Planning a revision session? Use our study places near me map to find libraries, community study rooms, and late-night spots.
Read in layers
1 second
Read the summary above.
10 seconds
Scan the first few sections below.
100 seconds
Jump into the section that matches your decision.
Quick study map
Concrete example: how to use this page
1 Circuit symbols & diagrams
2 Resistance, resistivity and internal resistance
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.
Quick study map
If you only have...
Focus on...
1 second
Current splits in parallel and p.d. splits in series
10 seconds
Symbols, Ohm's law, and Kirchhoff rules
100 seconds
The first circuit mini-drill
10 minutes
Internal resistance, sensors, and RC links
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.
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 Vout
. Mark the sensing node. Time limit = 30 s.
2 Resistance, resistivity and internal resistance
2.1 Ohm's law refresher
The definition is R=IV(Ω). Use it only when the graph through the origin is linear.
2.2 Microscopic link
For a uniform wire R=ρAl,
where ρ is resistivity, l (m) is length and A (m2) is cross-sectional area. Double l → double R; halve A → double R.
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=ε−Ir,
so increasing load current drops terminal p.d.
Graph cue: gradient = −r, intercept = ε. Quote ε in V not eV.
2.5 Output power and internal resistance
The power delivered to the external load R is
Pout=I2R=(r+Rε)2R.
When R is very small, most of the e.m.f. drives current through r, so Pout→0. When R is very large, current becomes negligible, so Pout→0 again. Output power therefore peaks at an intermediate load value. The maximum-power-transfer condition is R=r: the load resistance equals the internal resistance.
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.
3 Resistors in series & parallel
Arrangement
Combined resistance
Series
Rtot=R1+R2+…
Parallel
Rtot1=R11+R21+…
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
Vout=VinR1+R2R2.
4.2 Sensor combos
Brightness probe: replace R2 with LDR → Vout↑ in the dark.
Fire alarm: replace R2 with NTC → Vout↑ when hot.
Include a buffer op-amp in higher-ability tutorials to prevent loading.
5 I-V characteristics
Component
Key graph feature
Exam explanation
Ohmic resistor
Straight line through origin
Constant R
Filament lamp
Curve flattens as I↑
T↑⇒R↑ in tungsten
Diode
Conducts after ≈0.6V
Forward bias overcomes p−n barrier
NTC thermistor
Steep at low V
T↑⇒R↓ due to more carriers
Plot with current on the y-axis - SEAB marks for axis labels.
6 Capacitors in series & parallel
Arrangement
Combined capacitance
Series
Ctot1=C11+C21+…
Parallel
Ctot=C1+C2+…
Mnemonic: series for resistors adds R; series for capacitors adds 1/C.
7 RC circuits with d.c. source
7.1 Time constant
τ=RC.
At t=τ a discharging capacitor's Q,V or I falls to e1≈37% of its initial value.
7.2 Exponential laws
Charging: Q=Q0[1−e−t/τ],V=V0[1−e−t/τ].
Discharging: Q=Q0e−t/τ,V=V0e−t/τ,I=I0e−t/τ.
Plot lnV vs t to obtain a straight line of gradient −1/RC - a favourite Paper 4 practical.
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.
Time
Charging Q(t)/Qmax
Discharging Q(t)/Q0
t=0
0
1
t=τ
1−1/e≈0.63
1/e≈0.37
t=2τ
≈0.86
≈0.14
t=3τ
≈0.95
≈0.05
t→∞
1
0
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 I0=ε/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 Q curve, but flipped in the context of the circuit.
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)
Label units first for every numerical answer - avoids unit-free slips.
Sketch a quick circuit even if not asked; you see hidden series legs faster.
Log-log check: if your answer for R or C is < 0.1 or > 10 Ω/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=Aρl.
(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.
(f) explain the temperature dependence of the resistivity of typical metals (e.g. in a filament lamp) and semiconductors (e.g. in an NTC thermistor) in terms of the drift velocity and number density of charge carriers respectively.
(g) show an understanding of the effects of the internal resistance of a source of e.m.f. on the terminal potential difference and output power.
(h) solve problems using the formula for the combined resistance of two or more resistors in series.
(i) solve problems using the formula for the combined resistance of two or more resistors in parallel.
(j) solve problems involving series and parallel arrangements of resistors for one source of e.m.f., including potential divider circuits which may involve NTC thermistors and light-dependent resistors.
(k) solve problems using the formulae for the combined capacitance of two or more capacitors in series and in parallel.
(l) describe and represent the variation with time, of quantities like current, charge and potential difference, for a capacitor that is charging or discharging through a resistor, using equations of the form x=x0e−t/τ or x=x0[1−e−t/τ]
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
Quantity / concept
Expression / highlight
Ohm's law
V=IR
Resistivity relation
R=ρAl
Series resistors
Rtot=∑Ri
Parallel resistors
Rtot1=∑Ri1
Potential divider
Vout=VinR1+R2R2
Series capacitors
Ctot1=∑Ci1
Parallel capacitors
Ctot=∑Ci
RC charging equation
V(t)=V0(1−e−t/(RC))
RC discharging equation
V(t)=V0e−t/RC,;I(t)=I0e−t/RC
Derivations & reasoning to master
Potential divider: derive ratio using loop current, or use voltage drop proportionality.
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=x0e−t/τ and x=x0[1−e−t/τ] with τ=RC; the underlying derivation from dtdQ=RV−Q/C is not required. Skip the derivation unless you want extra calculus practice.
Sensor behaviour: analyse how LDR/NTC resistance changes V_out and relate to control systems.
ln-linearisation: rearrange V=V0e−t/RC to lnV=lnV0−t/RC
Worked example 1 - potential divider sensor
Design a circuit that outputs 3.0V when an LDR (resistance 12kOhm in dark, 2.0kOhm in bright light) is exposed to daylight using a 9.0V supply. Determine the fixed resistor value and predict the output in darkness.
Method: solve Vout=VinRfixed+RLDRRLDR for the bright condition; check the dark condition to ensure the alarm threshold.
A 47kOhm resistor and 100uF 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 5V logic, what is the voltage at 3τ?
Solution: The time constant is 4.7s(τ=RC).
V=V0(1−e−t/(RC))
Use this relation to solve for t and the specific voltages.
For 90\% charging: 0.90=1−e−t/τ⇒t=τln10=2.303τ≈10.8s.
At 3τ: V=V0(1−e−3)=0.950V0≈4.75V for V0=5V.
Worked example 3 - combined capacitance
Three capacitors: C1=6.0uF, C2=3.0uF, and C3=4.0uF. C1 and C2 are connected in parallel; this parallel combination is then connected in series with C3. Find the total capacitance.
Step 1 - parallel combination of C1 and C2:
CP=C1+C2=6.0+3.0=9.0uF.
Step 2 - CP in series with C3:
Ctot1=CP1+C31=9.01+4.01=364.0+9.0=3613.
Ctot=1336≈2.8uF.
Note: the series step always gives a result smaller than either branch - 2.8uF<4.0uF. Use this as a quick sanity check.
Practical & data tasks
Build potential divider with light sensor; logVout under different lux levels and fit calibration curve.
Record capacitor discharge using Logger Pro; plot lnV 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 mm2 to m2 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
In a potential divider, what happens to Vout if R2 decreases? - It decreases (assuming R1 is fixed).
How do you halve the time constant without changing capacitance? - Halve the resistance (since τ=RC).
What is the gradient of lnV vs t for a discharging capacitor? - −RC1.
Are thermistors ohmic? - No; resistance changes with temperature causing non-linear I−V behaviour.
Suggest one way to buffer a sensor output against loading. - Use an op-amp voltage follower.
Revision workflow
Redraw standard sensor-circuit templates and annotate expected Vout behaviour.
Practise using the given exponential equations and ln-linearisation (lnV vs t, gradient −1/RC) for RC data. Deriving the exponentials from dQ/dt is enrichment, not assessed.
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.
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.
