Alternating Current Class 12 Physics Formula Sheet 2026-27 | Important Formulas

Alternating Current Class 12 Physics Formula Sheet 2026–27

A board-focused Chapter 7 formula sheet and quick revision guide covering RMS values, R–L–C circuits, reactance, impedance, resonance, AC power, power factor, generator and transformer.

Class 12 PhysicsChapter 7CBSE 2026–27Formula SheetQuick Revision

What is this page? This is a compact, exam-focused formula reference for Alternating Current Class 12 Physics. It follows the current CBSE 2026–27 Chapter 7 scope. The official curriculum includes alternating current, peak and RMS values, reactance and impedance, the series LCR circuit at the phasors-only level, resonance, AC power, power factor, wattless current, AC generator and transformer. Unit IV, which contains Chapters 6 and 7, carries 18 marks in the 70-mark theory structure; CBSE does not prescribe a separate fixed Chapter 7 mark allocation.

Official CBSE Physics Curriculum 2026–27

Scope warning: Many online formula sheets add competitive-exam material such as quality factor/bandwidth. Those formulas are not needed as a core prerequisite here because Q-factor is not listed in the current CBSE 2026–27 Chapter 7 syllabus. This page therefore prioritises the formulas directly connected to the prescribed CBSE scope.

Formula-at-a-glance: For most CBSE Chapter 7 numericals, the main chain is RMS/peak → X_L, X_C → Z → I → φ/cosφ → P. For resonance use X_L = X_C; for a transformer use the turns ratio. This page keeps the core formula set compact rather than mixing in unrelated competitive-exam formulas.

Quick Symbol & Unit Guide

Symbol	Meaning	SI unit
V, V0	RMS and peak voltage	V
I, I0	RMS and peak current	A
f, T, ω	Frequency, time period, angular frequency	Hz, s, rad s−1
R, XL, XC, Z	Resistance, inductive reactance, capacitive reactance, impedance	Ω
L, C	Inductance and capacitance	H, F
φ	Phase angle between voltage and current	rad or °
P	Average/real AC power	W
N	Number of turns in a coil/transformer winding	dimensionless
B, A	Magnetic-field magnitude and coil area	T, m²

1. Core Alternating Current Formulas

1. Instantaneous AC voltage

v = V₀ sin(ωt + φ)

V₀ = peak voltage, ω = angular frequency, φ = phase constant.

SI unit of voltage: volt (V)

2. Instantaneous AC current

i = I₀ sin(ωt + φ)

I₀ = peak current.

SI unit of current: ampere (A)

3. Angular frequency

ω = 2πf = 2π/T

f = frequency and T = time period.

ω: rad s⁻¹; f: Hz; T: s

4. Time period and frequency

f = 1/T

One complete cycle takes time T.

Frequency: hertz (Hz)

5. RMS value of AC

I_rms = I₀/√2     V_rms = V₀/√2

For a sinusoidal AC waveform.

RMS current: A; RMS voltage: V

6. Peak value from RMS value

I₀ = √2 I_rms     V₀ = √2 V_rms

Use this whenever a problem gives an effective/RMS value and asks for peak value.

7. Average value over a full cycle

I_{avg, full cycle} = 0    V_{avg, full cycle} = 0

Positive and negative halves cancel over one complete sinusoidal cycle.

8. Average value over a half cycle

I_avg = 2I₀/π     V_avg = 2V₀/π

Use only when the question explicitly refers to the average over a half cycle.

2. Pure R, L and C Circuits

Pure resistor

I_rms = V_rms/R

Voltage and current are in phase: φ = 0.

Pure inductor

X_L = ωL = 2πfL

I_rms = V_rms/X_L

Current lags voltage by 90° in an ideal pure inductor.

Pure capacitor

X_C = 1/(ωC) = 1/(2πfC)

I_rms = V_rms/X_C

Current leads voltage by 90° in an ideal pure capacitor.

Frequency dependence

X_L ∝ f     X_C ∝ 1/f

Increasing frequency increases inductive reactance but decreases capacitive reactance.

Fast memory: In a pure L, current lags voltage. In a pure C, current leads voltage. A resistor keeps voltage and current in phase.

3. Series LCR Circuit — Phasor-Level Formula Set

Inductive and capacitive reactance

X_L = ωL     X_C = 1/(ωC)

Net reactance

X = X_L − X_C

X > 0: net inductive. X < 0: net capacitive.

Impedance

Z = √[R² + (X_L − X_C)²]

SI unit: ohm (Ω)

RMS current

I_rms = V_rms/Z

For a series LCR circuit connected to an AC source.

Phase angle

tan φ = (X_L − X_C)/R

φ > 0 indicates an inductive circuit; φ < 0 indicates a capacitive circuit.

Power factor

cos φ = R/Z

For a series LCR circuit.

4. Resonance in a Series LCR Circuit

Resonance condition

X_L = X_C

Equivalently, ωL = 1/(ωC).

Angular resonant frequency

ω₀ = 1/√(LC)

Resonant frequency

f₀ = 1/(2π√LC)

Unit: hertz (Hz)

Impedance at resonance

Z = R

Because X_L − X_C = 0.

Current at resonance

I_rms,max = V_rms/R

For fixed source voltage, current is maximum at series resonance.

Power factor at resonance

φ = 0     cos φ = 1

Current is in phase with source voltage.

Resonance logic: As frequency increases, X_L increases while X_C decreases. At the frequency where they become equal, the net reactance is zero, impedance is minimum (R), current is maximum, phase angle is zero and power factor is unity.

5. AC Power, Power Factor and Wattless Current

Average power

P_avg = V_rmsI_rmscosφ

SI unit: watt (W)

Power in a series LCR circuit

P_avg = I_rms²R = V_rmsI_rmscosφ

Since the resistor is the element that consumes average real power in the ideal series RLC model.

Power factor

cosφ = R/Z = P_avg/(V_rmsI_rms)

It measures the fraction of apparent power corresponding to average real power.

Wattless current

I_reactive = I_rmssinφ

Reactive current can exist while its average power transfer over a complete cycle is zero.

Common trap: “Zero average power” does not mean “zero current.” In an ideal pure inductor or capacitor, current flows but the average power over a complete cycle is zero.

6. AC Generator Formulas

Magnetic flux through the rotating coil

Φ = BA cos(ωt)

Here Φ is flux through one turn. For an N-turn coil, the flux linkage is NΦ.

Instantaneous induced EMF

e = NBAω sin(ωt)

This follows from e = −N dΦ/dt for the rotating-coil model.

Peak EMF

e₀ = NBAω

Hence e₀ increases with N, B, A or angular speed ω, when the other quantities are fixed.

Generator memory: An AC generator converts mechanical energy into electrical energy through electromagnetic induction. The current syllabus places the AC generator under Chapter 7.

7. Transformer Formula Sheet

Voltage / turns ratio

V_s/V_p = N_s/N_p

For an ideal transformer.

Current relation for an ideal transformer

V_pI_p = V_sI_s

I_s/I_p = N_p/N_s

Efficiency

η = (P_out/P_in) × 100%

An ideal transformer has η = 100%; practical transformers have losses.

Step-up / step-down condition

N_s > N_p → step-up
N_s < N_p → step-down

Why transformer needs AC: Transformer action depends on changing magnetic flux. A steady DC supply does not provide continuous changing flux after the initial transient, so a normal transformer does not operate as intended on steady DC.

8. Formula Selection Map: Which Formula Should I Use?

If the question gives/asks	Start with	Quick check
Peak value ↔ RMS value	Irms = I₀/√2 or Vrms = V₀/√2	Peak = √2 × RMS
Frequency and inductor	XL = 2πfL	XL rises with f
Frequency and capacitor	XC = 1/(2πfC)	XC falls with f
Series LCR current	Z = √[R² + (XL − XC)²], then I = V/Z	Use consistent RMS or peak quantities
Phase angle	tanφ = (XL − XC)/R	Sign tells inductive/capacitive nature
Resonance	XL = XC or f₀ = 1/(2π√LC)	At resonance Z = R
Average AC power	P = VrmsIrmscosφ	Power factor matters
Generator peak EMF	e₀ = NBAω	More B/N/A/ω → larger peak EMF
Transformer voltage	Vs/Vp = Ns/Np	Voltage ratio follows turns ratio

9. High-Yield Formula Traps

Trap 1 — RMS vs peak:
Do not substitute a peak value into P = V_rmsI_rmscosφ.

Trap 2 — Average value:
Average over a full cycle is zero; average over a half cycle is not zero.

Trap 3 — L and C phase:
In L, current lags voltage. In C, current leads voltage.

Trap 4 — Reactance:
X_L increases with frequency; X_C decreases with frequency.

Trap 5 — Resonance:
X_L = X_C does not mean voltage across L and C is individually zero.

Trap 6 — Power:
Zero average power in a pure reactive circuit does not mean zero current.

Trap 7 — Transformer:
Increasing voltage ideally decreases current in the same proportion; the transformer does not create energy.

Trap 8 — Frequency:
A transformer changes voltage/current levels, not the frequency of the AC supply.

10. 60-Second Quick Revision

✓ v = V₀ sinωt and i = I₀ sinωt

✓ ω = 2πf

✓ RMS = peak/√2 for sinusoidal AC

✓ X_L = ωL and X_C = 1/(ωC)

✓ Z = √[R² + (X_L − X_C)²]

✓ tanφ = (X_L − X_C)/R

✓ cosφ = R/Z

✓ P_avg = V_rmsI_rmscosφ

✓ Resonance: X_L = X_C, f₀ = 1/(2π√LC)

✓ At resonance: Z = R, I is maximum, cosφ = 1

✓ Generator: e₀ = NBAω

✓ Transformer: V_s/V_p = N_s/N_p

11. 5-Minute Board Numerical Method

1. Write the given data in SI units. Convert mH, μF, kHz and similar quantities before substitution.
2. Identify the circuit. Decide whether it is R, L, C or series LCR.
3. Choose the governing formula first. Do not start calculating before deciding whether the problem asks for X, Z, I, φ, P or resonance.
4. Keep RMS and peak quantities consistent. If the power formula is used, use RMS values.
5. Check the physical result. For example, at resonance X_L = X_C, Z = R and power factor = 1.

12. Frequently Asked Questions

What is the most important formula in Alternating Current?

There is no single formula for every problem. The highest-use relationships are RMS/peak conversion, X_L, X_C, LCR impedance, power factor, resonance frequency, AC power and transformer turns ratio.

What is the RMS value of a sinusoidal AC?

The RMS current is I₀/√2 and the RMS voltage is V₀/√2, where I₀ and V₀ are the peak values.

What is the resonance condition in a series LCR circuit?

Resonance occurs when X_L = X_C. Therefore ω₀ = 1/√LC and f₀ = 1/(2π√LC). At resonance, Z = R and current is maximum.

How does frequency affect inductive and capacitive reactance?

Inductive reactance increases with frequency because X_L = 2πfL. Capacitive reactance decreases with frequency because X_C = 1/(2πfC).

What is the power factor of a series LCR circuit?

Power factor is cosφ = R/Z. At series resonance, φ = 0 and the power factor is 1.

Why does a transformer require AC?

Transformer action requires changing magnetic flux. A steady DC supply cannot maintain the continuous changing flux required for normal transformer operation.

Is quality factor required for the current CBSE 2026–27 Chapter 7 formula sheet?

Quality factor is not listed in the core Chapter 7 scope of the official 2026–27 CBSE Physics curriculum, so it is not included as a required formula on this board-focused sheet.

13. Direct-Answer Revision Guide

What should I memorise first for Alternating Current?

Memorise the RMS relation, X_L, X_C, series-LCR impedance, phase-angle relation, power factor, resonance condition/frequency, AC power and transformer turns ratio. Then practise using them in numerical and reasoning questions.

What happens when frequency increases?

X_L increases, X_C decreases, and the net character of a series LCR circuit can move from capacitive toward resonance and then inductive as frequency passes through resonance.

What happens at series resonance?

X_L = X_C, so net reactance is zero, Z = R, current is maximum for a fixed source voltage, phase angle is zero and power factor is unity.

14. Continue Chapter 7 Preparation

Chapter 7 Complete Notes Important Questions MCQs Numericals Case-Based Questions Assertion–Reason PYQs with Solutions Chapter 6 — Electromagnetic Induction Notes Official CBSE Physics SQP 2026–27 Official CBSE Physics Marking Scheme 2026–27 Official NCERT Physics Part I — Chapter 7

Link and source audit: This page links only to published Learn Revise Hub Chapter 6/7 resources plus official CBSE curriculum/SQP/marking-scheme documents and the official NCERT Physics textbook portal. No future Chapter 7 Chapter Test URL is linked. The official CBSE SQP confirms the current 2026–27 paper structure and includes Chapter 7 applications such as transformer and series-LCR resonance in its long-answer section.

Research note: Formula selection and search-intent coverage were cross-checked against current Class 12 Alternating Current revision resources. The official CBSE curriculum and 2026–27 SQP/MS were used as the authority for syllabus boundaries and assessment alignment. This is an original Learn Revise Hub revision resource, not an official CBSE document.