Electronics InformationLesson 8 of 15
Capacitors and Inductors
What each stores, how each behaves in a circuit, and why they resist AC differently.
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These two components are studied together because they are mirror images. Almost every fact about one has a matching opposite about the other, and learning them as a pair is far less work than learning them separately.
What each is
A capacitor is two conducting plates separated by an insulator, called the dielectric. Applying a voltage pushes charge onto one plate and pulls it off the other, and the energy is stored in the electric field between them.
An inductor is a coil of wire, often around a core. Current through it creates a magnetic field, and the energy is stored in that field.
No charge crosses the dielectric in a capacitor. That is what makes it block DC, and it is the most consequential fact about the component.
The mirror
| Capacitor | Inductor | |
|---|---|---|
| Stores energy in | an electric field | a magnetic field |
| Physical form | plates and a dielectric | a coil, often on a core |
| Unit | farad | henry |
| Symbol on a schematic | two parallel lines | a series of loops |
| Opposes a change in | voltage | current |
| With steady DC | blocks it once charged | passes it freely |
| With AC | passes it, more easily at high frequency | opposes it, more strongly at high frequency |
| In series | total capacitance decreases | inductance adds |
| In parallel | capacitance adds | total decreases |
Read that table down both columns and the pattern is complete inversion.
Two rows deserve particular attention.
DC and AC
A capacitor blocks DC and passes AC.
Connect a capacitor to a steady voltage and current flows briefly while it charges, then stops. Nothing crosses the dielectric, so once it is charged the current is zero.
With AC the voltage is constantly reversing, so the capacitor is constantly charging and discharging, and current flows continuously in the circuit. The higher the frequency, the more easily it passes.
An inductor does the opposite. Steady DC produces a steady field and the coil is just a wire, so it passes DC freely. A changing current means a changing field, which induces a voltage opposing the change, so the higher the frequency, the more an inductor opposes it.
That pairing is the most useful thing in this lesson: capacitor blocks DC, inductor blocks high-frequency AC.
Reactance
The opposition each one offers to AC has a name. Capacitive reactance is a capacitor's opposition to AC; inductive reactance is an inductor's. Both are measured in ohms, and they move in opposite directions with frequency:
| As frequency rises | Reactance | Because |
|---|---|---|
| Capacitor | falls: double the frequency, half the reactance | it is inversely proportional to frequency |
| Inductor | rises: double the frequency, double the reactance | it is directly proportional to frequency |
That table is the pairing above restated in ohms: a capacitor passes high frequencies easily, an inductor resists them.
The timing differs too. In an inductor, current lags the voltage; in a capacitor, current leads it. The AC and DC lesson combines reactance and resistance into impedance.
Resonance
Put a capacitor and an inductor together and at one particular frequency their reactances are equal. Because they act in opposite directions, they cancel. That condition is resonance.
- In series, the cancellation leaves only the resistance, so the circuit's impedance is at its minimum and it passes that frequency strongly.
- In parallel, the pair presents a very high impedance at resonance.
Either way the circuit singles out one frequency, which is how a radio tuner selects a station.
Series and parallel are inverted
Capacitors in parallel add, and in series they combine like parallel resistors.
Inductors in series add, and in parallel they combine like parallel resistors, which is the same way resistors behave.
So inductors follow the resistor rules and capacitors invert them. That is the compact way to hold it, and it is exactly the shape of a question.
Two 10-microfarad capacitors in parallel give 20 microfarads. In series they give 5.
A charged capacitor holds its charge after the power is removed, sometimes for a long time, and can deliver it all at once. That is why equipment containing large capacitors carries warnings and why they are discharged before servicing. It is also the basis of a camera flash: charge slowly, release in an instant.
Capacitance
What determines it:
- Larger plate area means more capacitance.
- Smaller separation between the plates means more capacitance.
- The dielectric material matters; some materials store far more for the same geometry.
Bigger plates, closer together, better dielectric. Those three are asked as a set.
A farad is a very large unit, so real capacitors are usually measured in microfarads or picofarads.
Every capacitor has a voltage rating, set by the point at which its dielectric breaks down. Exceed it and the dielectric fails.
Charging takes time: the time constant
A capacitor charging through a resistor does not fill instantly. The time constant is resistance times capacitance - ohms times farads gives seconds - and it measures how quickly the capacitor charges.
A 10,000-ohm resistor and a 100-microfarad capacitor give what time constant?
100 microfarads is 0.0001 farads. 10,000 x 0.0001 = 1 second.
Two numbers go with it:
- After one time constant, a charging capacitor reaches about 63 percent of full voltage; a discharging one falls to about 37 percent.
- After five time constants it is considered fully charged (or fully discharged).
The only trap in the calculation is the unit: convert microfarads to farads by moving the decimal six places before multiplying.
Two types worth knowing
| Electrolytic | Ceramic | |
|---|---|---|
| Values | large | small |
| Polarity | polarized: must go in the right way round | non-polarized: either way |
| Typical job | power-supply filtering | high-frequency work and bypassing |
| Weakness | its electrolyte dries out, so it ages, and it is the component most likely to fail from heat | little to note |
Install a polarized capacitor backward and it can fail or rupture. On a schematic the polarized type is drawn with one curved plate and a plus sign. Small ceramic capacitors carry a number code instead of printed values because there is no room to print them.
Inductance
What determines it:
- More turns in the coil.
- An iron core rather than air.
- A tighter, smaller-diameter coil concentrates the field.
Those are the same three factors that strengthen an electromagnet, which is consistent, because an inductor is an electromagnet being used for its field rather than for its pull.
Uses
Capacitors: smoothing the output of a rectifier, blocking DC while letting a signal through, timing circuits, energy storage for a flash. A bypass capacitor gives AC noise a low-impedance path to ground so it does not reach the rest of the circuit.
Inductors: filtering out high frequencies, tuning a radio, and as the coils in transformers and motors.
Together they make tuned circuits, which select one frequency and reject others, which is how a radio picks a station.
The choke
An inductor used to block high frequencies is called a choke. Because an inductor opposes changes in current, a choke placed in a power line passes DC and low frequencies while blocking high-frequency noise, smoothing the flow.
What you can skip
Across all 1,358 Electronics Information questions in our bank:
- Reactance formulas. No question asks you to calculate a reactance from frequency and capacitance. The questions ask which way it moves and why, as in the table above.
- The resonant frequency formula never appears. Know that resonance is where the two reactances are equal and cancel.
- The inductor time constant (inductance over resistance) is not calculated. The time constant questions are the resistor-capacitor kind shown above.
Where people lose points
Saying a capacitor passes DC. It blocks it once charged.
Saying an inductor blocks DC. It passes it.
Applying the resistor rules to capacitors. Capacitors invert them; inductors follow them.
Swapping the units. Farad for capacitance, henry for inductance.
Saying a capacitor stores charge in a magnetic field. Electric field for a capacitor.
Forgetting a capacitor stays charged after the supply is disconnected.
Work one in under a minute
A circuit needs to pass an audio signal while blocking the steady DC voltage the previous stage sits at. Which component, and why?
A capacitor, in series with the signal.
The DC is steady, so the capacitor blocks it once charged. The audio signal is a changing voltage, so the capacitor charges and discharges with it and the signal passes through.
That arrangement has a name worth recognizing - a coupling capacitor - and it is the single commonest use of the component.
Where this leads
Inductors are the coils inside transformers and motors, and capacitors are what smooths a rectifier's output into usable DC.
Related lessonsReference
- Transformers, Motors and Generators - coils used for their induced voltage
- Diodes and Semiconductor Devices - rectification, and the capacitor that smooths it
- Radio and Antennas - tuned circuits made from the two together
- AC and DC - why frequency changes how these components behave
Practice this topic
Check that this lesson stuck. Answer questions on capacitors and inductors only, and see the right answer and why after each one.
Practice Capacitors and Inductors questions