A-Level Physics — 16) Circuits (IP-Friendly Guide)

TL;DR
Circuits is not “just Ohm's Law” — it is the control panel behind practical Paper 4 and every data-logger question. This guide turns the SEAB bullet-points into classroom-tested check-lists, sensor hacks and WA timing tricks.

1 Circuit symbols & diagrams

• Memorise SEAB 's full symbol set — cell, switch, fixed/variable resistor, LDR, NTC thermistor, diode, capacitor, ammeter and voltmeter. Symbols must be drawn with a ruler in Paper 2 for the mark.
• Parent tip: have your teen print the symbol sheet and stick it on the inside cover of their graph-book.

1.1 Mini-drill

Sketch a potential-divider with a fixed resistor and an LDR controlling \(V_\text{out}\). Mark the sensing node. Time limit = 30 s.

2 Resistance, resistivity and internal resistance

2.1 Ohm 's law refresher

The definition is \(R = \dfrac{V}{I}\) \((\Omega)\). Use it only when the graph through the origin is linear.

2.2 Microscopic link

For a uniform wire
\[ R = \rho \dfrac{l}{A}, \]
where \(\rho\) is resistivity, \(l \space (\text{m})\) is length and \(A \space (\text{m}^2)\) is cross-sectional area. Double \(l\) → double \(R\); halve \(A\) → double \(R\).

2.3 Temperature stories

• Metals: hotter lattice ⇒ more collisions ⇒ higher resistivity.
• NTC thermistors: heat frees charge carriers in the semiconductor ⇒ lower resistivity.

2.4 Internal resistance \((r)\)

Real cells obey
\[ V = \varepsilon - Ir, \]
so increasing load current drops terminal p.d.

Graph cue: gradient = \(-r\), intercept = \(\varepsilon\). Quote \(\varepsilon\) in V not eV.

3 Resistors in series & parallel

Be ready to spot hidden series chains in messy WA diagrams.

3.1 Timing hack

Write the total resistance before inserting numbers; algebra first reduces keypad slips.

4 Potential divider circuits

4.1 Core formula

\[ V_\text{out} = V_\text{in} \space \dfrac{R_2}{R_1 + R_2}. \]

4.2 Sensor combos

• Brightness probe: replace \(R_2\) with LDR → \(V_\text{out} \uparrow\) in the dark.
• Fire alarm: replace \(R_2\) with NTC → \(V_\text{out} \uparrow\) when hot.

Include a buffer op-amp in higher-ability tutorials to prevent loading.

5 I-V characteristics

Plot with current on the y-axis — SEAB marks for axis labels.

6 Capacitors in series & parallel

Mnemonic: series for resistors adds \(R\); series for capacitors adds \(1/C\).

7 RC circuits with d.c. source

7.1 Time constant

\[ \tau = RC. \]
At \(t = \tau\) a discharging capacitor's \(Q,\space V\) or \(I\) falls to \(\dfrac{1}{e} \approx37 \%\) of its initial value.

7.2 Exponential laws

Charging:
\[ Q = Q_0 \left[1 - e^{-t/\tau}\right], \quad V = V_0 \left[1 - e^{-t/\tau}\right]. \]

Discharging:
\[ Q = Q_0 e^{-t/\tau}, \quad V = V_0 e^{-t/\tau}, \quad I = I_0 e^{-t/\tau}. \]

Plot \(\ln V\) vs \(t\) to obtain a straight line of gradient \(-1/RC\) — a favourite Paper 4 practical.

8 Three WA timing rules (Circuits edition)

1. Label units first for every numerical answer — avoids unit-free slips.
2. Sketch a quick circuit even if not asked; you see hidden series legs faster.
3. Log-log check: if your answer for \(R\) or \(C\) is < 0.1 or > 10 \(\Omega / F\), re-read prefixes.

9 Further reading

• SEAB H2 Physics 9478 syllabus (2026)
• Save My Exams — Circuit Symbols
• OpenStax — Direct Current Circuits
• Lumen — Electromotive Force
• Electronics-Tutorials — RC Time Constant
• Savemyexams — Potential Dividers
• LibreTexts — Resistivity & Temperature
• Electronics-Notes — Filament Lamp I-V
• MME — Capacitor Charge & Discharge

10 Call-to-action

Parents: book a 60-min Circuit Masterclass four weeks before WA 2 — most careless marks hide in potential-divider algebra.
Students: screenshot the RC graphs above and recreate them without notes tomorrow.

Last updated 14 Jul 2025. Next review when SEAB issues the 2027 draft syllabus.