Capacitors & inductors

Resistors dissipate energy, but capacitors and inductors store it. They are the two reactive components, and they behave as mirror images of one another. A capacitor stores energy in an electric field; an inductor stores it in a magnetic field. Understanding this symmetry makes both components far easier to reason about.

What each one stores

A capacitor is two conductive plates separated by an insulator called the dielectric. When you apply a voltage, charge piles up: +Q on one plate, -Q on the other. The energy lives in the electric field in the gap between them. Its key property is capacitance, the charge stored per volt:

C = Q / V

Capacitance is measured in farads (F). A farad is enormous in practical terms, so real parts are rated in microfarads (uF), nanofarads (nF) or picofarads (pF).

An inductor is a coil of wire. When current flows, it generates a magnetic field, and that field holds the energy, E = 1/2 x L x I^2. Its key property is inductance L, measured in henries (H) (often mH or uH in practice), defined by how much voltage the coil produces for a given rate of change of current.

They oppose opposite changes

This is the heart of the matter, and the two are perfectly complementary.

• A capacitor opposes a change in voltage. Its voltage depends on stored charge, and charge can only move as fast as current flows in or out. So the voltage across a capacitor cannot jump instantly.
• An inductor opposes a change in current. A changing current induces a back-EMF given by V = L x dI/dt that fights the change. So the current through an inductor cannot jump instantly.

A simple memory aid: Capacitors smooth voltage; inductors smooth current.

Behaviour with DC and AC

Because of those rules, the two components treat steady and changing signals oppositely:

• A fully charged capacitor blocks steady DC (it becomes an open circuit) but passes AC.
• An inductor passes steady DC like a plain wire but opposes AC.

This frequency dependence is captured by reactance. Capacitive reactance X_C = 1 / (2 pi f C) falls as frequency rises, so capacitors pass high frequencies easily. Inductive reactance X_L = 2 pi f L rises with frequency, so inductors block high frequencies. They are opposites here too.

Common uses

Smoothing. In a power supply, a rectifier turns AC into a pulsing, rippling DC. A large reservoir capacitor across the output charges up on each voltage peak and discharges to fill the dips, holding the voltage steady and producing near-flat DC.

Decoupling. A small bypass capacitor placed right next to a chip’s power pins acts as a tiny local reservoir. When the chip switches and demands a sudden burst of current, the capacitor supplies it instantly, keeping the local supply voltage stable and shunting high-frequency switching noise to ground. Almost every IC on a board has one.

Filtering. Because their impedance depends on frequency, capacitors and inductors are the basis of filters. A capacitor to ground forms a simple low-pass filter (it shorts high frequencies away); an inductor in series does the same by blocking them. Combine an inductor and a capacitor and you get an LC filter or a resonant tank that selects a specific frequency, the principle behind radio tuning.

Energy buffering and timing. Inductors store energy in switching regulators, releasing it to maintain current when the switch opens. Capacitors set timing in oscillators and delay circuits, since the time to charge through a resistor depends on the R x C product.

A quick comparison

Seeing the two as a matched pair, electric versus magnetic, voltage versus current, blocking versus passing, turns a long list of facts into a single clear pattern. Once that symmetry clicks, smoothing, decoupling and filtering all follow from the same simple rules.