How They Work (without going into detail at all)

- Capacitors store electric charge (for various purposes)
- Each capacitor is made up of two metal plates, separated by a dielectric – a layer of insulation between them
- When a potential difference is applied across a capacitor, electrons will be sucked off of one plate, and the same number of electrons will be deposited on the bottom plate
- The capacitor then retains this charge until it is discharged, by connecting a wire between its plates
- Capacitance is measured in Farads (unit represented by the letter F)
- A 1F capacitor would develop 1V across it when 1C (one coulomb – unit of charge) is given to it
- That would be a very high capacitance – most capacitors are measured in milli, micro, nano or pico-Farrads
- Normal capacitors can be used either way ’round
- Electrolytic, or polarised, capacitors have more capacitance, but will explode/break if you connect positive and negative incorrectly

Charging / Discharging

- When connected directly across the supply, capacitors will charge instantly, for all intents and purposes
- Likewise, when the two ends of a capacitor are directly connected, it will effectively discharge instantly
- Putting a resistor in series with the capacitor’s charging / discharging route will make it take longer to charge / discharge
- This is because the escaping / arriving electrons have to squeeze through a resistor to create or neutralise the potential difference
- Capacitors charge exponentially – the rate at which they charge decreases as they get more charged
- They also discharge exponentially – they discharge slower the more they’ve discharged
- There are some useful approximations for the time it’ll take to fully charge/discharge and half charge/discharge, as well as detailed equations

The Formulae

- The first thing to do is to work out the time constant of the RC (Resistor and Capacitor) network
- T=RC, where T is the time constant, R is the resistance on the charging/discharging path (whichever the question is about) and C is the capacitance of the capacitor
- You multiply the resistor by the capacitor, basically, but beware of the standard form unit multiplier things! pF, nf, µF, mF, Ω, kΩ, mΩ
- You also need to work out whether the capacitor is charging or discharging – most timing networks charge or discharge the capacitor instantly, then discharge / charge it through the resistor gradually. Work out what’s going on.
- There are formulae for the time taken to reach a certain voltage, and formulae for the voltage reached after a certain time. They’re all given at the beginning of the ET2 paper, but you need to figure out which to use
- Vc is the voltage across the capacitor, and Vo is the supply voltage
- ln or e will be involved, because of the exponentials. Make sure you know how to do these on your calculator!

Approximations

- Don’t waste time working out how long the capacitor will take to reach a certain voltage, if that voltage happens to be half the supply voltage!
- The capacitor will half discharge or half charge in approximately 0.69RC seconds
- You multiply the time constant by 0.69, and that’s how long it’ll take to half charge/half discharge. This one is in practically every paper.
- The formulae are a very good model for capacitor charging, but using a true exponential, capacitors would never fully charge or discharge – they’d just get closer and slightly closer and slightly slightly closer… ad infinitum
- In reality, there will eventually be a point when that final electron moves, and it’s fully charged
- You can bet it’ll be fully charged or discharged by 5RC seconds
- So, if you’re asked how long it’ll take to fully charge / discharge, multiply the time constant by 5

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