Capacitors – AS Electronics Revision

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

    Capacitor voltage step-response.

    Capacitor voltage step-response. (Photo credit: Wikipedia)

  • 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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About Matt

I like writing, filmmaking, programming and gaming, and prefer creating media to consuming it. On the topic of consumption, I'm also a big fan of eating.
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