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Second year Lesson 3 of 13 About 15 min

Capacité

What you’ll learn

  • What a capacitor is and the one thing it does: oppose a change in voltage.
  • The farad, and why real capacitors are in microfarads.
  • Charging and discharging through a resistor, and the RC time constant.
  • Why current leads voltage by 90° in a pure capacitance on AC.
  • Why capacitors in motors, drives and power supplies stay dangerous after the power is off.

A capacitor is two conductive plates with an insulator between them, and it stores electric charge. Its habit is the mirror image of a coil’s: it opposes any change in voltage. Charge it and its voltage rises gradually; disconnect it and it holds that voltage — sometimes for a long time. On AC it charges and discharges every half-cycle, and the current it draws runs a quarter-cycle ahead of the voltage.

Plates, a gap and a charge

Connect a capacitor to a battery and electrons pile onto one plate while the same number are pulled off the other. The gap (the dielectric — air, paper, plastic film, ceramic or an oxide layer) stops them crossing. The more charge it holds per volt, the bigger its capacitance, C, measured in farads (F). A farad is enormous, so real parts are in microfarads (µF, millionths), nanofarads (nF) and picofarads (pF). Bigger plates, a thinner gap and a better dielectric all mean more capacitance.

  • Q = C × Vcharge, coulombs
  • E = ½ × C × V²energy stored, joules
  • τ = R × Ctime constant, seconds

Charging through a resistor

Charge a capacitor through a resistor and its voltage climbs along the same curve a coil’s current follows: 63.2% of the way after one time constant, 86.5% after two, 95% after three, 98.2% after four, 99.3% after five. Discharging runs the same curve downward: each time constant takes away 63.2% of what is left.

63.2% at 1τ 99.3% at 5τ Vs 0 1τ 2τ 3τ 4τ 5τ R C Vs + −
Voltage across a capacitor charging through a resistor. The shape is the same for every RC circuit; only the time scale (τ = R × C) changes.

1. How long to charge

  1. 10 kΩ in series with 100 µF. Convert: 10,000 Ω and 0.0001 F.
  2. τ = R × C = 10,000 × 0.0001 = 1 s.
  3. Fully charged (5τ): 5 s.

2. The bleeder resistor

  1. A 470 µF capacitor charged to 340 V DC, with a 10 kΩ bleeder resistor across it.
  2. τ = 10,000 × 0.00047 = 4.7 s.
  3. After 5τ (23.5 s) the voltage is 340 × e−5 ≈ 340 × 0.0067 = 2.3 V.
  4. Energy it held at 340 V: ½ × 0.00047 × 340² ≈ 27 J. If the bleeder has failed, all of that is still there — so you meter it, every time.

3. Series and parallel

  1. Two 10 µF capacitors in parallel: they add, 20 µF (more plate area).
  2. In series: 1 ÷ (1/10 + 1/10) = 5 µF (a thicker gap, in effect).
  3. That is the reverse of resistors — worth writing on your formula sheet.

On AC: current leads voltage

On AC the capacitor charges one way, discharges, charges the other way and discharges again, every cycle. The current is biggest when the voltage is changing fastest — as it crosses zero — and zero when the voltage is at its peak. So the current peaks 90° before the voltage. The opposition a capacitor gives to AC is its capacitive reactance, XC, and unlike a coil’s it gets smaller as frequency rises.

ELI the ICE man

In a coil (L), voltage E comes before current I: ELI. In a capacitor (C), current I comes before voltage E: ICE. Coils make current lag; capacitors make it lead — which is exactly why capacitors can correct a motor load’s power factor.

Try one: 1 MΩ and 10 µF — how long to charge?

τ = 1,000,000 × 0.00001 = 10 s, so about 50 s to charge fully. Big resistance and big capacitance make slow circuits — that is how simple timers work.

Sur le chantier

Tips from the job

  • Start and run capacitors on single-phase motors, the DC bus in every drive, power-factor correction banks and electronic power supplies can all hold a charge after the circuit is off.
  • Discharge a motor capacitor through a proper resistor tool, never a screwdriver — then meter it to prove it is at zero.
  • A capacitor that has bulged, leaked or split has failed. Replace it with the same µF and at least the same voltage rating.
  • Many meters have a capacitance function (µF). Discharge the capacitor and take it out of circuit before you test it.

Common mistakes

  • Assuming “power off” means “no voltage”. A capacitor is a small battery until it is discharged and proved dead.
  • Combining series capacitors by adding them. Series capacitance goes DOWN; parallel adds.
  • Replacing a run capacitor with a lower voltage rating because the µF matches.
  • Swapping “leads” and “lags”. ICE: current before voltage in a capacitor.

Check yourself

7 questions. Tap an answer — it is marked straight away and the reason opens under it. Get 80% or better and the lesson is ticked off on the year page.

Not started yet.

  1. What is a capacitor, at its simplest?

    Answer and why

    B. Two plates and a gap (the dielectric). Charge collects on the plates; no current actually crosses the gap.

  2. A capacitor opposes a change in…

    Answer and why

    B. A coil fights a change in current; a capacitor fights a change in voltage. Its voltage can only change as fast as charge can flow in or out.

  3. Time constant of a 10 kΩ resistor charging a 100 µF capacitor?

    Answer and why

    B. τ = R × C = 10,000 × 0.0001 = 1 s. Fully charged (99.3%) after 5τ = 5 s.

  4. In a pure capacitance on AC, the current…

    Answer and why

    C. ICE: in a capacitor (C) the current (I) comes before the voltage (E). Current leads by 90°.

  5. Two 10 µF capacitors connected in series give…

    Answer and why

    C. Capacitors in series combine like resistors in parallel: 1 ÷ (1/10 + 1/10) = 5 µF. In parallel they simply add: 20 µF.

  6. You have locked out a variable-frequency drive. Before touching the DC bus, you should…

    Answer and why

    B. Drive capacitors hold a lethal charge after the supply is off. Wait the discharge time the maker gives, then verify zero with a rated meter before you work.

  7. A 470 µF capacitor is charged to 340 V. Roughly how much energy is it holding?

    Answer and why

    C. E = ½ × C × V² = 0.5 × 0.00047 × 340² = 0.5 × 0.00047 × 115,600 ≈ 27.2 J — easily enough to hurt.

Questions fréquentes

Does current flow through a capacitor?

Not across the gap — the dielectric is an insulator. But as the capacitor charges and discharges, charge flows onto one plate and off the other, so in the wires around it a current flows just as if it went through. On AC that happens continuously, which is why a capacitor “passes” AC but blocks steady DC.

What happens to a capacitor on DC?

It charges up to the supply voltage along the RC curve, then current stops. After about five time constants it is fully charged and looks like an open circuit to the DC.

Voir aussi

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