medium difficulty9 min

Capacitors and Capacitance

A capacitor is a device that stores equal and opposite charges on two conductors separated by an insulating medium. Capacitance is the charge stored per unit potential difference between the conductors.

In one line: Capacitance is storage per volt: more area stores more, more separation stores less.

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Understand it

Capacitance measures the ability of a conductor arrangement to store charge.
It depends on geometry and the medium, not directly on the charge placed on it.
For a parallel-plate capacitor without dielectric, C = ε₀ A/d.
Inserting a dielectric of relative permittivity kappa increases capacitance to kappa ε₀ A/d when it fully fills the space.
In parallel combination, capacitances add; in series combination, reciprocals add.

Example

A camera flash or energy backup circuit uses capacitors because they can store charge and release energy quickly when connected in a circuit.

Formula and rule

C = Q/V, where C is in farad, Q in coulomb, and V in volt.

For parallel plates, C = ε₀ A/d; with dielectric fully inserted, C = kappa ε₀ A/d.

Parallel: Ceq = C₁ + C₂ + ... .

Series: 1/Ceq = 1/C1 + 1/C2 + ... .

These assume ideal plates, negligible edge effects, and electrostatic conditions.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

A parallel-plate capacitor has A = 2.0 × 10⁻³ m² and d = 1.0 × 10⁻³ m.

1In air, C = ε₀ A/d = (8.85 × 10⁻¹²)(2.0 × 10⁻³)/(1.0 × 10⁻³) = 1.77 × 10⁻¹¹ F.
2If a dielectric of kappa = 4 fully fills the space, C becomes 7.08 × 10⁻¹¹ F.

Method you can reuse

Identify the capacitor type; write the correct capacitance formula; convert area and separation into SI units; include kappa only when dielectric is present; for combinations reduce series or parallel groups step by step; then use Q = CV if charge or voltage is asked.

Sketch it in your answer

Draw two parallel conducting plates with +Q and -Q, plate area A, separation d, uniform electric field E between plates, potential difference V, and dielectric slab if present. For combinations, label series and parallel connections distinctly.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What happens to the capacitance of a parallel-plate capacitor when plate separation is doubled?

Think first, then show answer

The capacitance becomes half because C = ε₀ A/d, so capacitance is inversely proportional to separation when plate area and medium remain unchanged.

Common wrong answer

Using C = V/Q reverses the definition and gives the wrong unit relation.

Don't mix this up

A frequent error is to assume capacitance increases just because charge increases. For a given capacitor, Q increases with V, but C remains fixed unless geometry or dielectric changes.

Exam tip

For capacitor combinations, first identify whether the same potential difference is across capacitors or the same charge is on them. Same V usually indicates parallel; same Q usually indicates series.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Board-style questions ask for definitions, derivation of parallel-plate capacitance, dielectric effect, equivalent capacitance in series or parallel, and numerical charge-voltage calculations.

1
Enough for 1 mark
A capacitor is a device that stores equal and opposite charges on two conductors separated by an insulating medium. Capacitance is the charge stored per unit potential difference between the conductors.
2
Add for 2 marks
Example: A camera flash or energy backup circuit uses capacitors because they can store charge and release energy quickly when connected in a circuit.
3
Add for 3 marks
Capacitance measures the ability of a conductor arrangement to store charge.

Practice

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