H2 Physics DC Circuits & RC Notes | A-Level 9478

Q: What does A-Level Physics: 16) Circuits Guide cover?
A: From resistor networks to exponential RC transients, this post unpacks Topic 16 of the 2026 H2 Physics syllabus for IP students and parents.

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.

Concrete example: how to use this page

For a mixed circuit, redraw it in stages. Combine obvious series or parallel parts first, then apply Kirchhoff rules only where the circuit cannot be simplified cleanly.

Keep the full circuits + electromagnetism toolkit handy via the H2 Physics notes hub; it links this post with the preceding Currents/Electric Fields chapters and the upcoming electromagnetism topics.

Circuit-solving decision map

Use this map before substituting numbers. Most lost marks happen when students choose the right formula too early but apply it to the wrong part of the circuit.

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

2.2 Microscopic link

For a uniform wire
$$R=\rho \frac{l}{A},$$ where $\rho$ is resistivity, $l$ ($\text{m}$) is length and $A$ (${\text{m}}^2$

2.3 Temperature stories

• Metals (e.g. filament lamp): the number density of charge carriers is essentially fixed - nearly all conduction electrons are already free. As temperature rises, increased lattice vibrations scatter electrons more frequently, reducing the drift velocity for a given applied field. Lower drift velocity means lower current at the same voltage, so resistivity increases.
• Semiconductors (e.g. NTC thermistor): thermal excitation promotes electrons across the band gap, sharply increasing the number density of charge carriers. This increase outweighs any reduction in drift velocity, so resistivity falls with rising temperature.

Exam cue: outcome (f) asks you to use the phrases "drift velocity" (metals) and "number density of charge carriers" (semiconductors) - include both explicitly for full marks.

2.4 Internal resistance $(r)$

Real cells obey
$$V=\epsilon -Ir,$$ so increasing load current drops terminal p.d.

Graph cue: gradient = $-r$, intercept = $\epsilon$. Quote $\epsilon$ in V not eV.

2.5 Output power and internal resistance

The power delivered to the external load $R$ is

$$P_{\text{out}}=I^{2}R={\left(\frac{\epsilon }{r+R}\right)}^{2}R.$$

When $R$ is very small, most of the e.m.f. drives current through $r$, so $P_{\text{out}}\to 0$. When $R$ is very large, current becomes negligible, so $P_{\text{out}}\to 0$

Exam cue: questions on outcome (g) can ask you to state both effects - terminal p.d. falls as $I$ increases, and output power varies with load, peaking when $R=r$. Quoting the formula above is sufficient; no calculus derivation is required.

Internal-resistance load-change checkpoint

When the external load $R$ changes, track current, terminal p.d., and useful power separately. They do not all peak at the same load.

Worked check: a cell has $\epsilon =6.0\mathrm{V}$ and $r=2.0\mathrm{\Omega }$. With $R=2.0\mathrm{\Omega }$, $I=6.0/(2.0+2.0)=1.5\mathrm{A}$

Misconception check: maximum terminal p.d. is not maximum output power. In an open-circuit limit, terminal p.d. is close to $\epsilon$, but current is close to zero, so useful power is close to zero.

3 Resistors in series & parallel

Series-parallel reduction checkpoint

Before using a final current or p.d. formula, reduce only the parts that are genuinely in series or genuinely in parallel. Work from the simplest hidden group outward.

Worked check: a $4.0\mathrm{\Omega }$ resistor is in series with a parallel pair of $6.0\mathrm{\Omega }$ and $3.0\mathrm{\Omega }$. First reduce the parallel pair:

$$\frac{1}{R_{\text{parallel}}}=\frac{1}{6.0}+\frac{1}{3.0}=\frac{1}{2.0},$$

so $R_{\text{parallel}}=2.0\mathrm{\Omega }$. Then add the series resistor: $R_{\text{total}}=4.0\mathrm{\Omega }+2.0\mathrm{\Omega }=6.0\mathrm{\Omega }$

Misconception check: the $4.0\mathrm{\Omega }$ resistor is not in parallel with the two-branch group. It sits before the split, so all current passes through it before the current divides.

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

Kirchhoff setup checkpoint

Use Kirchhoff's laws when the circuit cannot be reduced cleanly into one series-parallel equivalent. The first mark is usually for defining current directions and loop signs consistently.

Worked check: for a single-loop circuit with e.m.f. $\epsilon$, internal resistance $r$, and external resistor $R$, moving around the loop with the current gives

$$+\epsilon -Ir-IR=0,$$

so $\epsilon =I(R+r)$ and the terminal p.d. across the external resistor is $V=IR=\epsilon -Ir$.

Misconception check: Kirchhoff equations are bookkeeping, not a new formula set. If the chosen current direction turns out wrong, the solved current will be negative; the circuit is not invalid.

3.1 Timing hack

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

4 Potential divider circuits

4.1 Core formula

$$V_{\text{out}}=V_{\text{in}}\frac{R_2}{R_1+R_2}.$$

4.2 Potential-divider output checkpoint

Before deciding whether $V_{\text{out}}$ rises or falls, mark the output leg in the diagram. The output voltage is the p.d. across the component connected between the output node and the reference line.

Misconception check: do not memorise "LDR in bright light means higher output voltage". The answer flips when the sensor moves from the lower leg to the upper leg.

4.3 Sensor combos

• Brightness probe: replace $R_2$ with LDR, so $V_{\text{out}}$ increases in the dark.
• Fire alarm: replace $R_1$ with NTC, so $V_{\text{out}}$

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.

I-V graph resistance checkpoint

Before reading resistance from an I-V graph, check whether the component is ohmic and which axis is plotted vertically. Resistance is $V/I$, so the graph shape decides whether one constant gradient is enough.

Worked check: if an ohmic resistor's $I$-against-$V$ graph has gradient $0.25\mathrm{A}\cdot {\mathrm{V}}^{-1}$, then $R=1/0.25=4.0\mathrm{\Omega }$. If the axes were reversed, the same numerical gradient would instead mean $0.25\mathrm{\Omega }$.

Misconception check: "gradient" is not automatically resistance. It is resistance only when voltage is on the vertical axis and current is on the horizontal axis.

6 Capacitors in series & parallel

Mnemonic: series for resistors adds $R$; series for capacitors adds $1/C$.

Capacitor combination checkpoint

After finding the equivalent capacitance, decide what stays the same in the actual circuit. This prevents mixing the resistor rules with the capacitor rules.

Worked check: two capacitors, $2.0\mathrm{uF}$ and $6.0\mathrm{uF}$, are connected in series to a $12\mathrm{V}$ supply. Their equivalent capacitance is ${\left(1/2.0+1/6.0\right)}^{-1}=1.5\mathrm{uF}$, so the series charge is $Q=C_{\text{tot}}V=18\mathrm{uC}$

Misconception check: in series, capacitors do not share the supply voltage equally unless their capacitances are equal. They share the same charge; the voltage divides in inverse proportion to capacitance.

7 RC circuits with d.c. source

7.1 Time constant

$$\tau =RC.$$ At $t=\tau$ a discharging capacitor's $Q,V$ or $I$ falls to $\frac{1}{e}\approx 37\%$

7.2 Exponential laws

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

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

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

RC linear-plot checkpoint

Use a logarithmic plot only after deciding which exponential form you have. For a discharging capacitor, $V=V_0{e}^{-t/RC}$, so

$$\ln V=\ln V_0-\frac{t}{RC}.$$

Worked check: if a discharge graph of $\ln V$ against $t$ has gradient $-0.50{\mathrm{s}}^{-1}$, then

$$RC=-\frac{1}{-0.50}=2.0\mathrm{s}.$$

Common trap: the y-intercept gives $\ln V_0$, not $V_0$. Undo the logarithm before quoting the initial voltage.

7.3 Variation with time - key checkpoints

The table below summarises how charge $Q$, voltage $V$, and current $I$ behave at notable time points. All values are fractions of the initial (discharging) or maximum (charging) quantity.

The same fractions apply to $V$ throughout. For current: during discharging, $I$ follows the same decaying exponential shape as $Q$ and $V$. During charging, $I$ does the opposite - it starts at its maximum value $I_0=\epsilon /R$ and decays to zero as the capacitor approaches full charge. In other words, the charging current curve has the same shape as a discharging

Revision cue: "one time constant = 63% charged (or 37% remaining)" is the most tested number - learn it as a reflex.

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.

Need structured practice on Circuits? Our H2 Physics tuition programme covers this topic with weekly problem sets and Paper 4 practical drills.

Comprehensive revision pack

9478 Section V, Topic 16 Syllabus outcomes

Candidates should be able to:

• (a) recall and use appropriate circuit symbols.
• (b) draw and interpret circuit diagrams containing sources, switches, resistors (fixed and variable), ammeters, voltmeters, lamps, thermistors, light-dependent resistors, diodes, capacitors and any other type of component referred to in the syllabus.
• (c) define the resistance of a circuit component as the ratio of the potential difference across the component to the current in it, and solve problems using the equation $V=IR$.
• (d) recall and solve problems using the equation relating resistance to resistivity, length and cross-sectional area, $R=\frac{\rho l}{A}$.
• (e) sketch and interpret the I-V characteristics of various electrical components in a d.c. circuit, such as an ohmic resistor, a semiconductor diode, a filament lamp and a negative temperature coefficient (NTC) thermistor.

Concept map (in words)

Start with circuit symbols to communicate clearly. Use Ohm's law and resistivity for basic components. Combine resistors/capacitors systematically. Potential dividers convert sensor resistance to voltage signals. RC circuits introduce exponential behaviour governed by time constant RC.

Key relations

Derivations & reasoning to master

1. Potential divider: derive ratio using loop current, or use voltage drop proportionality.
2. RC exponential forms - use, don't derive: RC charging and discharging are assessable under 9478 Topic 16 outcome (l). Candidates are expected to use the given forms $x=x_0{e}^{-t/\tau }$ and $x=x_0\left[1-e^{-t/\tau }\right]$

Worked example 1 - potential divider sensor

Design a circuit that outputs $3.0\mathrm{V}$ when an LDR (resistance $12\mathrm{kOhm}$ in dark, $2.0\mathrm{kOhm}$ in bright light) is exposed to daylight using a $9.0\mathrm{V}$ supply. Determine the fixed resistor value and predict the output in darkness.

Method: solve $V_{\text{out}}=V_{\text{in}}\frac{R_{\text{LDR}}}{R_{\text{fixed}}+R_{\text{LDR}}}$

Bright light: $3.0=9.0\times \frac{2.0}{R_{\text{fixed}}+2.0}$ (k$\Omega$) ⇒ $R_{\text{fixed}}=4.0\mathrm{kOhm}$

Darkness: $V_{\text{out}}=9.0\times \frac{12}{4.0+12}=6.75\mathrm{V}$.

Worked example 2 - RC timing

A $47\mathrm{kOhm}$ resistor and $100\mathrm{uF}$ capacitor form a delay circuit.
(a) Find the time constant.
(b) How long until the capacitor voltage reaches 90 percent of the supply?
(c) If used with $5\mathrm{V}$ logic, what is the voltage at $3\tau$?

Solution: The time constant is $4.7\mathrm{s}$ $\left(\tau =RC\right)$.

$$V=V_0(1-e^{-t/(RC)})$$

Use this relation to solve for $t$ and the specific voltages.

For 90\% charging: $0.90=1-e^{-t/\tau }\Rightarrow t=\tau \ln 10=2.303\tau \approx 10.8\mathrm{s}$.

At $3\tau$: $V=V_0(1-e^{-3})=0.950V_0\approx 4.75\mathrm{V}$

Worked example 3 - combined capacitance

Three capacitors: $C_1=6.0\mathrm{uF}$, $C_2=3.0\mathrm{uF}$, and $C_3=4.0\mathrm{uF}$

Step 1 - parallel combination of $C_1$ and $C_2$:

$$C_{\text{P}}=C_1+C_2=6.0+3.0=9.0\mathrm{uF}.$$

Step 2 - $C_{\text{P}}$ in series with $C_3$:

$$\frac{1}{C_{\text{tot}}}=\frac{1}{C_{\text{P}}}+\frac{1}{C_3}=\frac{1}{9.0}+\frac{1}{4.0}=\frac{4.0+9.0}{36}=\frac{13}{36}.$$

$$C_{\text{tot}}=\frac{36}{13}\approx 2.8\mathrm{uF}.$$

Note: the series step always gives a result smaller than either branch - $2.8\mathrm{uF}<4.0\mathrm{uF}$. Use this as a quick sanity check.

Practical & data tasks

• Build potential divider with light sensor; $\log V_{\text{out}}$ under different lux levels and fit calibration curve.
• Record capacitor discharge using Logger Pro; plot $\ln V$ vs $t$ to extract $-1/RC$.
• Investigate loading effect by attaching low-resistance voltmeter to a divider; observe output change.

Common misconceptions & exam traps

• Forgetting to convert $\mathrm{m}{\mathrm{m}}^2$ to ${\mathrm{m}}^2$ when using resistivity equation.
• Mixing up series/parallel rules for capacitors vs resistors.
• Ignoring meter resistance when measuring delicate dividers (loading).
• Failing to state exponential behaviour explicitly in written explanations.

Quick self-check quiz

1. In a potential divider, what happens to $V_{\text{out}}$ if \( R2 \) decreases? - _It decreases (assuming $R_1$ is fixed).
2. How do you halve the time constant without changing capacitance? - Halve the resistance (since $\tau =RC$).
3. What is the gradient of $\ln V$ vs

Revision workflow

1. Redraw standard sensor-circuit templates and annotate expected $V_{\text{out}}$ behaviour.
2. Solve mixed resistor-capacitor combination problems weekly.
3. Practise using the given exponential equations and ln-linearisation ($\ln V$ vs $t$, gradient $-1/RC$) for RC data. Deriving the exponentials from $\mathrm{d}Q/\mathrm{d}t$ is enrichment, not assessed.
4. Run a mock Paper 4 analysis on sample RC data to stay familiar with gradient extraction.

Practice Quiz

Test yourself on the key concepts from this guide.

9 Further reading

• SEAB H2 Physics 9478 syllabus (2026)
• Save My Exams - Circuit Symbols
• Khan Academy - RC circuits

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.