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

Phasors: adding AC voltages that refuse to line up

Science · Electricity & Magnetism · ages 20-21
Name ______________________   Date ____________

  1. The inductive reactance XL of a coil at angular frequency omega equals what?

    • 1 over omega C
    • R times omega
    • omega times L

  2. A lone capacitor sits on an AC supply. How do current and voltage line up?

    • Current leads voltage by a quarter cycle
    • Voltage leads current by a quarter cycle
    • They peak together

  3. In a series RLC phasor diagram, the resistor voltage arrow points along the current arrow.

    Circle one:   True   False

  4. A series RLC circuit is driven below resonance, so the capacitor rules. How do current and supply voltage line up?

    • Current lags
    • They stay in step
    • Current leads

  5. A series circuit has R equal to 3 ohm, XL equal to 7 ohm, and Xc equal to 3 ohm. What is Z?

    • 13 ohm
    • 5 ohm
    • 4 ohm

  6. A supply of amplitude 10 V drives a circuit with Z equal to 5 ohm. What is the current amplitude?

    • 2 A
    • 50 A
    • 0.5 A

  7. In a series circuit XL exactly equals Xc. What does the supply see?

    • A wall: no current flows at all
    • Pure inductance, with current lagging
    • Pure resistance R, with current in phase and peaking

  8. A student adds VR, VC, and VL as plain numbers to get the supply voltage. What is the error?

    • Plain addition is fine since all are voltages
    • The three arrows point different ways, so they must add as vectors
    • Only the resistor voltage counts
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Answer key

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

Phasors: adding AC voltages that refuse to line up W1-mt_vQVlVWv2ln-s1

  1. omega times L · Faster changes provoke fiercer back emf, so XL equals omega L.
  2. Current leads voltage by a quarter cycle · The capacitor passes current first, with voltage lagging a quarter cycle.
  3. True · Resistor voltage stays in step with current, so the arrows share a direction.
  4. Current leads · Capacitor dominance means current-first behavior, so current leads.
  5. 5 ohm · Net reactance is 4 ohm, so Z equals sqrt(9 plus 16), which is 5 ohm.
  6. 2 A · AC Ohm says current amplitude equals voltage amplitude over Z: 10 over 5 is 2.
  7. Pure resistance R, with current in phase and peaking · The reactances cancel in the diagram, leaving bare R and peak in-step current.
  8. The three arrows point different ways, so they must add as vectors · The voltages peak at different times, so only vector addition gives the true total.
Worksheet · LightMySky