Circuits: Complete A Level H2 Physics Cheatsheet
A Level Physics (H2), Chapter 16 · 9478 Topic 16 · Read time: ~12 minutes
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Key Formulas
Resistance, resistivity and I-V characteristics
Resistance = p.d. ÷ current, R = V/I. For a uniform wire, R = ρl/A, where ρ is the resistivity of the material.
Ohmic resistor: straight line through the origin. Filament lamp: curves towards the V axis, because as the metal heats, lattice ions vibrate more and impede the drift of electrons, so resistivity rises.
Semiconductor diode: conducts in one direction once the forward p.d. exceeds about 0.6 V. NTC thermistor: resistance falls as temperature rises, because the number density of charge carriers increases sharply.
Trap: Explain metals and semiconductors differently. In a metal, n is roughly constant and drift is hindered more. In a semiconductor, n increases a lot, outweighing everything else.
Internal resistance
A real source has internal resistance r. E = I(R + r), so the terminal p.d. = E − Ir, which falls as more current is drawn.
Terminal p.d. equals the e.m.f. only when no current flows. Output power to the external load is greatest when R = r.
Series, parallel and potential dividers
Resistors: series R = R₁ + R₂; parallel 1/R = 1/R₁ + 1/R₂.
In a potential divider, the output across R₂ is V × R₂/(R₁ + R₂). Replacing one resistor with an NTC thermistor or an LDR makes the output respond to temperature or light.
Capacitors combine the opposite way: parallel C = C₁ + C₂, series 1/C = 1/C₁ + 1/C₂.
Trick: Equal components check: two equal resistors in parallel give half; two equal capacitors in parallel give double.
RC circuits
A capacitor discharging through a resistor: charge, p.d. and current all decay exponentially, x = x₀e^(−t/τ), with time constant τ = RC.
After one τ a discharging quantity falls to about 37% of its start value. When charging, Q and V rise as x₀[1 − e^(−t/τ)], reaching 63% after one τ, while the current decays.
The time to halve is τ ln 2 ≈ 0.69RC. After about 5τ the process is effectively complete.
Trap: During charging the current falls, even though the charge rises. Only Q and V grow.
Worked Example
A battery of e.m.f. 9.0 V and internal resistance 0.50 Ω is connected to a 4.0 Ω resistor. Separately, a 470 μF capacitor charged to 12 V discharges through a 10 kΩ resistor.
(a) Calculate the current from the battery and its terminal p.d. [2]
I = E / (R + r) = 9.0 ÷ 4.5 = 2.0 A
Terminal p.d. = 9.0 − 2.0 × 0.50 = 8.0 V
(b) A second 4.0 Ω resistor is added in parallel. Explain what happens to the terminal p.d. [2]
External resistance falls to 2.0 Ω, so the current rises (to 3.6 A).
More p.d. is lost across r, so terminal p.d. falls (to 7.2 V).
(c) For the capacitor, calculate τ and the p.d. after 5.0 s. [2]
τ = RC = 10 × 10³ × 470 × 10⁻⁶ = 4.7 s
V = 12 e^(−5.0/4.7) = 4.1 V
(d) Calculate the time for the capacitor's p.d. to fall to 6.0 V. [1]
Halving time = τ ln 2 = 4.7 × 0.693 = 3.3 s
Why this question is a good test of the topic: part (b) chains parallel resistance with internal resistance, and the capacitor parts check unit prefixes and the halving-time shortcut.
Frequently Asked Questions
Why does a filament lamp's resistance increase with current?
The filament heats up, its lattice ions vibrate more and impede the drift of electrons, so its resistivity increases.
Why does an NTC thermistor's resistance fall when it is heated?
More charge carriers are released, so the number density of carriers increases sharply.
When does terminal p.d. equal e.m.f.?
Only when no current flows. Any current causes a p.d. across the internal resistance.
What is the time constant of an RC circuit?
τ = RC. After one τ, a discharging capacitor's charge, p.d. and current fall to about 37% of their initial values.
How do capacitors combine in series and parallel?
The opposite of resistors: in parallel capacitances add, in series their reciprocals add.
Internal resistance and RC circuits costing marks?
Small group A Level H2 Physics classes at TGC Academy's Bishan, Bukit Timah and Potong Pasir centres, helmed by Andrew Seah, MOE Award-Winning Teacher and Marshall Cavendish textbook author, with a team of tutors.