Alternating Current
Class 12 · Physics
4 ideas in Class 12 Physics, explained in plain words, with games and quizzes to practise.
RMS Values and AC Through Resistor
Part of: RMS Values and Single Elements
Alternating voltage swings sinusoidally, so its heating effect is quoted as rms, the peak divided by root two. Phasors picture each quantity as a spinning arrow whose projection gives the instant value. Through a resistor, current and voltage phasors point together, rising and falling in step.
Why it matters. Mains 220 V is an rms value, and meters read rms. Mixing peak with rms overstates heating by 41 percent.
Formulas
- RMS from peak: Vrms = V0 / sqrt(2)
- Peak from RMS: V0 = sqrt(2) x Vrms
- Resistor power: P = Vrms x Irms
Key words
- RMS value
- : Steady equivalent of AC for heating, equal to peak over root two.
- Phasor
- : Rotating arrow whose projection gives the instant AC value.
- Peak value
- : Maximum reached by voltage or current in each half cycle.
Try it in two minutes
- Divide the peak by 1.414 for the rms value.
- Draw voltage and current arrows pointing the same way.
- Square the rms current times resistance for heating power.
Try at home. Find the peak of the 220 V mains supply.
AC Through Inductor and Capacitor
Part of: RMS Values and Single Elements
An inductor fights change, so its current lags voltage by a quarter cycle, with reactance omega L that grows with frequency. A capacitor fills and empties, so its current leads by a quarter cycle, with reactance 1 over omega C that shrinks with frequency. Pure L or C averages zero power over a cycle.
Why it matters. Filters, tuners and choke coils all exploit reactance. Swapping lag with lead, or expecting power loss in ideal L or C, breaks AC analysis.
Formulas
- Inductive: XL = w L, current lags by 90 degrees
- Capacitive: XC = 1 / (w C), current leads by 90 degrees
- Average power in pure L or C = 0
Key words
- Reactance
- : Opposition of an inductor or capacitor to AC, changing with frequency.
- Inductive reactance
- : Omega L, growing with frequency.
- Capacitive reactance
- : One over omega C, shrinking with frequency.
Try it in two minutes
- Multiply 2 pi f by L for inductive reactance.
- Divide one by 2 pi f C for capacitive reactance.
- Draw current a quarter turn behind voltage for L, ahead for C.
Try at home. Predict what happens to each reactance when frequency doubles.
Series LCR Circuit and Resonance
Part of: LCR Circuit and Resonance
In series LCR, resistance and net reactance combine as the hypotenuse Z, and current lags or leads by the phase angle. At resonance the reactances cancel, impedance is smallest and current peaks at V over R, with frequency 1 over 2 pi root LC.
Why it matters. Radios tune by resonance and mains circuits avoid it. Adding reactances directly instead of as a phasor difference gives wrong impedance and phase.
Formulas
- Impedance: Z = sqrt(R^2 + (XL - XC)^2)
- Phase: tan(phi) = (XL - XC) / R
- Resonance: w0 = 1 / sqrt(L C)
Key words
- Impedance
- : Total AC opposition of a circuit, combining resistance and reactance.
- Resonance
- : State where inductive and capacitive reactances cancel and current peaks.
- Phase angle
- : Lag or lead of current behind or ahead of voltage.
- Q factor
- : Sharpness of resonance, higher for lower resistance.
Try it in two minutes
- Subtract XC from XL, keeping the sign.
- Combine with R as a hypotenuse for Z.
- Set XL equal to XC to find resonance.
Try at home. Predict whether a given circuit is inductive or capacitive from XL versus XC.
AC Power and Transformers
Part of: AC Power and Transformers
Average AC power is Vrms times Irms times cosine of phase; pure L or C draws wattless current with zero average power. A transformer trades voltage for current through its turns ratio, stepping up for transmission and down for use, with laminated cores cutting eddy-current loss.
Why it matters. Bills, transmission lines and chargers all hinge on these ideas. Ignoring power factor overstates useful power, and expecting DC transformation fails.
Formulas
- Average power: P = Vrms Irms cos(phi)
- Turns: Vs/Vp = Ns/Np, Is/Ip = Np/Ns
- Ideal: input power = output power
Key words
- Power factor
- : Cosine of phase angle, the fraction of current doing real work.
- Wattless current
- : Current with zero average power from 90-degree phase shift.
- Step-up transformer
- : Transformer giving higher secondary voltage with lower current.
- Laminated core
- : Stacked thin sheets that block eddy currents in transformers.
Try it in two minutes
- Multiply Vrms, Irms and cos phi for average power.
- Scale voltage by turns ratio for the secondary.
- Scale current inversely to keep power balanced.
Try at home. Explain why phone chargers are small step-down transformers.
What your child will practise
- AC Power and Transformers: Desert Quick Fire (Quick Fire)
- AC Through Inductor and Capacitor: Jungle Puzzle (Clue Puzzle)
- AC Through Inductor and Capacitor: Space Quick Fire (Quick Fire)
- RMS Values and AC Through Resistor: Ocean Quick Fire (Quick Fire)
- Series LCR Circuit and Resonance: Desert Puzzle (Clue Puzzle)
- Quiz: AC Power and Transformers (8 questions)
- Quiz: AC Through Inductor and Capacitor (8 questions)
- Quiz: RMS Values and AC Through Resistor (8 questions)
- Quiz: Series LCR Circuit and Resonance (8 questions)