The parallel-plate capacitor
A capacitor stores charge because two plates and a gap between them set up an electric field. So build one and change it. Slide the plate area, separation or voltage, or swap in a dielectric, and every reading — capacitance, charge, field strength, stored energy — updates instantly from C = Kε₀A/d.
The ideas you're seeing
Capacitance formula
C = Kε₀A/d. Capacitance grows with bigger plates or a smaller gap, and shrinks the other way — it's purely geometric, and doesn't depend on V or Q individually.
The role of a dielectric
Inserting an insulator between the plates always increases capacitance (K>1 for every real dielectric) — it partially cancels the field via induced polarisation charges on its surfaces.
Charge vs field
With the battery connected, V stays fixed, so Q = CV changes whenever C changes (via K, A or d) — but the field E = V/d only depends on V and d, not on K or A directly.
Energy stored
U = ½CV² is the energy stored in the electric field between the plates — this is literally why capacitors are used to store electrical energy, from flash circuits to energy buffers.
Part of the Electrostatic Potential and Capacitance chapter — read the notes, grab the formula sheet and take the quiz. One of Priodemy for School, free with every EduSuite school.
What capacitance actually measures
Capacitance is geometry, not charge
Capacitance is defined as C = Q/V, which makes it look as though it depends on how much charge you put on. It does not. Double the charge and the voltage doubles too, leaving the ratio unchanged. For a parallel-plate capacitor the value is fixed entirely by its construction: C = ε₀A/d — the plate area, the separation, and nothing else.
That is why increasing the area raises capacitance while increasing the gap lowers it. A bigger area gives the charge more room to spread, so the same charge produces a lower potential difference. A wider gap means the field acts over a longer distance, so the same charge produces a larger voltage, and C falls. Drag the separation here and watch Q and V trade off while C tracks the geometry alone.
Why a dielectric helps
Slide an insulating slab between the plates and the capacitance rises by the factor K, the dielectric constant: C = Kε₀A/d. The molecules of the dielectric polarise, lining up so that their induced charges partly cancel the field from the plates. The net field between the plates weakens, so the voltage across them falls, so C = Q/V rises.
A dielectric earns its place three times over: it multiplies the capacitance, it keeps the plates apart mechanically, and it withstands a higher field before breaking down than air does. This is why practical capacitors are not simply two plates with a gap.
Two different experiments
What happens when you insert the dielectric depends on whether the battery is still connected, and questions turn on this constantly. With the battery connected, V is held fixed, so Q must rise to satisfy Q = CV, and the stored energy increases — the battery supplies it. With the battery disconnected, Q is trapped on the plates and cannot change, so V falls instead, and the stored energy decreases. Same slab, opposite conclusions.
The energy stored is U = ½CV² = ½QV = Q²/2C. All three forms are equivalent, but choosing the right one saves work: use ½CV² when voltage is held constant, and Q²/2C when charge is held constant.
Mistakes that cost marks
Assuming capacitance changes when you charge it. Adding charge changes Q and V together. C is a property of the object, like the volume of a bottle — filling the bottle does not change its size.
Getting the series and parallel formulas backwards. Capacitors are the reverse of resistors. In parallel capacitances add; in series the reciprocals add. If you remember the resistor rules, remember that these are the other way round.
Forgetting which quantity is fixed. Before answering any "what happens if…" question, decide first whether the battery is connected. Getting this wrong reverses the answer for charge, voltage and energy all at once.