphs correctly, explaining shape in terms of resistance change
✓ Explain LDR and thermistor behavior in terms of resistance changes
✓ Use V = E - Ir confidently for internal resistance problems
✓ Apply Kirchhoff's Laws to complex circuits systematically
✓ Apply Maximum Power Transfer theorem (R = r)
✓ Solve resistivity problems, especially with constant volume (R ∝ L²)
✓ Use the "Four Changes" strategy to understand problem requirements
✓ Check for common pitfalls: diameter vs radius, unit conversions, rounding errors
✓ Verify answers are physically reasonable for the context
A-Level Physics: Electricity – Complete Study Notes
Based on CIE 9702 Syllabus (2019–2023)
- Current & Charge
- Potential & EMF
- Resistance
- I-V Characteristics
- Power & Energy
- Kirchhoff's Laws
- Internal Resistance
- Potential Dividers
- Drift Velocity
- Formula Summary
1. Current & Charge
Electric Current
Rate of flow of electric charge.
I = Q / t
Unit: Ampere (A) = Coulomb per second (C s⁻¹)
Charge & Quantisation
Charge is quantised:
Q = n × e
where e = 1.60 × 10⁻¹⁹ C (elementary charge)
n = Q / e
Additional Formulas
Total charge: Q = I × t
Number of electrons: N = Q / e
Charge flow: ΔQ = I × Δt
2. Potential Difference & EMF
Potential Difference (p.d.)
Work done per unit charge moving between two points.
V = W / Q
Unit: Volt (V) = Joule per Coulomb (J C⁻¹)
Electromotive Force (e.m.f.)
Energy converted from other forms to electrical energy per unit charge in the source.
E = W / Q
Related Formulas
Work done: W = Q × V
Electric field strength: E = V / d
where d = distance between plates
Energy transfer: ΔE = Q × ΔV
💡 Key Difference: p.d. = energy transferred TO component; e.m.f. = energy supplied BY source.
3. Resistance & Resistivity
Ohm's Law
For a metallic conductor at constant temperature:
V = I × R
Resistance Formulas
R = V / I
ρ = (R × A) / L
R = (ρ × L) / A
where: ρ = resistivity, A = cross-sectional area, L = length
Resistors in Series & Parallel
Series:
Rtotal = R₁ + R₂ + R₃ + ...
Parallel:
1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃ + ...
For two resistors: Rtotal = (R₁ × R₂) / (R₁ + R₂)
Factors Affecting Resistance
| Factor | Relationship | Formula Relationship |
|---|---|---|
| Length | R ∝ L | R = kL (k constant) |
| Area | R ∝ 1/A | R = k/A |
| Temperature (Metals) | R increases | RT = R₀[1 + α(T - T₀)] |
| Temperature (NTC Thermistor) | R decreases | R ∝ e1/T |
4. I-V Characteristics
| Component | I–V Graph | Resistance Formula | Key Feature |
|---|---|---|---|
| Ohmic conductor | Straight line through origin | R = V/I (constant) | Obeys Ohm's Law |
| Filament lamp | Curve flattening as V increases | R = V/I (increases with V) | Non-linear due to heating |
| Semiconductor diode | Forward bias only (~0.6V threshold) | Very high R in reverse bias | One-way conduction |
| Thermistor (NTC) | Steeper with increasing V | R decreases exponentially with T | Self-heating effect |
| LDR | Steeper with light intensity | R ∝ 1/illumination | Light-dependent |
Calculating Resistance from I-V Graph
R = V / I
(gradient of line from origin to point)
For non-linear: use tangent gradient for specific point
Gradient of tangent = 1/R at that point
⚠️ Warning: Only metallic conductors at constant temperature obey Ohm's Law (V ∝ I)!
5. Power & Energy in Circuits
Electrical Power
Rate of energy transfer.
P = W / t = V × I
Unit: Watt (W) = Joule per second (J s⁻¹)
Power Formulas
P = V × I
P = I² × R
P = V² / R
P = E / t
Energy Formulas
E = P × t
E = V × I × t
E = I² × R × t
E = (V² / R) × t
Units: Joule (J) or kilowatt-hour (kWh)
1 kWh = 3.6 × 10⁶ J
💡 How to choose formula:
• Use P = VI when both V and I are known
• Use P = I²R when I and R are known
• Use P = V²/R when V and R are known
• For energy, multiply power by time: E = P × t
• Use P = VI when both V and I are known
• Use P = I²R when I and R are known
• Use P = V²/R when V and R are known
• For energy, multiply power by time: E = P × t
6. Kirchhoff's Laws
Kirchhoff's First Law (Junction Rule)
Conservation of charge at a junction.
∑Iin = ∑Iout
Kirchhoff's Second Law (Loop Rule)
Conservation of energy around a closed loop.
∑E = ∑(I × R)
Sum of e.m.f.s = Sum of potential differences
Applying to Circuits
For series: I is constant, Vtotal = V₁ + V₂ + V₃
For parallel: V is constant, Itotal = I₁ + I₂ + I₃
Loop equation: E₁ - E₂ = I₁R₁ - I₂R₂ + I₃R₃
7. Internal Resistance & Cells
Internal Resistance (r)
Resistance within the source causing energy loss.
V = E - I × r
where: V = terminal p.d., E = e.m.f., I = current
Key Formulas
Terminal p.d.: V = E - I × r
Lost volts: Vlost = I × r
Current: I = E / (R + r)
Power to external: Pext = I² × R = V × I
Power lost internally: Plost = I² × r
Total power: Ptotal = E × I = I² × (R + r)
Efficiency: η = [R / (R + r)] × 100%
Max power transfer: when R = r
Combining Cells
| Configuration | Total e.m.f. | Total Internal Resistance | Formula |
|---|---|---|---|
| Series (n identical) | nE | nr | Etotal = nE, rtotal = nr |
| Parallel (n identical) | E | r/n | Etotal = E, rtotal = r/n |
💡 Important: Terminal p.d. = e.m.f. only when:
- Circuit is open (I = 0)
- Internal resistance is negligible (r = 0)
8. Potential Dividers & Potentiometers
Potential Divider Rule
For two resistors in series:
Vout = [R₂ / (R₁ + R₂)] × Vin
Potential Divider Formulas
V₁ = [R₁ / (R₁ + R₂)] × Vin
V₂ = [R₂ / (R₁ + R₂)] × Vin
For multiple resistors: Vn = [Rn / Rtotal] × Vin
Current in divider: I = Vin / (R₁ + R₂)
Potentiometer Principle
Comparing e.m.f.s using a uniform wire:
E₁ / E₂ = l₁ / l₂
where l₁, l₂ = balancing lengths
Potentiometer Formulas
For comparing cells: E₁ / E₂ = l₁ / l₂
For measuring e.m.f.: E = (l / L) × Vdriver
Internal resistance: r = R × [(l₁ - l₂) / l₂]
where l₁ = balancing length with open circuit, l₂ = with known resistor R
Potential gradient: k = Vdriver / L
9. Drift Velocity & Charge Carrier Density
Fundamental Relationship
I = n × A × v × q
where:
- n = number density of charge carriers (m⁻³)
- A = cross-sectional area (m²)
- v = average drift velocity (m s⁻¹)
- q = charge on each carrier (C)
Derived Formulas
Drift velocity: v = I / (n × A × q)
For electrons: v = I / (n × A × e) where e = 1.6 × 10⁻¹⁹ C
Number of charge carriers: N = n × A × L
Total charge in wire: Q = n × A × L × q
Charge carrier density: n = I / (A × v × q)
Key Proportional Relationships
| Relationship | Formula | Explanation |
|---|---|---|
| v ∝ Current | v ∝ I | More current = faster drift |
| v ∝ 1/Area | v ∝ 1/A | Thinner wire = faster drift for same I |
| v ∝ 1/Carrier density | v ∝ 1/n | More carriers = slower individual drift |
| Series circuit | v ∝ 1/A (I constant) | In series, I same everywhere |
⚠️ Remember: Drift velocity is VERY slow (~10⁻⁴ m/s in copper)! The electrical signal (wave) travels at ~3 × 10⁸ m/s, but individual electrons drift slowly.
10. Complete Formula Summary
Current & Charge
I = Q / t
Q = I × t
Q = n × e
n = Q / e
ΔQ = I × Δt
Potential & Energy
V = W / Q
W = Q × V
E = W / Q (e.m.f.)
E = V / d (electric field)
ΔE = Q × ΔV
Resistance
R = V / I
ρ = (R × A) / L
R = (ρ × L) / A
Series: RT = R₁ + R₂ + ...
Parallel: 1/RT = 1/R₁ + 1/R₂ + ...
For two parallel: RT = (R₁ × R₂) / (R₁ + R₂)
Power & Energy
P = V × I = I² × R = V² / R
E = P × t = V × I × t = I² × R × t = (V² / R) × t
1 kWh = 3.6 × 10⁶ J
Internal Resistance
V = E - I × r
I = E / (R + r)
Pext = I² × R = V × I
Plost = I² × r
Ptotal = E × I
η = [R / (R + r)] × 100%
Max power when R = r
Drift Velocity
I = n × A × v × q
v = I / (n × A × q)
N = n × A × L
Q = n × A × L × q
Potential Dividers
Vout = [R₂ / (R₁ + R₂)] × Vin
V₁ = [R₁ / (R₁ + R₂)] × Vin
Potentiometer: E₁ / E₂ = l₁ / l₂
Internal resistance: r = R × [(l₁ - l₂) / l₂]
🎯 Exam Success Strategy:
- Know ALL formulas - this summary is your checklist
- Practice unit conversions - mm² to m², mA to A, etc.
- Show ALL steps - method marks can save you
- Time management - PP1: ~1 min/question, PP2: allocate time per section
- Check units in answers - wrong unit = wrong answer