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 with different phases

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

  1. What is the inductive reactance XL of an ideal inductor at angular frequency omega?

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

  2. For an ideal capacitor in sinusoidal steady state, how do current and voltage line up?

    • Current leads voltage by a quarter cycle
    • Current lags voltage by a quarter cycle
    • Current and voltage peak at the same time

  3. In an ideal series RLC phasor diagram, the resistor voltage arrow points in the same direction as the current arrow.

    Circle one:   True   False

  4. An ideal series RLC circuit with R > 0 is driven below resonance. How does current line up with supply voltage?

    • Current lags
    • They stay in step
    • Current leads

  5. An ideal series RLC circuit has R = 3 ohm, XL = 7 ohm and Xc = 3 ohm. What is its impedance magnitude Z?

    • 13 ohm
    • 5 ohm
    • 4 ohm

  6. A sinusoidal supply of voltage amplitude 15 V drives a circuit with impedance magnitude Z = 5 ohm. What is the current amplitude?

    • 3 A
    • 75 A
    • 0.33 A

  7. A series RLC circuit has R = 4 ohm, XL = 9 ohm and Xc = 5 ohm. What is phi, defined as supply voltage phase minus current phase?

    • 45 degrees; current leads voltage
    • 0 degrees; current stays in phase
    • 45 degrees; current lags voltage

  8. In a series RLC circuit, voltage amplitudes are VR = 5 V, VL = 15 V and VC = 3 V. Sam adds all three and gets 23 V. What is the supply voltage amplitude?

    • 23 V, from adding all peaks
    • 13 V, from the phasor sum
    • 12 V, from cancelling R too
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Answer key

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Phasors: adding AC voltages with different phases W1-mt_vQVlVWv2ln-s1

  1. omega times L · Inductive reactance is XL = omega L, measured in ohms.
  2. Current leads voltage by a quarter cycle · The current reaches its positive peak a quarter cycle before the capacitor voltage reaches its positive peak.
  3. True · Resistor voltage and current are in phase, so their phasors point in the same direction.
  4. Current leads · Below resonance Xc > XL. The net reactance is capacitive, so current leads supply voltage.
  5. 5 ohm · The net reactance is 7 - 3 = 4 ohm. Z = sqrt(3^2 + 4^2) = 5 ohm.
  6. 3 A · I0 = V0/Z = 15/5 = 3 A. Both voltage and current are amplitudes.
  7. 45 degrees; current lags voltage · tan phi = (9 - 5)/4 = 1, so phi = 45 degrees. Positive phi means current lags supply voltage.
  8. 13 V, from the phasor sum · VL and VC oppose, giving 12 V. Combine that with VR: V0 = sqrt(5^2 + 12^2) = 13 V. Adding the positive amplitudes gives Sam's 23 V.
Worksheet · LightMySky