Parallel-plate capacitor

Nothing moves

Two plates whose size, spacing and filling you choose: C against 1/d gives ε₀, and pushing the voltage too far breaks the material down.

Fields — Action at a distance: gravitational, electric and magnetic fields and the paths in them.

Open it in The Lab The equations behind it

Experiments already set up on it

Capacitance against the gap
The headline: C against 1/d is straight, with gradient ε₀ε_r A.
- C = ε₀ε_r A/d
- So C against 1/d is a straight line through the origin
- A capacitance is decided by the shape, not by the charge on it
Bigger plates
C goes straight up with the area, so it goes as the square of the side.
- C ∝ A, and A = a² for square plates
- So C against a² is straight — which is a better graph than C against a
Energy stored
Half CV², so doubling the voltage stores four times as much.
- E = ½CV², so energy against V² is straight
- The half is there because the charge went on a bit at a time
- And Q = CV, so the charge is proportional to V but the energy is not
How far can you push it?
Past a certain field the air gives way and there is no capacitor left.
- The field is V/d, so a small gap reaches a huge field at a modest voltage
- Every material has a field it cannot stand
- Which is why a capacitor is rated in volts as well as farads

What you can measure

Each of these can be recorded over time, aggregated over a run, or read at the moment something happens — through an instrument that carries its own uncertainty.

CapacitanceC (pF)
Charge storedQ (nC)
Field between the platesE (V/m)
Energy storedW (uJ)
Area of a plateA (m^2)
1/dinvd (1/m)
Relative permittivityε_r
The material has given waybd

What you can change

Any of these can be the thing you vary, and every combination of the ones you choose is run as its own trial.

Side of the platesa (cm)
Gap between themd (mm)
Potential differenceV (V)

The equations behind it

What parallel-plate capacitor is built on. Every one of these is in the lab's formula reference too, where it copies straight into a write-up.

Electric fields

$F = \frac{k q _{1} q _{2}}{r ^{2}}$
Coulomb’s law
$k = \frac{1}{4 π ε _{0}}$
Coulomb constant
$E = \frac{F}{q} = \frac{k Q}{r ^{2}}$
Electric field strength
$V_{e} = \frac{k Q}{r}$
Electric potential
$E_{p} = q V_{e}$
Electric potential energy
$W = q Δ V$
Work done moving a charge
$E = \frac{V}{d}$
Field between parallel plates

Capacitance

$C = \frac{q}{V}$
Capacitance
$C = \frac{ε _{0} ε _{r} A}{d}$
Parallel plate capacitor
$E = \frac{1}{2} C V^{2}$
Energy stored
$τ = R C$
Time constant
$q = q_{0} e^{- t / R C}$
Discharging a capacitor

Also in Fields

Experiments already set up on it

Capacitance against the gap

The headline: C against 1/d is straight, with gradient ε₀ε_r A.

C = ε₀ε_r A/d
So C against 1/d is a straight line through the origin
A capacitance is decided by the shape, not by the charge on it

Bigger plates

C goes straight up with the area, so it goes as the square of the side.

C ∝ A, and A = a² for square plates
So C against a² is straight — which is a better graph than C against a

Energy stored

Half CV², so doubling the voltage stores four times as much.

E = ½CV², so energy against V² is straight
The half is there because the charge went on a bit at a time
And Q = CV, so the charge is proportional to V but the energy is not

How far can you push it?

Past a certain field the air gives way and there is no capacitor left.

The field is V/d, so a small gap reaches a huge field at a modest voltage
Every material has a field it cannot stand
Which is why a capacitor is rated in volts as well as farads

What you can measure

Each of these can be recorded over time, aggregated over a run, or read at the moment something happens — through an instrument that carries its own uncertainty.

CapacitanceC (pF)

Charge storedQ (nC)

Field between the platesE (V/m)

Energy storedW (uJ)

Area of a plateA (m^2)

1/dinvd (1/m)

Relative permittivityε_r

The material has given waybd

The equations behind it

What parallel-plate capacitor is built on. Every one of these is in the lab's formula reference too, where it copies straight into a write-up.

Electric fields

$F = \frac{k q _{1} q _{2}}{r ^{2}}$
Coulomb’s law
$k = \frac{1}{4 π ε _{0}}$
Coulomb constant
$E = \frac{F}{q} = \frac{k Q}{r ^{2}}$
Electric field strength
$V_{e} = \frac{k Q}{r}$
Electric potential
$E_{p} = q V_{e}$
Electric potential energy
$W = q Δ V$
Work done moving a charge
$E = \frac{V}{d}$
Field between parallel plates

Capacitance

$C = \frac{q}{V}$
Capacitance
$C = \frac{ε _{0} ε _{r} A}{d}$
Parallel plate capacitor
$E = \frac{1}{2} C V^{2}$
Energy stored
$τ = R C$
Time constant
$q = q_{0} e^{- t / R C}$
Discharging a capacitor

Parallel-plate capacitor

Experiments already set up on it

Capacitance against the gap

Bigger plates

Energy stored

How far can you push it?

What you can measure

What you can change

The equations behind it

Electric fields

Capacitance

Also in Fields

Orbits & gravitation

Charged particle in a field

Electromagnetic induction

AC generator

Electric charges & fields

Parallel-plate capacitor

Experiments already set up on it

Capacitance against the gap

Bigger plates

Energy stored

How far can you push it?

What you can measure

What you can change

The equations behind it

Electric fields

Capacitance

Also in Fields

Orbits & gravitation

Charged particle in a field

Electromagnetic induction

AC generator

Electric charges & fields