Definition
A capacitor is a passive two-terminal component that stores electric charge and energy in an electric field between two conductors separated by a dielectric. Its capacitance, measured in farads (F), is the ratio of stored charge to voltage.
Learning objectives
- Define capacitance and calculate the charge stored at a given voltage.
- Calculate stored energy, capacitive reactance and an RC time constant.
- Combine capacitors in series and parallel and identify polarity requirements.
- Discharge and test a capacitor safely with appropriate instruments.
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Progressive explanation
Start with the plain-language idea, then move into the engineering detail. Each level stands on its own, so you can stop at the depth you need.
Beginner The core idea
A capacitor is like a small, very fast reservoir for electric charge. When voltage is applied, charge accumulates on the plates and the capacitor starts to fill; when the voltage is removed, the stored charge can supply a circuit for a short time. Unlike a battery, a capacitor does not create energy — it only stores energy temporarily.
Capacitors are used to smooth a power supply, filter noise, couple signals between stages, set timing and provide a short burst of energy. Two everyday cautions follow from the way they work: a large capacitor can stay charged after the power is switched off, and some types are polarized, so reversing them can damage the part or cause it to fail violently.
Capacitors are used to smooth a power supply, filter noise, couple signals between stages, set timing and provide a short burst of energy. Two everyday cautions follow from the way they work: a large capacitor can stay charged after the power is switched off, and some types are polarized, so reversing them can damage the part or cause it to fail violently.
Intermediate How it behaves in a circuit
The fundamental relationship is C = Q / V: for a given voltage, a larger capacitance stores more charge. The energy stored is E = ½ C V², which is why the stored energy grows with the square of voltage and why high-voltage capacitors demand respect even at modest capacitance.
In parallel, capacitances add because the plate area effectively increases. In series, the reciprocal of the total capacitance is the sum of reciprocals, so the equivalent is always smaller than the smallest capacitor. A capacitor opposes changes in voltage: in a DC circuit it charges through the resistance of the surrounding circuit with a time constant τ = RC, reaching about 63 % of the final voltage in one time constant. In AC, its reactance Xc = 1 / (2π f C) falls as frequency rises, so it passes high frequencies more easily than low ones.
In parallel, capacitances add because the plate area effectively increases. In series, the reciprocal of the total capacitance is the sum of reciprocals, so the equivalent is always smaller than the smallest capacitor. A capacitor opposes changes in voltage: in a DC circuit it charges through the resistance of the surrounding circuit with a time constant τ = RC, reaching about 63 % of the final voltage in one time constant. In AC, its reactance Xc = 1 / (2π f C) falls as frequency rises, so it passes high frequencies more easily than low ones.
Advanced Limits, assumptions, engineering detail
Real capacitors are defined by more than capacitance: equivalent series resistance (ESR), equivalent series inductance (ESL), leakage current, dielectric absorption, voltage coefficient and temperature behaviour all matter. Electrolytic capacitors lose capacitance and gain ESR as they age, which is a common cause of power-supply ripple and start-up faults; ceramic capacitors can lose substantial capacitance under DC bias and with temperature, depending on the dielectric class.
At high frequency the device becomes a series RLC network, and self-resonance limits its effectiveness as a bypass element. Dielectric absorption causes a capacitor to recover part of its charge after discharge, so a supposedly discharged high-voltage capacitor can regain a dangerous voltage. Safety design therefore includes bleed resistors, discharge procedures and, where required, stored-energy warning labels.
At high frequency the device becomes a series RLC network, and self-resonance limits its effectiveness as a bypass element. Dielectric absorption causes a capacitor to recover part of its charge after discharge, so a supposedly discharged high-voltage capacitor can regain a dangerous voltage. Safety design therefore includes bleed resistors, discharge procedures and, where required, stored-energy warning labels.
Formulas and variables
Charge–voltage relationship
Q = C × V
Q Stored charge · coulomb (C)
C Capacitance · farad (F)
V Voltage across the capacitor · V
A 1000 µF capacitor at 50 V stores Q = 1000 × 10⁻⁶ × 50 = 0.05 C.
Stored energy
E = ½ × C × V²
E Stored energy · joule (J)
C Capacitance · F
V Voltage · V
The same 1000 µF at 50 V stores E = 0.5 × 0.001 × 2500 = 1.25 J.
Series and parallel equivalents
Cparallel = C1 + C2 + … ; 1/Cseries = 1/C1 + 1/C2 + …
Cparallel Equivalent parallel capacitance · F
Cseries Equivalent series capacitance · F
C1, C2 Individual capacitances · F
Two 100 µF capacitors in series give 50 µF; in parallel they give 200 µF.
Capacitive reactance and RC time constant
Xc = 1 / (2π × f × C) ; τ = R × C
Xc Capacitive reactance · Ω
f Frequency · Hz
C Capacitance · F
τ Time constant · s
R Series resistance · Ω
100 µF at 50 Hz has Xc = 1 / (2π × 50 × 100 × 10⁻⁶) ≈ 31.8 Ω.
Units of measurement
| Quantity | Symbol | Unit |
|---|---|---|
| Capacitance | C | farad (F) |
| Charge | Q | coulomb (C) |
| Energy | E | joule (J) |
| Reactance | Xc | ohm (Ω) |
Worked examples
Worked example
Charge and energy in a smoothing capacitor
Problem. A 1000 µF capacitor is charged to 50 V. Find the stored charge and the stored energy.
Solution. Q = C × V = 0.001 F × 50 V = 0.05 C. E = ½ C V² = 0.5 × 0.001 × 50² = 1.25 J.
Q = 0.05 C and E = 1.25 J; the energy is modest, but the 50 V is still hazardous to touch.
Worked example
Capacitive reactance at two frequencies
Problem. Find the reactance of a 100 µF capacitor at 50 Hz and at 500 Hz.
Solution. At 50 Hz: Xc = 1 / (2π × 50 × 0.0001) = 31.83 Ω. At 500 Hz: Xc = 1 / (2π × 500 × 0.0001) = 3.18 Ω.
Xc falls from about 31.8 Ω to about 3.2 Ω as frequency rises tenfold, so the capacitor passes the higher frequency more easily.
Practical applications
- Smoothing rectified DC in power supplies and suppressing ripple
- Decoupling and bypassing integrated circuits close to their power pins
- Coupling AC signals while blocking DC offset between stages
- Timing, filtering, motor start/run assistance and energy storage for short pulses
Automotive applications
Vehicles rely on capacitors in engine control units, audio amplifiers, LED drivers and start-stop systems, where a small supercapacitor or capacitor bank can support electronics during a cranking voltage dip. Capacitors also suppress alternator ripple, absorb ignition noise and provide local energy for airbag firing circuits. Automotive parts must tolerate vibration, humidity, salt spray and a wide temperature range, and high-voltage EV capacitors must be treated as live until proven discharged.
Industrial applications
Industrial systems use capacitors for power-factor correction, DC-link smoothing in drives, snubbers across switching devices, motor starting and energy storage in uninterruptible supplies. Power-factor correction banks are switched in steps and protected against overvoltage and resonance; DC-link capacitors in a drive can remain charged long after the supply is removed, so discharge and verification are part of lockout procedure.
Measurement procedure
- Isolate the circuit, verify dead, then discharge the capacitor through an appropriate resistor and measure the voltage again before touching it.
- Remove the capacitor from the circuit or disconnect one terminal before measuring capacitance; parallel paths corrupt the reading.
- Use the meter’s capacitance mode for small parts, and an ESR meter for electrolytic capacitors where ripple or start-up faults are suspected.
- Check leakage current and polarity where specified; a capacitor that heats, bulges or leaks should be replaced rather than trusted.
- For high-voltage capacitors, use a meter and probe rated for the voltage and confirm zero volts at the terminals, not only at the supply.
Common mistakes
- Assuming the capacitor is discharged because the equipment is switched off; stored charge can remain for a long time.
- Reversing a polarized electrolytic capacitor, which can cause leakage, venting or rupture.
- Replacing a capacitor by capacitance alone while ignoring ESR, voltage rating, temperature rating and ripple current.
- Using a ceramic capacitor without checking DC-bias derating, then finding far less capacitance than the marking suggests.
Safety considerations
- Capacitors store energy after power is removed: discharge them with a suitable resistor and verify zero voltage before touching terminals.
- Respect the voltage rating, polarity and ripple-current rating; a capacitor operated beyond them can vent, leak or explode.
- On mains and industrial DC-link circuits, use insulated tools, appropriate PPE and a proven lockout procedure.
- In electric vehicles, high-voltage capacitors may be part of the traction system; only trained personnel should work on them.
Frequently asked questions
Why does a capacitor block DC but pass AC?
In steady DC the capacitor charges to the applied voltage and then current stops, apart from a small leakage current. In AC the voltage keeps changing, so charge flows in and out continuously; the higher the frequency, the less the capacitor opposes that current.
Can I replace a capacitor with a larger capacitance?
Sometimes, but not automatically. A larger value may change timing, inrush current, stability, resonance or physical fit. Check the circuit function, voltage rating, ESR and ripple current before substituting; the original value and type are usually part of the design.
How long does a capacitor stay charged?
It depends on capacitance, the bleed resistor and leakage paths. Large high-voltage capacitors can hold a dangerous charge for minutes or longer. Do not rely on time; discharge with a rated resistor and verify with a meter.
Do capacitors wear out?
Electrolytic capacitors in particular age: the electrolyte dries, capacitance falls and ESR rises, which can cause ripple, instability or start-up failure. Heat accelerates ageing, so replacement should match the temperature and ripple ratings, not just the capacitance.