Resonance and Power in AC Circuits · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Hitting the sweet spot: resonance and AC power

Science · Electricity & Magnetism · ages 20-22
Name ______________________   Date ____________

  1. Which formula gives the average power delivered by an AC supply?

    • Peak current times peak voltage
    • Irms Vrms cos phi
    • Irms plus Vrms

  2. A series RLC circuit resonates at omega0. What is omega0?

    • 1 over sqrt(LC)
    • sqrt(LC)
    • R over L

  3. A lone ideal inductor draws net energy from the supply over a full cycle.

    Circle one:   True   False

  4. A circuit has Irms equal to 2 A, Vrms equal to 10 V, and cos phi equal to 0.5. What is the average power?

    • 20 W
    • 10 W
    • 5 W

  5. A series RLC circuit is driven exactly at resonance. What is its impedance?

    • Zero
    • Infinite
    • Bare R

  6. Why does a lone capacitor take no net energy over a full cycle?

    • Current and voltage sit a quarter cycle apart, so each joule borrowed is refunded
    • It takes plenty: capacitors always consume power
    • Its reactance is zero at all frequencies

  7. A radio hisses with two stations at once. What should the tuner do?

    • Raise R to broaden the peak
    • Park the circuit resonance exactly on the wanted frequency
    • Lower the antenna voltage

  8. Two RLC circuits share L and C, but one has smaller R. How do their resonance curves differ?

    • Larger R gives the taller peak
    • R changes nothing about the peak
    • Smaller R gives a taller, narrower peak
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Hitting the sweet spot: resonance and AC power W1-mt_wviaR0dJud-s1

  1. Irms Vrms cos phi · Only the in-step share counts, which is what cos phi selects.
  2. 1 over sqrt(LC) · Reactances match when omega0 equals 1 over sqrt(LC).
  3. False · Borrowed energy is fully refunded each cycle, so the net is zero.
  4. 10 W · Multiply 2 times 10 times 0.5 to get 10 W.
  5. Bare R · The reactances cancel, leaving only the resistance R.
  6. Current and voltage sit a quarter cycle apart, so each joule borrowed is refunded · Quarter-cycle timing means borrowing and refunding balance exactly.
  7. Park the circuit resonance exactly on the wanted frequency · Centring omega0 on the wanted station peaks it while rivals die on the flanks.
  8. Smaller R gives a taller, narrower peak · Smaller R raises Q, so the peak climbs higher and sharpens.
Worksheet · LightMySky