Impedance, filters & resonance
Impedance generalizes resistance to AC. It’s the total opposition to alternating current, measured in ohms and written Z, and it includes plain resistance plus reactance, the frequency-dependent opposition from capacitors and inductors. A capacitor’s reactance falls as frequency rises, so fast signals pass easily. An inductor’s rises, so fast signals get blocked.
That frequency dependence is what makes filters possible. A resistor feeding a capacitor to ground forms a low-pass filter: slow signals pass untouched while fast ones get shunted away, with the boundary at the cutoff frequency f = 1 / (2πRC). Swap the two parts and you get a high-pass. Filters built from R, C, and L are how circuits keep the frequencies they want and reject the rest.
Put an inductor and a capacitor together and at one particular frequency their reactances are equal and opposite, so they cancel. That’s resonance. The LC pair passes or rejects that single frequency dramatically, as a sharp peak or notch. It’s how a radio picks one station out of the whole spectrum, and how oscillators settle on a frequency.
Key points
- Impedance (Z) is total AC opposition: resistance plus frequency-dependent reactance.
- Capacitive reactance falls with frequency; inductive reactance rises.
- RC low-pass and high-pass filters split slow from fast at cutoff f = 1 / (2πRC).
- At resonance, L and C cancel and select one frequency. Tuning and oscillators depend on it.
Practice
0 of 2 answered · Not startedWrong answers just let you try again, and hints are there if you want them. Answering every question first time, without hints, is what earns mastery.
- 1
How does a capacitor's reactance change as frequency rises?
- 2
What happens at the resonant frequency of an LC circuit?
