Playbook
Alternating Current
Reactance, impedance, resonance and power in an LCR circuit. It has shrunk by about half since the early papers.
- Questions in the bank
- 113
- q/paper in 2025–26
- 0.49
- Numeric answer
- 34%
- Notes pages
- 5
Tier: Long tail
When you’ll see it
A sinusoidal source, an rms meter reading, or a circuit of R, L and C where reactance, phase or resonance decides the answer.
How this chapter is tested
Much of this chapter is the series LCR circuit and its resonance. It rests on three facts: meters and ratings give rms values, an inductor's reactance rises with frequency while a capacitor's falls, and voltages and reactances in series combine at right angles rather than by plain addition.
The pages build that in order: rms values and timing on a sine wave, the reactance of each part, impedance with phase and power, resonance with its quality factor and bandwidth, and last LC oscillations and transformers. The arithmetic is short once the facts are in place.
The chapter is asked less often than in the early papers, so it sits in the long tail. Marks are lost on mixing peak and rms values, on using f where ω belongs, and on a transformer ratio turned upside down. The emf comes from a coil turning in a field, as in Electromagnetic Induction, and LC oscillations follow the same equation as a mass on a spring in Oscillations.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
RMS values and timing
The rms value is the steady current that heats a resistor at the same rate: I₀/√2 for a sine wave; for a constant plus a sinusoid the squares add.
Reactance of L and C
X_L = ωL rises with frequency and X_C = 1/ωC falls; in an inductor the voltage leads the current by a quarter cycle, in a capacitor the current leads.
Impedance, phase and power
Z = √(R² + (X_L − X_C)²), power factor cos φ = R/Z, and only the resistance takes power: P = I_rms²R.
Resonance, Q and bandwidth
At ω₀ = 1/√(LC) the reactances cancel, Z = R and the current is largest; Q = ω₀L/R sets how sharp the peak is, and the band edges are the half-power points.
LC oscillations and transformers
Energy swaps between capacitor and inductor at ω = 1/√(LC); a transformer changes voltage in the ratio of its turns while the power, less its losses, carries through.
Traps to expect
Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.
Peak or rms
A meter reading or a rating like 220 V is rms. E₀ sin ωt gives the peak current; divide by √2 for the meter.
f where ω belongs
In sin(200πt) the coefficient is already ω. Multiplying by 2π again, or using f₀ in Q = ω₀L/R, is off by 2π.
Adding the voltages
V_R + V_L + V_C is not the supply voltage. The parts are out of phase, so V² = V_R² + (V_L − V_C)².
The turns ratio upside down
Voltage follows the turns, current goes the other way. Write V_s/V_p = N_s/N_p before putting numbers in.
Learn it before you drill it
This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each page. Read the notes once, then drill page by page below.
Alternating Current notesDrill every Alternating Current question
113 questions from the bank, across 5 subtopics.
Drill one subtopic at a time
The 5 subtopics, in teaching order.
- RMS Values and Timing in ACDrill RMS Values and Timing in AC
- Reactance of a Resistor, Inductor and CapacitorDrill Reactance of a Resistor, Inductor and Capacitor
- Series LCR: Impedance, Phase and PowerDrill Series LCR: Impedance, Phase and Power
- Resonance, Quality Factor and BandwidthDrill Resonance, Quality Factor and Bandwidth
- LC Oscillations, Transformers and AC DevicesDrill LC Oscillations, Transformers and AC Devices
Related playbooks
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