Inductors & AC The third passive component, and the one people skip. You do not need it for an LED, but you cannot understand filters, switching supplies, motors or noise without it — and every one of those will show up.

Current through a coil creates a magnetic field; changing that current means changing the field, and the field fights back. So where a capacitor resists a change in voltage, an inductor resists a change in current. Measured in henries (H), with real parts usually in millihenries (mH) or microhenries (µH).

Where you meet them in practice: relay and motor coils (the reason for flyback diodes), switching regulators (the energy-shuttling element that makes them efficient), filters and ferrite beads (blocking high-frequency noise), and transformers (two coils sharing a field).

Capacitive reactance   Xc = 1 / (2πfC)   falls as frequency rises
Inductive reactance    XL = 2πfL         rises as frequency rises

Impedance (Z) = the combined opposition of R, Xc and XL at a given frequency.

Two consequences worth carrying around:

• A capacitor that is an open circuit to DC can be nearly a short circuit at radio frequencies — which is exactly why a 100nF decoupling capacitor works on fast switching spikes while doing nothing to the steady 3.3V rail.
• A wire is an inductor at high enough frequency. This is why decoupling must be physically close, why ground planes exist, and why long breadboard jumpers cause problems that identical short ones do not.

The cutoff frequency is where the output has fallen to about 70% of the input (−3dB). It is not a wall: a first-order filter rolls off gradually, at 20dB per decade. To get a sharper transition you cascade stages or use an LC filter, where inductor and capacitor together give a steeper slope.

Where you will actually use one: smoothing a noisy analogue sensor before the ADC, removing switching ripple from a supply feeding an analogue circuit, coupling audio between stages while blocking DC offset, and turning a PWM output into a real analogue voltage — a low-pass filter with a cutoff well below the PWM frequency is a poor man's DAC, and it genuinely works.

Resonance, briefly

An inductor and capacitor together have a frequency at which their reactances cancel: f = 1 / (2π√(LC)). That is a resonant circuit — the basis of radio tuning, oscillators and the ringing you see on a scope when something switches sharply. You do not need to design one yet, but recognising ringing as LC resonance rather than "noise" is a real diagnostic skill.

For a sine wave:
  peak-to-peak = 2 × peak
  RMS          = peak / √2  = peak × 0.707

UK mains: 230V RMS  ->  325V peak  ->  650V peak-to-peak

RMS is the value that delivers the same heating as an equivalent DC voltage, which is why it is the number quoted for supplies and the number a multimeter shows in AC mode. A scope, by contrast, shows you peak-to-peak directly — so the same signal appears as two very different numbers on two instruments, and knowing which is which prevents a lot of confusion.

Note the mains figures above: the peak is well above the quoted 230V, which is one reason rectifier and capacitor voltage ratings in mains equipment look surprisingly high, and another reason not to work on it.

Frequency and period: f = 1/T. 50Hz means a 20ms period. Being able to flip between the two in your head makes scope work far quicker.