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Unit 11: Alternating-Current Circuits

Voltage and current that never sit still: resistors, capacitors, and inductors each fighting an AC source their own way, tracked with a rotating phasor arrow.

9 topics · 33 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

AC Sources and Sinusoidal Voltage

  1. How it worksHow does a generator's spinning coil naturally produce a voltage that varies over time as a sine wave?
  2. Worked exampleFind the peak voltage of an AC source with an RMS voltage of 120 volts.
  3. Ties togetherHow does an AC source's sinusoidal voltage connect back to the emf produced by a rotating generator coil?
Your turn1 of 2
Find the peak voltage of an AC source with an RMS voltage of 212 volts.

Resistors in AC Circuits

  1. How it worksHow do the voltage and current across a resistor in an AC circuit stay perfectly in step with each other?
  2. Worked exampleFind the RMS current through a 50 ohm resistor connected to a 120 volt RMS AC source.
  3. Common mistakeWhy doesn't a plain resistor's behavior in an AC circuit depend on the source's frequency at all?
Your turn1 of 2
Find the RMS current through a 141 ohm resistor connected to a 198 volt RMS AC source.

Capacitive Reactance

  1. How it worksHow does a capacitor's opposition to AC current, its reactance, come from how fast it can charge and discharge?
  2. Worked exampleFind the capacitive reactance of a 10 microfarad capacitor at a frequency of 60 Hz.
  3. Common mistakeWhy doesn't a capacitor's reactance behave like an ordinary resistance that dissipates energy as heat?
  4. Going furtherWhat happens to a capacitor's reactance as the frequency of the AC source driving it increases?
Your turn1 of 2
Find the capacitive reactance of a 35 microfarad capacitor at a frequency of 653 Hz.

Inductive Reactance

  1. How it worksHow does an inductor's back emf grow with frequency to create its own frequency-dependent reactance?
  2. Worked exampleFind the inductive reactance of a 0.1 henry inductor at a frequency of 60 Hz.
  3. Common mistakeWhy doesn't an inductor's reactance dissipate any energy as heat the way a resistor's resistance does?
  4. Going furtherWhat happens to an inductor's reactance as the frequency of its AC source approaches zero?
Your turn1 of 2
Find the inductive reactance of a 14 times 0.1 henry inductor at a frequency of 653 Hz.

Phasor Diagrams

  1. How it worksHow does a phasor's angle track a sinusoidal quantity's phase as it rotates at the source's own frequency?
  2. How it worksWalk me through drawing the phasor diagram for a resistor, a capacitor, and an inductor all driven by the same source.
  3. Ties togetherHow does watching a phasor diagram rotate connect directly to the sine wave it traces on a voltage-versus-time graph?
Your turn1 of 2
In an AC circuit, a resistor's voltage and an inductor's voltage are both nonzero. Why can't you just add their voltage magnitudes directly to get the total voltage across both in series?

Impedance of a Series RLC Circuit

  1. How it worksHow do resistance and the two reactances combine into an impedance using a phasor triangle instead of plain addition?
  2. Worked exampleFind the impedance of a series RLC circuit with R = 40 ohms, inductive reactance 60 ohms, and capacitive reactance 30 ohms.
  3. Common mistakeWhy doesn't a series RLC circuit's total impedance ever come out smaller than its resistance alone?
  4. Going furtherWhat happens to a series RLC circuit's impedance when its inductive and capacitive reactances happen to be equal?
  5. How it worksHow does a series RLC circuit's impedance triangle show resistance and net reactance as two perpendicular sides?
Your turn1 of 2
Find the impedance of a series RLC circuit with R = 71 ohms, inductive reactance 67 ohms, and capacitive reactance 94 ohms.

Power in an AC Circuit

  1. How it worksHow does the phase difference between voltage and current in an AC circuit determine its power factor?
  2. Worked exampleFind the average power delivered to a circuit with RMS voltage 120 volts, RMS current 2 amps, and a power factor of 0.8.
  3. Common mistakeWhy isn't average power in an AC circuit simply the plain product of RMS voltage and RMS current?
Your turn1 of 2
Find the average power delivered to a circuit with RMS voltage 212 volts, RMS current 13 amps, and a power factor of 9 times 0.1.

Resonance in an RLC Circuit

  1. How it worksHow does resonance happen exactly when the inductive and capacitive reactances cancel each other out?
  2. Worked exampleFind the resonant frequency of an RLC circuit with L = 0.02 henries and C = 5 microfarads.
  3. Common mistakeWhy doesn't a circuit at resonance end up with zero impedance, even once its reactances have canceled?
  4. Going furtherWhat happens to how sharply an RLC circuit's current peaks at resonance as its resistance is made smaller?
  5. Worked exampleFind the current amplitude at resonance in a series RLC circuit with R = 20 ohms driven by a 10 volt peak AC source.
Your turn1 of 2
Find the resonant frequency of an RLC circuit with L = 141 millihenries and C = 13 microfarads.

Transformers

  1. How it worksHow does a changing flux linking a primary and secondary coil step voltage up or down by their turns ratio?
  2. Worked exampleFind the secondary voltage of a transformer with 100 primary turns and 500 secondary turns, given a 12 volt primary source.
  3. Going furtherWhat happens to the current in a transformer's secondary coil compared to its primary once the voltage is stepped up?
Your turn1 of 2
Find the secondary voltage of a transformer with 142 primary turns and 328 secondary turns, given a 224 volt primary source.