Resistors, Capacitors and Inductors Refresher

The three basic passive parts

Resistors, capacitors and inductors are called passive because they do not add energy to a circuit; they resist, store or release it. Almost every circuit uses them, so their datasheets are some of the first ones worth learning to read. This refresher covers what each part does and which parameters usually matter.

Real parts are not ideal. Each one has stray effects that become important in some conditions, which is why the datasheet lists more than a single value.

Resistors

A resistor opposes current flow. Ohm’s law relates the voltage across it, the current through it and its resistance: V = I x R. Resistance is measured in ohms. Resistors are used to set currents, divide voltages, limit current through other parts and set bias points.

Power turned into heat in a resistor is P = V x I, which can also be written as P = I squared x R or P = V squared / R.

Key datasheet parameters:

• Resistance value, often from a standard series of preferred values.
• Tolerance, the allowed deviation from the stated value, commonly written as a percentage.
• Power rating, the amount of power the part can dissipate, which depends on temperature. A derating curve usually shows how the allowed power falls as the ambient temperature rises.
• Voltage rating, a limit on the voltage across the part even when the power is low.
• Temperature coefficient, how much the value drifts with temperature.
• Noise and stability, relevant for precision circuits.
• Type, such as film, wire-wound or surface-mount, which affects size, stability and behaviour at high frequency.

Check the power rating against real use with a margin. The article on derating and design margins shows a worked resistor example.

Capacitors

A capacitor stores energy in an electric field. Its capacitance, measured in farads, relates the charge stored to the voltage across it. For changing voltages, the current through an ideal capacitor is proportional to the rate of change of voltage: I = C x dV/dt. Practically, that means a capacitor passes changing signals and blocks steady direct current once charged.

Uses include smoothing and decoupling power supplies, filtering signals, timing and storing short bursts of energy.

Key datasheet parameters:

• Capacitance and tolerance. Some capacitor types have wide tolerances and can be far from the marked value.
• Voltage rating. Operating at a sensible fraction of this rating is usual practice. Some ceramic types lose effective capacitance when a DC voltage is applied, so the usable value can be less than the nominal one.
• Dielectric or type, such as ceramic, electrolytic or film, which determines stability, size, polarity and ageing. Polarised types must be connected the right way round.
• Equivalent series resistance (ESR) and inductance (ESL), the real-world imperfections that matter for decoupling and high-frequency use.
• Leakage current, particularly significant for electrolytic types.
• Temperature range and ripple current rating, important in power circuits.
• Lifetime ratings, given for some types, under stated conditions.

A capacitor’s opposition to alternating current falls as frequency rises. For an ideal capacitor the magnitude of its impedance is 1 / (2 x pi x f x C).

Inductors

An inductor stores energy in a magnetic field. Inductance is measured in henries. The voltage across an ideal inductor is proportional to the rate of change of current: V = L x dI/dt. An inductor resists sudden changes in current, which is why it is used in filters, switching power supplies, and in tuned circuits.

Opposition to alternating current rises with frequency; the magnitude of an ideal inductor’s impedance is 2 x pi x f x L.

Key datasheet parameters:

• Inductance and tolerance.
• DC resistance (DCR), the resistance of the winding, which causes losses and heat.
• Rated current and saturation current. The core can saturate when the current is high, and the inductance falls sharply. Manufacturers sometimes define these ratings differently, such as by a percentage fall in inductance or by a temperature rise, so read the definition.
• Self-resonant frequency, above which the part stops behaving like an inductor because of its stray capacitance.
• Shielding and core type, relevant to stray magnetic fields and neighbouring components.
• Quality factor (Q), relevant for tuned and radio-frequency circuits.

How they combine: a time-constant example

A resistor and capacitor in series have a time constant equal to R x C. It is a rough measure of how quickly the capacitor charges or discharges. As an illustration with simple numbers, a 10 kilohm resistor and a 100 nanofarad capacitor give:

• 10 kilohm = 10,000 ohms
• 100 nanofarad = 100 x 10^-9 farad = 10^-7 farad
• 10,000 x 10^-7 = 10^-3 seconds = 1 millisecond

After one time constant a charging capacitor has reached roughly 63 percent of its final voltage. Your numbers must also account for the tolerances of both parts, which could change the time by a noticeable amount. Handling prefixes and powers of ten with care is worth the effort; scientific notation and SI prefixes both help avoid slips here.

Real parts and parasitics

Every real resistor has a little inductance and capacitance, every real capacitor has resistance and inductance, and every real inductor has resistance and capacitance. At low frequencies these are negligible. At higher frequencies they can dominate, and a part can behave as a different component than its label suggests. That is why datasheets for capacitors and inductors show impedance graphs and self-resonance information.

Reading the datasheet for these parts

1. Confirm the value, tolerance and type.
2. Compare operating voltage, current and power against the ratings, with a margin.
3. Check how the value changes with temperature, applied voltage or current.
4. For capacitors and inductors, check the frequency behaviour.
5. Check the package and temperature range.
6. Use the worst-case end of the specification columns for each parameter.

These parts look simple, but selecting them carefully is a core skill. For safety-related or regulated products, requirements vary by country and industry; follow the standards that apply to your work.