Capacitors

What is a capacitor?

An electrical component that stores charge on two separated metallic plates with an insulator between them.

What is capacitance?

The charge stored per unit potential difference across a capacitor.

What is the formula for capacitance?

C = Q/V

What is the unit of capacitance?

Farad (F)

What happens when a capacitor is connected to a DC supply?

A brief current flows as electrons are transferred from one plate to the other.

Why are the charges on capacitor plates equal and opposite?

Due to conservation of charge.

When does current stop flowing while charging?

When the p.d. across the capacitor equals the supply e.m.f.

What is a dielectric?

An insulating material placed between capacitor plates.

Why is a dielectric used?

To prevent charge flow and increase capacitance.

How does a dielectric increase capacitance?

It polarises in the electric field, increasing stored charge.

What property describes a dielectric’s effectiveness?

Permittivity.

Why is air/vacuum a poor dielectric?

It polarises weakly or not at all.

State Kirchhoff’s voltage law.

Sum of e.m.f.s equals sum of p.d.s in a closed loop.

What is the rule for capacitors in series?

1/C_total = 1/C1 + 1/C2 + 1/C3 + …

What is constant for capacitors in series?

Charge on each capacitor.

What is shared between capacitors in series?

Total voltage is divided.

What is the rule for capacitors in parallel?

C_total = C1 + C2 + C3 + …

What is constant for capacitors in parallel?

Voltage across each capacitor.

What is shared in parallel capacitors?

Charge is divided.

Why is work done when charging a capacitor?

Because electrons are forced onto a plate against repulsion.

What does the area under a Q–V graph represent?

Energy stored.

What is the energy stored formula (basic)?

E = ½QV

What are other energy formulae?

E = ½CV² and E = Q²/(2C)

Why are capacitors useful for energy pulses?

They discharge large energy quickly.

Give an example use of pulse discharge.

Camera flash.

How are capacitors used in power supplies?

In UPS backup systems.

How are capacitors used in rectification?

They smooth rectified AC signals.

What is capacitor smoothing?

Charging on peaks and discharging on troughs to reduce ripple.

How is a capacitor discharged?

By connecting it through a component (usually a resistor).

Why use a resistor to discharge?

To control current and time constant.

What happens to electrons during discharge?

They flow through the circuit, releasing heat in the resistor.

When does discharge stop?

When p.d. and charge reach zero.

What affects discharge time?

Resistance and capacitance.

How does resistance affect discharge?

Higher R → slower discharge.

How does capacitance affect discharge?

Higher C → more charge → longer discharge.

What is the time constant symbol?

τ (tau)

What is the time constant formula?

τ = RC

What does the time constant represent?

Time for charge/voltage/current to fall to 37%.

What is the charge decay equation?

Q = Q₀e^(−t/RC)

What is the voltage decay equation?

V = V₀e^(−t/RC)

What is the current decay equation?

I = I₀e^(−t/RC)

What type of graph is capacitor discharge?

Exponential decay.

What is the charging voltage equation?

Vc = V₀(1 − e^(−t/RC))

What law is used in charging derivations?

Kirchhoff’s voltage law.

At t = 0 in discharge, what is current?

I = V₀/R

Why does current fall during discharge?

Voltage falls as charge decreases.

What equipment measures capacitor experiments?

Ammeter, voltmeter, DC supply, resistor, capacitor.

Why use a data logger?

Capacitors discharge quickly.

How is experimental τ found?

From voltage/current vs time graphs.

How does plate area affect capacitance?

C ∝ A

How does plate separation affect capacitance?

C ∝ 1/d

Capacitance formula for parallel plates in vacuum?

C = ε₀A/d

What is ε₀?

Permittivity of free space.

How does a dielectric change capacitance?

Increases permittivity.

General capacitance formula with dielectric?

C = εA/d

What is ε?

Absolute permittivity of the dielectric.

Relationship between ε, εr, ε₀?

ε = εrε₀