🔖 Topics

  • Sinusoidal EMFs
  • RMS values
  • Reactance
  • Impedance
  • Phase angle

🎯 Objectives

  • Solve for the RMS value of a sinusoidal wave
  • Calculate the reactances of capacitors and inductors in AC circuits
  • Analyze the series RLC AC circuit

📋 Sequence

  • AC vs DC voltage
  • Sinusoidal voltages
  • RMS values
  • Reactance vs. resistance
  • Impedance
  • Phase angle
  • The series AC RLC circuit

🖥️ Animations, Simulations, Activities

N/A

📝 Practice Problems

  1. A lightbulb is connected to a 120 V (rms), 30 Hz source. How many times per second does the current reverse direction?
  2. A 1500 W heater runs on 120 V (rms).
    • What is the peak current through the heater?
    • What is the RMS current through the heater?
  3. A 1500 W electric hair dryer is designed to work in the United States where the AC voltage is 120 V (rms).
    • What is the power dissipated in the hair dryer when it is plugged into a 240 V (rms) socket in Europe?
    • What might happen to the hair dryer if you plug it into a socket in Europe?
  4. A sinusoidal EMF from an AC generator has an RMS EMF of 4.0 V. What is the maximum and minimum value the EMF will take?
  5. At what frequency is the reactance of a \( 12 \: \mu F \) capacitor equal to \( 1.0 \: k \Omega \)?
  6. At what frequency is the reactance of a \( 20 \: mH \) inductor equal to \( 1.0 \: k \Omega \)?
  7. A \( 0.250 \: \mu F \) capacitor is connected to a \( 220 \: V \) rms AC source running at 50.0 Hz.
    • What is the reactance of the capacitor?
    • What is the RMS current through the capacitor?
  8. An inductor has a total impedance of \( 30 \: \Omega \) and an internal resistance of \( 20 \: \Omega \) at a frequency of 50.0 Hz. What is its inductance?

✅ Partial Solutions

  1. 60 times per second
  2. 17.7 A peak, 12.5 A rms
  3. 6000 W - you might burn out the hair dryer and potentially cause a fire
  4. -5.7 V to +5.7 V
  5. 13.3 Hz
  6. 7957.7 Hz
  7. \( 12.7 \: k\Omega \), \( 17 \: mA \)
  8. 71.2 mH

📘 Connected Resources

  • Giambattista, Alan, et al. College Physics With an Integrated Approach to Forces and Kinematics. 5th ed., McGraw-Hill Education, 2020.