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IB Physics Capacitance: 3 Worked Examples and an Examiner IA Checklist

IB Physics Capacitance: 3 Worked Examples and an Examiner IA Checklist

13 min readOliver Kidd (Co-founder)3 Oct 2026

Capacitance measures how much charge a component stores per volt applied, written as C = Q/V. Its SI unit is the farad (F), though most IB problems use microfarads (μF) or picofarads (pF) because a farad is a huge amount of charge storage. The formula you will reach for most often is energy stored, E = 1/2 CV², alongside its equivalent forms Q²/2C and 1/2 QV.

TL;DR:

  • Capacitance increases fourfold when a dielectric with a high dielectric constant replaces air and the plate area doubles while the separation halves.
  • When capacitors are connected in series, the total capacitance is one-third of each individual capacitor, significantly reducing the stored energy for the same voltage.
  • The energy stored in a capacitor is most efficiently calculated using the E = 1/2 CV² formula when voltage and capacitance are known, or Q²/2C when charge is given.
  • The time constant τ = RC determines the charging or discharging speed, with about 63.2% of the full charge or discharge achieved at t equal to τ.
  • During IB exams, precise unit conversions and correctly analyzing voltage and charge distribution in series or parallel configurations are key to earning full marks.
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Table of Contents

Core definitions and the formulas you need to know

The relationship C = Q/V comes directly from the definition: capacitance is simply the charge a conductor pair can hold for each volt of potential difference across it. Rearranged, this gives Q = CV and V = Q/C, both of which appear constantly in IB exam algebra once a question gives you two of the three quantities.

Core definitions and the formulas you need to know — overview diagram

Unit conversion trips up more students than the physics itself. A farad is defined as one coulomb per volt, as set out by the University of Tennessee’s capacitor module, but practical capacitors sit far below that scale.

Keep these conversions ready during revision:

  • 1 farad (F) = 1 million microfarads (μF)
  • 1 microfarad (μF) = 1000 nanofarads (nF)
  • 1 nanofarad (nF) = 1000 picofarads (pF)

Always write your final answer with the correct unit label. Examiners read a bare number as incomplete working, even when the digits are right.

Where the energy stored in a capacitor comes from

A capacitor does not charge up instantly at a fixed voltage. Each extra bit of charge arrives against a rising potential difference, so the work done to fully charge the plates is the area under a straight-line charge-voltage graph, giving E = 1/2 QV. Substituting Q = CV or V = Q/C produces the two other forms you will see on exam papers: E = 1/2 CV² and E = Q²/2C, confirmed by HyperPhysics’ derivation of stored energy.

Choosing the right version saves time: use 1/2 CV² when you know capacitance and voltage, and Q²/2C when charge is the given quantity. HyperPhysics also notes that this energy physically sits in the electric field occupying the space between the plates, not in the plates themselves, which matters for HL questions on energy density in that field.

Parallel-plate geometry and the role of dielectrics

The geometric formula for a parallel-plate capacitor, taken from OpenStax College Physics, is C = κε₀A/d. Here κ is the dielectric constant of the material between the plates, ε₀ is the permittivity of free space (8.85 × 10⁻¹² F m⁻¹), A is plate area, and d is plate separation.

Three relationships are worth memorising for quick exam reasoning:

  • Capacitance rises in direct proportion to plate area A.
  • Capacitance falls in inverse proportion to plate separation d.
  • Inserting a dielectric with κ greater than 1 raises capacitance by that same factor.

A dielectric works by polarising under the applied field, which partially cancels the field inside the material and lets the plates hold more charge for the same voltage. Every real dielectric also has a maximum field it can withstand before it breaks down and conducts, found from E = V/d, so a thinner dielectric boosts capacitance but lowers the safe operating voltage. Finite plates also lose a little capacitance at the edges compared with the idealised infinite-plate formula.

Pro Tip: When a question doubles the area and halves the separation at the same time, capacitance quadruples, not doubles, because the two effects multiply rather than add.

Parallel plate capacitance scaling relationship

Combining capacitors in series and parallel circuits

Capacitor networks behave in the opposite way to resistor networks, which is exactly why IB examiners like testing the distinction.

  1. Parallel combination: total capacitance simply adds, C_total = C₁ + C₂ + C₃, because each capacitor sees the full voltage and contributes its own charge.
  2. Series combination: reciprocals add, 1/C_total = 1/C₁ + 1/C₂ + 1/C₃, because each capacitor carries the same charge but only a share of the total voltage.
  3. Worked check: three identical capacitors of value C in series give 1/C_total = 1/C + 1/C + 1/C = 3/C, so C_total = C/3, a ninth of the stored energy per capacitor if the same total voltage is reapplied, since energy scales with the square of voltage.

In series, voltage splits unevenly if the capacitors differ in value, with the smallest capacitor taking the largest share of the voltage since charge stays constant across the chain. In parallel, voltage is identical across every branch, and it is charge that splits according to each capacitor’s size. Getting this split right is often worth more marks than the arithmetic itself, since examiners frequently ask students to justify which capacitor holds the most charge or the highest voltage before any numbers are plugged in.

RC circuits, time constants and exponential behaviour

Charging and discharging curves are a guaranteed topic across IB physics papers, and the equations always follow the same exponential pattern. According to OpenStax University Physics, a charging capacitor follows q(t) = Cε(1 − e^(−t/RC)), while a discharging one follows q(t) = Qe^(−t/RC).

  1. Identify τ: the time constant τ = RC tells you how quickly the circuit responds, with larger resistance or capacitance slowing the process.
  2. Apply the 63.2% rule: at t = τ, the charging capacitor has reached roughly 63.2% of its final charge, a figure confirmed in the OpenStax RC circuits chapter.
  3. Solve for an unknown: if a question gives you the time to reach a certain fraction of charge, rearrange the exponential, take natural logs on both sides, then solve for R or C directly.

At t = τ, a charging capacitor reaches approximately 63.2% of its final charge, which is the key well-known figure frequently tested in this topic.

Always check your units before submitting an answer: R in ohms multiplied by C in farads gives seconds, and any mismatch usually signals a conversion was missed somewhere in the working.

Worked IB-style examples and how to present your answer

  1. Series capacitance: three identical capacitors each with the same capacitance in series combine to a total capacitance that is a fraction (one third) of the individual value, resulting in a lower total capacitance than a single capacitor.
  2. Energy stored: a 4 μF capacitor charged to 10 V stores E = 1/2 × (4 × 10⁻⁶) × 10² = 2 × 10⁻⁴ J, using the CV² form since both quantities were given directly.
  3. Time constant: for R = 2,000 Ω and C = 5 × 10⁻⁶ F, τ = RC = 0.01 s, so after one time constant the capacitor voltage reaches about 63.2% of its supply value.

For full marks, always write the formula first, substitute values with units shown, then state the final answer with correct significant figures and units. Examiners reward visible logic even when a final numerical slip occurs.

Practical advice for IAs and extended essays on capacitance

Building a capacitance investigation around an idealised infinite parallel plate is a common mistake. Real plates are finite, so edge correction effects reduce measured capacitance slightly below the textbook formula, and a strong IA states this approximation openly rather than ignoring it.

  • Measure plate separation with a method precise enough that its uncertainty does not swamp your result, since capacitance scales as 1/d.
  • Record area measurements independently of separation and propagate both uncertainties through your final calculation.
  • Note any calibration limits of your measuring equipment as a systematic error, not just a random one.

Pro Tip: Examiners consistently reward a short, honest limitations paragraph over a longer one that hides uncertainty behind vague wording.

Making capacitance work for you across SL and HL

Capacitance sits comfortably across both SL and HL papers, though HL adds heavier calculus-style reasoning and energy density questions. Split your revision roughly evenly between formula recall, numerical practice and one circuit-based practical, then test retention with Tiber Tutor’s cram sheets and a full mock exam under timed conditions.

— Oliver

Revising capacitance with Tiber Tutor

Formula recall only gets you partway. What separates a strong capacitance answer from an average one is practice under exam conditions, with feedback that tells you exactly where marks were lost.

Tibertutor

Tiber Tutor’s IB Physics resources are written by practising IB examiners, which means every cram sheet, mock exam and test question mirrors the exact phrasing and mark allocation you will meet on the real paper. Our test builder lets you assemble a quiz focused purely on capacitance and RC circuits, while performance analytics track which formula or step is costing you marks across attempts, a level of interlinked, exam-mapped tracking no other IB physics resource currently offers. Try a mock exam or check the All-Access and Per-Subject plans to see where your preparation stands.

Sources

FAQ

What is capacitance in simple terms?

Capacitance describes how much charge a component can store for each volt of potential difference applied across it, expressed as C = Q/V. Its SI unit is the farad, though most practical devices are rated in microfarads or picofarads.

How do you calculate the energy stored in a capacitor?

Energy stored can be found with any of three equivalent formulas depending on what you are given: E = 1/2 CV², E = Q²/2C or E = 1/2 QV. All three come from the same derivation of stored energy based on the work done charging the plates.

What happens to capacitance when you add a dielectric?

A dielectric increases capacitance by a factor equal to its dielectric constant κ, following C = κε₀A/d as set out in OpenStax’s treatment of dielectrics. It works by polarising under the applied field, which partially cancels the internal field and allows more charge to be stored at the same voltage.

What does the time constant in an RC circuit represent?

The time constant τ = RC indicates how quickly a capacitor charges or discharges through a resistor. At t = τ, a charging capacitor reaches approximately 63.2% of its final charge, a figure worth memorising for exam calculations.

Why do capacitors in series store less total capacitance?

Capacitors in series share the same charge but divide the total voltage between them, which is why their reciprocals add rather than the capacitances themselves. This gives a total capacitance smaller than any single capacitor in the chain, the opposite pattern to resistors in series.