Quick answer: Alternating Current is 4–5 marks in boards and a regular numerical in JEE/NEET. Once you handle impedance like a right triangle, every question is simple.
Basics
- V = V₀ sin ωt; Vrms = V₀/√2 (220 V mains → V₀ = 311 V)
- Average over a full cycle = 0; over a half cycle = 2V₀/π
Pure elements
| Element | Opposition | Phase |
|---|---|---|
| R | R | V and I in phase |
| L | XL = ωL | I lags V by 90° |
| C | XC = 1/ωC | I leads V by 90° |
Series LCR
- Impedance Z = √[R² + (XL − XC)²]
- tan φ = (XL − XC)/R
- Resonance: XL = XC → ω₀ = 1/√(LC), Z = R (minimum), current maximum, φ = 0
- Quality factor Q = ω₀L/R = 1/(ω₀CR); sharper resonance for lower R
Power
- P = Vrms Irms cos φ; power factor cos φ = R/Z
- Pure L or C: cos φ = 0 → wattless current
- LC oscillations: f = 1/(2π√(LC)); energy swaps between ½LI² and ½q²/C
Transformer
- Vs/Vp = Ns/Np = Ip/Is (ideal)
- Step-up: Ns > Np; losses: copper (I²R), eddy currents (laminated core), hysteresis, flux leakage
- Works only on AC
Example
R = 30 Ω, L = 0.4 H, C = 100 μF at ω = 100 rad/s: XL = 40 Ω, XC = 100 Ω, Z = √(900 + 3600) = 67 Ω; current leads (capacitive); cos φ = 30/67 = 0.45.
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Common mistakes
- Adding R and X arithmetically instead of vectorially
- Using peak values in one place and rms in another
- Saying a transformer changes power (it changes voltage and current)
Related: Magnetic effects of current.
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Frequently asked questions
Are these Alternating Current Class 12 Formulas notes enough for the exam?
They cover every formula, definition and question type that appears in school and board papers for this chapter. Use them with the NCERT examples, exercise questions and the last five years' papers to be fully prepared.
How should I revise Alternating Current Class 12 Formulas?
Revise the notes after 1 day, 7 days and 30 days. Solve five questions each time instead of only reading, and keep an error list of the steps you get wrong.
What if I get stuck on a alternating current class 12 question?
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