Class 12 · Chapter 7
Overview, notes, short notes, formula sheet, daily practice problems, previous year questions, and videos for this chapter — all in one place.
14 formulas across 4 topics in Alternating Current.
Updated 2026-07-09 · v1.0.0
An alternating quantity averages to zero over a cycle, so 'average current' as commonly meant is really the RMS value — the DC equivalent that would dissipate the same power.
I = I₀ sin(ωt + φ)
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| I₀ | peak (maximum) value of current | A | [A] |
| ω | angular frequency of the AC supply | rad/s | [T⁻¹] |
| φ | phase constant / initial phase | rad | [M⁰L⁰T⁰] |
I(rms) = I₀/√2 , V(rms) = V₀/√2
√(mean of I² over one full cycle) — the DC current that dissipates the same average power in a resistor
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| I(rms) | RMS current — what AC ammeters/voltmeters actually read | A | [A] |
Valid when
Common mistakes
I(avg) = 2I₀/π (over a half cycle)
Valid when
Each pure circuit element shifts the phase between current and voltage differently — a resistor keeps them in step, an inductor makes current lag, a capacitor makes it lead.
X(L) = ωL = 2πfL
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| X(L) | inductive reactance — an inductor's opposition to AC | Ω | [ML²T⁻³A⁻²] |
Valid when
Common mistakes
X(C) = 1/(ωC) = 1/(2πfC)
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| X(C) | capacitive reactance — a capacitor's opposition to AC | Ω | [ML²T⁻³A⁻²] |
Valid when
Common mistakes
Worth remembering
Combining R with L and/or C mixes in-phase and out-of-phase behaviour — impedance (not simple resistance) governs the circuit, and at resonance the reactive parts cancel entirely.
Z = √(R² + X(L)²) , tanφ = X(L)/R
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| Z | impedance — total AC opposition of the circuit | Ω | [ML²T⁻³A⁻²] |
| φ | phase angle by which current lags voltage | rad | [M⁰L⁰T⁰] |
Z = √(R² + X(C)²) , tanφ = X(C)/R
Z = √(R² + (X(L) − X(C))²) , tanφ = (X(L) − X(C))/R
Phasor sum: V(L) and V(C) are exactly antiparallel (180° apart), so their net reactive voltage is (X(L)−X(C))I, combined with V(R) at 90° to that
Valid when
Common mistakes
ω₀ = 1/√(LC) , f₀ = 1/(2π√(LC))
Resonance occurs when X(L) = X(C): ωL = 1/(ωC), solved for ω
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| ω₀ | angular resonant frequency | rad/s | [T⁻¹] |
Valid when
Q = ω₀L/R = (1/R)√(L/C) = ω₀/Δω
Ratio of the voltage across L (or C) at resonance to the applied voltage — measures how 'sharp' the resonance peak is
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| Q | quality factor, dimensionless | dimensionless | [M⁰L⁰T⁰] |
| Δω | bandwidth — width of the resonance curve between half-power points | rad/s | [T⁻¹] |
Valid when
Δω = R/L
Width of the current-vs-frequency curve between the two half-power points
Valid when
JEE Advanced frequently gives Z, R, and one reactance and asks for the other, or gives resonance data and asks to reconstruct L or C — practise algebraic manipulation of these three impedance formulas, not just memorisation.
Unlike DC, power in an AC circuit depends on the phase angle between current and voltage — only the in-phase component of current does any net work over a cycle.
P(avg) = V(rms) I(rms) cosφ
Time-average of instantaneous power P = VI over one complete cycle, using V and I both sinusoidal with phase difference φ
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| cosφ | power factor | dimensionless | [M⁰L⁰T⁰] |
Valid when
cosφ = R/Z
Valid when
I(wattless) = I(rms) sinφ
The component of current 90° out of phase with voltage — contributes to current flow but zero to average power
Valid when
Common mistakes
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