Unit 2 in two days

• V = W/Q
• I = ΔQ/Δt
• R = V/I
• P = VI = I²R = V²/R
• W = VIt
• R = R₁ + R₂ + …
• 1/R = 1/R₁ + 1/R₂ + …
• N = It/e
• 1 kWh = 3.6 × 10⁶ J

Know cold

• Series: the same current everywhere, and the p.d.s add up to the supply.
• Parallel: the same p.d. across every branch, and the branch currents add up. Two in parallel give R₁R₂/(R₁ + R₂), always less than the smallest one.
• For “the power in one resistor”, first find the current through that resistor only (or the p.d. across it).
• Number of electrons = charge ÷ 1.60 × 10⁻¹⁹ C.
• Derivations they’ve asked for: the parallel formula (same V, currents add, so V/R = V/R₁ + V/R₂) and P = V²/R (put I = V/R into P = VI).
• “Assess whether both lamps work normally”: work out the actual p.d. or current for each lamp and compare it with its rating.

Try: June 2025 Q16, January 2026 Q15 and Q16, June 2026 Q11 and Q12.

• R = ρl/A
• A = πd²/4

Know cold

• Resistivity is RA/l: the resistance of a piece of the material 1 m long with a 1 m² cross-section. Unit Ω m. It depends on the material (and temperature), not the shape.
• Practical: measure the diameter with a micrometer at several points, rotating it, and average. Length with a metre rule. Ammeter in series, voltmeter across the wire (or an ohmmeter). Change the length with a crocodile clip and plot R against l: the gradient is ρ/A, so ρ = gradient × A. Keep the current small and switch off between readings so the wire doesn’t heat up.
• Same material: R ∝ l/d². Stretch a wire to twice the length at constant volume and its area halves, so R goes up four times.
• Traps: convert mm to m before squaring (mm² × 10⁻⁶ = m²), and don’t use the diameter as the radius.

Try: June 2026 Q17, October 2025 Q13 (the practical), October 2024 Q15.

• V_out = V_in × R/R_total
• V₁/V₂ = R₁/R₂

Know cold

• Parts in series carry the same current, so they share the supply p.d. in the ratio of their resistances.
• Bigger resistance, bigger share. When a thermistor warms (or an LDR gets more light) its resistance falls, so the p.d. across it falls and the fixed resistor’s p.d. rises by the same amount.
• “Deduce whether the heater switches on”: read R off the graph, work out the p.d. across whichever component the output is taken from, compare it with the switching value, conclude.
• A voltmeter that isn’t very high-resistance lowers the resistance of the part it’s connected across, so it reads low.
• Along a uniform wire the p.d. is proportional to the length: V = V_total × x/l.

Try: October 2025 Q17, June 2026 Q14, October 2023 Q14.

• ε = I(R + r)
• V = ε − Ir

Know cold

• e.m.f. is the energy transferred to each unit of charge by the source (chemical to electrical). “An e.m.f. of 6.0 V” means 6.0 J for every coulomb.
• p.d. is the energy transferred from each unit of charge by a component.
• When current flows, the terminal p.d. is less than ε because some energy per coulomb is transferred in the internal resistance. Those “lost volts” are Ir.
• A high-resistance voltmeter across a cell with nothing else connected reads ε: the current is almost zero, so Ir is almost zero.
• Bigger external R, smaller current, fewer lost volts, so the terminal p.d. gets closer to ε. Maximum current is ε/r.
• A battery heats up under heavy load because a large current dissipates I²r inside it. An old battery has a bigger r, so more lost volts and too little p.d. for a high-current motor.
• Cells in series: ε and r both add. Identical cells in parallel: the same ε, with r divided by the number of cells.
• Practical: cell, ammeter and variable resistor in series, voltmeter across the cell. Vary R, record V and I, plot V against I: the y-intercept is ε and the gradient is −r. If they make you plot R against 1/I, the gradient is ε and the intercept is −r. A straight line means r is constant.

Try: January 2026 Q13, June 2026 Q15, January 2024 Q14.

• I = nqvA
• I = ΔQ/Δt

Know cold

• n is the number of charge carriers per m³, q = 1.60 × 10⁻¹⁹ C, v is the drift velocity and A the cross-sectional area.
• Drift velocity in a metal is tiny because n is enormous (about 10²⁸ to 10²⁹ per m³).
• Same current through two wires in series: v ∝ 1/(nA). Double the diameter, four times the area, a quarter of the drift velocity.
• Copper vs nichrome of the same size carrying the same current: nichrome has fewer conduction electrons per m³, so its electrons drift faster.
• Semiconductors have far smaller n than metals, which is why their resistivity is so much higher.

Try: January 2026 Q11, October 2025 Q11, January 2023 Q13.

The chains examiners mark

• Metal or filament getting hotter: the ions vibrate more, conduction electrons collide with them more often, the current (drift velocity) falls for the same p.d., so R = V/I rises. The number of conduction electrons stays about the same.
• NTC thermistor getting hotter: electrons gain energy and more conduction electrons are released (n rises). This outweighs the extra vibration, so the current rises for the same p.d. (I = nqvA) and R falls.
• LDR in brighter light: absorbed photons release more conduction electrons, n rises, R falls.
• I–V shapes: a resistor is a straight line through the origin. A filament lamp is an S-curve bending towards the V-axis. A thermistor curves towards the I-axis as it heats. A diode passes almost no current until about 0.6–0.7 V forward, and none in reverse.

Try: January 2026 Q12, October 2025 Q12(b), January 2021 Q16.

• E = hf
• v = fλ (c = fλ)
• hf = φ + ½mv²_max
• 1 eV = 1.60 × 10⁻¹⁹ J
• f₀ = φ/h

Know cold

• Work function φ: the minimum energy needed to release an electron from the surface of the metal. Threshold frequency f₀: the lowest frequency that releases electrons, f₀ = φ/h.
• The calculation chain: λ, then f = c/λ, then E = hf, then E_k(max) = hf − φ, then v = √(2E_k/m). Keep everything in joules, or everything in eV.
• Brighter light at the same frequency (above f₀): more photons per second, more electrons per second, a bigger current. E_k(max) doesn’t change.
• Longer wavelength: lower frequency, less energy per photon, lower E_k(max). Below f₀ nothing comes out, however bright.
• Why the electrons have a range of kinetic energies: φ is only the minimum. Electrons from deeper in the metal lose energy in collisions on the way out.
• Graph of E_k(max) against f: the gradient is h, the x-intercept is f₀ and the y-intercept is −φ.
• “Why this proves light is photons” is skeleton A in the 6-mark bank.

Try: October 2025 Q15, January 2026 Q21, June 2026 Q19.

• I = P/A
• efficiency = useful power out ÷ total power in
• A = 4πr² (point source)
• photons per second = P/(hf)

Know cold

• Intensity is power per unit area (W m⁻²). From a point source it follows the inverse square law: twice the distance, a quarter of the intensity.
• Solar panel: power in = intensity × area, and efficiency = electrical power out ÷ power in.
• Photons per second = power ÷ energy of one photon = Pλ/(hc). Electrons per second = current ÷ e. Percentage of photons that release electrons = electrons per second ÷ photons per second × 100.

Try: June 2025 Q18, June 2026 Q18(a), January 2021 Q20.

• λ = h/p
• p = mv
• E_k = ½mv²
• E_k = eV (electron accelerated through V volts)

Know cold

• Electron diffraction, a ring pattern from graphite or a thin metal foil, is the evidence that electrons behave as waves, because diffraction is a wave property. It shows up because the electrons’ wavelength is similar to the spacing between atoms (about 10⁻¹⁰ m).
• Raise the accelerating p.d. and the electrons go faster, with more momentum, so a shorter wavelength, less diffraction and smaller rings.
• Accelerated electron: E_k = eV in joules, then v = √(2E_k/m), then λ = h/(mv).
• Everyday objects like a car have a wavelength far too small to ever diffract.

Try: January 2026 Q14, June 2025 Q15, October 2023 Q15.

• E = hf
• hf = E₁ − E₂
• λ = hc/ΔE

Know cold

• Levels are negative. 0 eV means the electron has left the atom (ionised), and the most negative level is the ground state.
• Calculation: the gap in eV × 1.60 × 10⁻¹⁹ gives joules, then f = ΔE/h, then λ = c/f.
• A photon is absorbed only if its energy exactly matches a gap: all or nothing, otherwise the atom stays as it was. A colliding electron can hand over part of its energy and keep the rest.
• Discrete levels mean only certain gaps, so only certain frequencies: a line spectrum. Different elements have different levels, so different spectra.
• Number of possible lines from level n down to the ground state: n(n − 1)/2. Also an MCQ in almost every paper where it isn’t in Section B.

Try: June 2026 Q13, June 2024 Q17, October 2021 Q16.

• n = c/v
• n₁ sin θ₁ = n₂ sin θ₂
• sin C = 1/n
• sin C = n₂/n₁ (between two materials)

Know cold

• Refraction is a change in direction when a wave crosses into a medium where its speed is different. The frequency stays the same; speed and wavelength change.
• Slowing down bends the ray towards the normal, speeding up bends it away. Along the normal there’s no change in direction, because the whole wavefront slows at the same moment.
• TIR needs both: travelling from higher n to lower n, and an angle of incidence bigger than C. At exactly C the refracted ray runs along the boundary. Below C, part reflects and part refracts.
• “Deduce whether TIR happens”: work out C, get the angle of incidence from the geometry (angles in a triangle add to 180°), compare, conclude.
• Useful values: glass (n = 1.5) has C ≈ 42°, water (n = 1.33) has C ≈ 49°.
• Optical fibre: the cladding has a lower n than the core. It makes C bigger than a core-to-air boundary would, but protects the core. A lower-n cladding gives a smaller C, so more light is trapped. Pulses spread out because rays take paths of different lengths.
• Measuring n: ray box and glass block, measure i and r at several angles, plot sin i against sin r, and the gradient is n.
• Two materials with similar n (a bead in water, skin on glass) barely refract or reflect at the boundary, so the edge “disappears” and TIR stops where they touch.

Try: January 2026 Q20, October 2025 Q14, October 2024 Q17.

• v = √(T/μ)
• v = fλ
• W = mg
• node to node = λ/2
• string: λ = 2L
• closed tube: L = λ/4

Know cold

• How it forms (the 3-mark version): the wave reflects at the end, the incident and reflected waves (same frequency and amplitude) travel in opposite directions and superpose, giving nodes where they always cancel and antinodes where they reinforce. The 6-mark version is skeleton D.
• String fixed at both ends: fundamental λ = 2L. Tube closed at one end: a node at the closed end and an antinode at the open end, fundamental L = λ/4. Tube open at both ends: L = λ/2.
• Combine the formulas: f = (1/2L)√(T/μ), so f ∝ √T, f ∝ 1/L and f ∝ 1/√μ. A graph of f² against T is a straight line through the origin with gradient 1/(4L²μ). A graph of node spacing against 1/f has gradient v/2.
• μ is mass per unit length (kg m⁻¹). Tension from a hanging mass is mg, with g = 9.81.
• Points between two neighbouring nodes are in phase; points in neighbouring loops are in antiphase. Amplitude varies with position.
• Stationary vs progressive: stationary has no net energy transfer, has nodes and antinodes, and the same phase within a loop. Progressive transfers energy, has the same amplitude everywhere, and its phase changes along the wave.
• Practical: vibration generator, string over a pulley with hanging masses. Change f until the pattern is clear. Node positions are hard to judge, so measure across several loops.

Try: June 2026 Q16, June 2025 Q17, October 2024 Q18.

• nλ = d sin θ
• d = 1/N (N = lines per metre)
• tan θ = x/D

Know cold

• Diffraction is waves spreading out as they pass through a gap or around an obstacle. It’s biggest when the gap is about one wavelength wide.
• Huygens’ construction: every point on a wavefront acts as a source of secondary wavelets, and the new wavefront is the line touching all of them.
• Lines per mm × 1000 = lines per m, and d = 1 ÷ that. x is the distance from the central maximum to the maximum, D the grating-to-screen distance.
• Highest possible order: n ≤ d/λ, rounded down, because sin θ can’t be more than 1. That’s also why a third order can be impossible.
• Why there’s a bright maximum: light diffracts at each slit, waves from neighbouring slits superpose, and at the maximum the path difference is a whole number of wavelengths, so they arrive in phase and interfere constructively.
• White light: a white central maximum (every colour has zero path difference there), then spectra with violet nearest the centre and red furthest out, because shorter λ gives smaller θ.
• Practical: don’t look into the laser and avoid reflections. Measure between the first orders on both sides and halve it, and use a large grating-to-screen distance to cut the percentage uncertainty.

Try: January 2026 Q17, October 2025 Q16, October 2024 Q16.

• phase difference = (path difference ÷ λ) × 360°

Know cold

• Superposition: where waves meet, the resultant displacement is the sum of their individual displacements.
• Coherent: the same frequency and a constant phase difference. Two separate lamps aren’t coherent, so they can’t give a steady pattern.
• Constructive: in phase, path difference nλ, maximum amplitude (loud, bright).
• Destructive: antiphase (180°, π rad), path difference (n + ½)λ, minimum amplitude (quiet, dark).
• Quiet spots aren’t totally silent because the two waves arrive with different amplitudes.
• Beats: two slightly different frequencies aren’t coherent, so the phase difference keeps changing and the loudness rises and falls.
• Noise-cancelling: send out sound in antiphase so it interferes destructively.

Try: January 2023 Q15, January 2024 Q17, October 2022 Q15.

• v = fλ
• f = 1/T

Know cold

• Transverse: oscillations perpendicular to the direction the wave travels (light, waves on a string). Longitudinal: oscillations parallel to it (sound). Compressions have high pressure and density, rarefactions low. The displacement is zero at the centre of each.
• A displacement–distance graph gives λ and amplitude. A displacement–time graph gives the period and amplitude, never λ.
• Oscilloscope: period = number of divisions × time-base. Measure across several cycles.
• Speed of sound practical: the signal generator drives the loudspeaker and one oscilloscope trace, the microphone gives the other trace. Move the microphone until the traces are back in phase: that distance is one λ (measure across several). Then v = fλ, or plot λ against 1/f and the gradient is v.

Try: June 2021 Q17 (the speed of sound practical), June 2024 Q15, October 2025 Q2 to Q5.

Know cold

• Unpolarised: oscillations in all planes (every direction perpendicular to the direction of travel). Plane polarised: oscillations in one plane only. That’s the 3-mark “explain the difference” answer.
• Only transverse waves can be polarised, which is how we know light is transverse and why sound can’t be polarised.
• Test: look through one filter and rotate it. Unpolarised light: no change in brightness. Plane-polarised light: brightness goes from maximum to zero every 90°.
• Two filters: bright when lined up, dark at 90°. Three filters with the outer two crossed: turning the middle one to 45° lets some light through.
• Reflected glare is partly polarised, so polarising sunglasses cut it. Phone and LCD screens give out polarised light, so they look black through sunglasses turned 90°. A receiving aerial has to line up with the transmitter’s polarisation.
• Stress: between crossed filters, stressed plastic shows coloured fringes; closely packed fringes mean high stress.

Try: October 2025 Q18, June 2025 Q12(b), January 2026 Q18(c).

• distance = speed × time ÷ 2

Know cold

• A transducer sends short pulses. Part of each pulse reflects at a boundary between materials of different density (a crack, an air gap), the echo time is measured, the speed is known, and distance = vt/2 because the pulse goes there and back. Full version: skeleton E.
• Shorter pulses give better resolution: with a long pulse, echoes from boundaries close together overlap.
• Higher frequency means shorter λ, so smaller detail shows up. That’s why cracks are scanned with MHz, not kHz.
• The gap between pulses has to be longer than the echo time from the furthest target.

Try: January 2026 Q19, June 2025 Q13, June 2024 Q13.