शि

Schooling · Class 12 · Physics · Alternating Current · Chapter on a page

CBSE Class 12 · Physics · NCERT Physics Part-I

Alternating Current: chapter on a page

A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).

About the notes: Written by Shishya's AI on 27 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.

This note's current text has no applied fact-check on record.

Mind map

Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.

Mind map of Alternating Current: Key ideas, Formulas and facts, Watch out forKey ideasAn alternating current varies…The root-mean-square (RMS) value of…In a pure resistor, current and…Inductive reactance is X_L = ωL and…The impedance of a series LCR…Resonance occurs in a series LCR…Average power in an AC circuit is P…Formulas and factsi = i₀ sin(ωt)RMS valuesX_L = ωL = 2πfLX_C = 1/(ωC) = 1/(2πfC)Z = √[R² + (X_L − X_C)²]ω₀ = 1/√(LC)P = V_rms I_rms cos φWatch out forConfusing peak and RMS valuesIgnoring phase when adding voltages…Thinking reactance is the same as…Assuming power is V_rms × I_rms in…Using DC formulas directly for AC…Alternating Current
The mind map as a list
  • Key ideas
    • An alternating current varies…
    • The root-mean-square (RMS) value of…
    • In a pure resistor, current and…
    • Inductive reactance is X_L = ωL and…
    • The impedance of a series LCR…
    • Resonance occurs in a series LCR…
    • Average power in an AC circuit is P…
  • Formulas and facts
    • i = i₀ sin(ωt)
    • RMS values
    • X_L = ωL = 2πfL
    • X_C = 1/(ωC) = 1/(2πfC)
    • Z = √[R² + (X_L − X_C)²]
    • ω₀ = 1/√(LC)
    • P = V_rms I_rms cos φ
  • Watch out for
    • Confusing peak and RMS values
    • Ignoring phase when adding voltages…
    • Thinking reactance is the same as…
    • Assuming power is V_rms × I_rms in…
    • Using DC formulas directly for AC…

What this chapter is about

This chapter introduces alternating current (AC), the form of electric current that reverses direction periodically. While earlier chapters dealt with direct current (DC) that flows steadily in one direction, AC is what powers homes, schools and industries across India. Understanding AC is essential because the electricity supplied by power stations is alternating, not direct.

Key ideas

  • An alternating current varies sinusoidally as i = i₀ sin(ωt), where i₀ is the peak (maximum) current and ω = 2πf is the angular frequency; voltage follows a similar form v = v₀ sin(ωt + φ), where φ is the phase angle.
  • The root-mean-square (RMS) value of an AC quantity is its effective value for power calculations: I_rms = i₀ / √2 and V_rms = v₀ / √2.
  • In a pure resistor, current and voltage are in phase; in a pure inductor, current lags voltage by 90°; in a pure capacitor, current leads voltage by 90°.
  • Inductive reactance is X_L = ωL and capacitive reactance is X_C = 1/(ωC); both have the unit ohm.
  • The impedance of a series LCR circuit is Z = √[R² + (X_L − X_C)²], and the phase angle φ satisfies tan φ = (X_L − X_C) / R.
  • Resonance occurs in a series LCR circuit when X_L = X_C, giving ω₀ = 1/√(LC); at resonance, impedance is minimum (equal to R) and current is maximum.
  • Average power in an AC circuit is P = V_rms I_rms cos φ, where cos φ is called the power factor.
  • A transformer changes AC voltage by electromagnetic induction; the voltage ratio equals the turns ratio: V_s / V_p = N_s / N_p.

Formulas and facts to remember

  • Instantaneous current: i = i₀ sin(ωt); instantaneous voltage: v = v₀ sin(ωt + φ).
  • RMS values: I_rms = i₀ / √2 ≈ 0.707 i₀; V_rms = v₀ / √2.
  • Inductive reactance: X_L = ωL = 2πfL (ohm).
  • Capacitive reactance: X_C = 1/(ωC) = 1/(2πfC) (ohm).
  • Impedance of series LCR circuit: Z = √[R² + (X_L − X_C)²].
  • Resonant angular frequency: ω₀ = 1/√(LC); resonant frequency f₀ = 1/(2π√(LC)).
  • Average power: P = V_rms I_rms cos φ; for a pure resistor cos φ = 1, for pure L or pure C cos φ = 0.
  • Transformer relation: V_s / V_p = N_s / N_p = I_p / I_s (ideal transformer, no energy loss).

Common mistakes

  • Confusing peak and RMS values → Always divide peak values by √2 to get RMS; household 220 V is already RMS.
  • Ignoring phase when adding voltages in LCR circuits → Voltages across L and C are 180° apart, so they subtract; add by phasor method, not arithmetic.
  • Thinking reactance is the same as resistance → Reactance depends on frequency; resistance does not.
  • Assuming power is V_rms × I_rms in all circuits → Multiply by cos φ; in a pure inductor or capacitor, average power is zero.
  • Using DC formulas directly for AC capacitors and inductors → Capacitors block DC but pass AC; inductors pass DC easily but oppose rapid AC changes.

Quick revision

  • AC quantities vary sinusoidally; RMS value = peak value / √2.
  • In a pure inductor current lags voltage by 90°; in a pure capacitor current leads by 90°.
  • Impedance Z = √[R² + (X_L − X_C)²]; minimum at resonance when X_L = X_C.
  • Power factor cos φ determines real power; purely reactive circuits consume zero average power.
  • Transformers change voltage level; step-up increases voltage, step-down decreases it; works only with AC.