Capacitors, explained with examples

By The STEM-Tutor team · Updated October 2026

A capacitor stores charge, and with it energy, on two conducting plates separated by an insulator. Capacitors smooth power supplies, power camera flashes and time circuits, and they are a key A level Physics topic.

What a capacitor does

A simple capacitor is two parallel metal plates separated by an insulator called a dielectric. When it is connected to a battery, electrons flow onto one plate and off the other, so one plate becomes negatively charged and the other equally positively charged. No charge crosses the gap. Charging stops when the potential difference across the capacitor equals the emf of the supply.

Capacitance

Capacitance is the charge stored per unit potential difference:

C = Q/V

Its unit is the farad (F), which is one coulomb per volt. A farad is very large, so most capacitors are measured in microfarads (μF, 10⁻⁶ F), nanofarads (nF) or picofarads (pF). For a parallel-plate capacitor, C = ε₀ε_rA/d, so larger plates, a smaller gap or a dielectric with higher relative permittivity ε_r all increase the capacitance.

Capacitors in series and parallel

The rules are the opposite way round to resistors:

• Parallel: C_total = C₁ + C₂ + …
• Series: 1/C_total = 1/C₁ + 1/C₂ + …

In parallel, each capacitor has the same potential difference and the charges add. In series, each capacitor carries the same charge and the potential differences add.

Energy stored

The energy stored is the area under a graph of potential difference against charge, which is a triangle:

E = ½QV = ½CV² = ½Q²/C

Only half the energy supplied by the battery is stored; the other half is dissipated as heat in the resistance of the circuit during charging. Because E ∝ V², doubling the voltage quadruples the energy.

Worked examples

Example 1: charge stored

A 470 μF capacitor is charged to 9.0 V. Find the charge and the energy stored.

• Q = CV = 470 × 10⁻⁶ × 9.0 ≈ 4.2 × 10⁻³ C.
• E = ½CV² = ½ × 470 × 10⁻⁶ × 81 ≈ 0.019 J.

Example 2: combining capacitors

Find the total capacitance of 6 μF and 3 μF in series, and in parallel.

• Series: 1/C = 1/6 + 1/3 = 1/2, so C = 2 μF.
• Parallel: C = 9 μF.

Charging and discharging through a resistor

When a capacitor discharges through a resistor, the current is large at first, because the potential difference is large. As charge flows away, the potential difference falls, so the current falls too. The result is exponential decay:

• Q = Q₀ e^−t/RC
• V = V₀ e^−t/RC and I = I₀ e^−t/RC

When charging from a supply of emf V₀, the charge and potential difference rise towards their final values: Q = Q₀(1 − e^−t/RC), while the current still decays as I = I₀e^−t/RC.

The time constant

The product RC is the time constant, τ, measured in seconds. After one time constant of discharging, the charge has fallen to e⁻¹, about 37% of its starting value. After one time constant of charging, it has reached about 63% of its final value. After about 5RC, the capacitor is effectively fully charged or discharged. The time to halve, the half-life of the discharge, is T_½ = RC ln 2 ≈ 0.69RC.

Example 3: the time constant

A 100 μF capacitor discharges through a 20 kΩ resistor. Find the time constant and the time for the charge to halve.

• RC = 100 × 10⁻⁶ × 20 × 10³ = 2.0 s.
• T_½ = 0.693 × 2.0 ≈ 1.4 s.

Example 4: voltage after a time

A capacitor charged to 12 V discharges with RC = 5.0 s. Find V after 8.0 s.

• V = 12 e^−8/5 = 12 × 0.202.
• V ≈ 2.4 V.

Example 5: time to reach a voltage

With the same circuit, how long until V falls to 3.0 V?

• 3 = 12e^−t/5, so e^−t/5 = 0.25 and t = 5 ln 4.
• t ≈ 6.9 s, which is exactly two half-lives, since 12 → 6 → 3.

Uses of capacitors

Capacitors release their stored energy quickly, which suits camera flashes and defibrillators. In power supplies, they smooth out the ripples left after converting alternating current to direct current. Because RC sets a predictable time, capacitors are also used in timing circuits, such as the delay before a light switches off.

Logarithmic graphs and the required practical

In the required practical, a capacitor is charged and then discharged through a resistor while the potential difference is recorded at regular intervals, using a voltmeter and stopwatch or a data logger. Taking natural logs of V = V₀e^−t/RC gives

ln V = ln V₀ − t/RC

so a graph of ln V against t is a straight line with gradient −1/RC and y-intercept ln V₀. Measuring the gradient gives the time constant, and if R is known, the capacitance. A straight line also confirms that the discharge really is exponential.

Common mistakes

• Using the resistor rules for capacitors; they are the other way round.
• Forgetting to convert μF to F or kΩ to Ω.
• Writing E = QV instead of ½QV.
• Using 37% for charging; after one time constant a charging capacitor is at 63%.

Practice questions

Try each one before opening the answer.

Frequently asked questions

Are capacitors in AS or A level Physics?

In most specifications, capacitors are a second-year topic. Some boards, such as OCR A, place them in a specific module; check your specification.

Are capacitors in AP Physics?

Yes. Capacitors appear in AP Physics 2 and AP Physics C: Electricity and Magnetism, including RC circuits in Physics C.

Key takeaways

• C = Q/V, measured in farads.
• Parallel capacitances add; in series, reciprocals add.
• E = ½QV = ½CV².
• Discharge is exponential with time constant RC.
• Plot ln V against t: the gradient is −1/RC.

Related guides

• A level Physics electricity
• A level Physics required practicals
• Differential equations