Alternating Current Class 12 Important Questions 2026-27 | RMS, LCR & Resonance

Alternating Current Class 12 Important Questions 2026–27

Chapter 7 — CBSE-focused important questions with answers covering RMS values, R/L/C circuits, reactance, series LCR, resonance, AC power, power factor, wattless current, AC generator and transformer.

Class 12 PhysicsChapter 7CBSE 2026–27Important QuestionsBoard Exam Practice

Quick answer: For CBSE Class 12 Physics Chapter 7, the core practice areas are peak and RMS values, AC through R/L/C, reactance, series LCR phasors, impedance, resonance, AC power, power factor, wattless current, AC generator and transformer. For a sinusoidal AC, I_rms = I₀/√2 and V_rms = V₀/√2; in series LCR, Z = √[R² + (X_L − X_C)²], and resonance occurs when X_L = X_C.

How to use this page: Practise the questions in mark-wise order, then revisit the linked Alternating Current Notes for concepts and formulas. The selection is based on the current CBSE syllabus, official sample-paper structure and recurring topic patterns in recent board-question compilations; it is not a prediction of exact board questions.

2026–27 syllabus boundary: Chapter 7 includes alternating current, peak and RMS values, reactance and impedance, series LCR circuit (phasors only), resonance, power in AC circuits, power factor, wattless current, AC generator and transformer. This page stays within that boundary. Official CBSE Physics Curriculum 2026–27 · Official Class XII 2026–27 SQP & Marking Scheme

Important: “Important” means high-value practice based on syllabus relevance, recurring concepts and question formats—not a guarantee that CBSE will ask the same wording or marks in the board examination.

1. What This Question Bank Covers

1-mark / objective
Definitions, formula recognition, phase relations, graphs and quick conceptual checks.

2-mark
Short explanations, direct calculations, comparisons and formula-based reasoning.

3-mark
Multi-step numericals, phasor reasoning, power-factor and application questions.

4-mark case-style thinking
Linked conceptual and numerical situations suitable for competency-based practice.

5-mark
Structured derivations/explanations, generator and transformer, LCR and integrated numerical questions.

Higher-order practice
Frequency changes, graph interpretation, comparison and “what happens if” reasoning.

2. 1-Mark Important Questions

Q1 · 1 mark

What is the angular frequency of an AC source of frequency f?

Answer: ω = 2πf

Q2 · 1 mark

For a sinusoidal current with peak value I₀, write its RMS value.

Answer: I_rms = I₀/√2

Q3 · 1 mark

What is the algebraic average of a pure sinusoidal AC over one complete cycle?

Answer: Zero.

Q4 · 1 mark

What is the phase relation between voltage and current in a pure resistive AC circuit?

Answer: Voltage and current are in phase; φ = 0.

Q5 · 1 mark

In a pure inductive circuit, does current lead or lag voltage?

Answer: Current lags voltage by 90°.

Q6 · 1 mark

In a pure capacitive circuit, does current lead or lag voltage?

Answer: Current leads voltage by 90°.

Q7 · 1 mark

Write the expression for inductive reactance.

Answer: X_L = ωL = 2πfL

Q8 · 1 mark

Write the expression for capacitive reactance.

Answer: X_C = 1/(ωC) = 1/(2πfC)

Q9 · 1 mark

What happens to X_L when frequency is increased?

Answer: It increases.

Q10 · 1 mark

What happens to X_C when frequency is increased?

Answer: It decreases.

Q11 · 1 mark

Write the impedance of a series LCR circuit.

Answer: Z = √[R² + (X_L − X_C)²]

Q12 · 1 mark

What is the condition for series resonance?

Answer: X_L = X_C.

Q13 · 1 mark

Write the resonant angular frequency of a series LCR circuit.

Answer: ω₀ = 1/√(LC)

Q14 · 1 mark

What is the power factor of a series LCR circuit at resonance?

Answer: Unity, cosφ = 1.

Q15 · 1 mark

Write the average-power expression for an AC circuit.

Answer: P_avg = V_rmsI_rmscosφ

Q16 · 1 mark

What is meant by wattless current?

Answer: The reactive component of current associated with zero average power transfer in an ideal purely reactive circuit.

Q17 · 1 mark

Write the peak EMF of an N-turn AC generator coil of area A rotating with angular speed ω in magnetic field B.

Answer: E₀ = NBAω

Q18 · 1 mark

Which type of rings are used in an AC generator?

Answer: Slip rings.

Q19 · 1 mark

Write the ideal-transformer turns relation.

Answer: V_s/V_p = N_s/N_p

Q20 · 1 mark

Why does a transformer not operate normally on steady DC?

Answer: Normal transformer action requires changing magnetic flux; steady DC cannot maintain that changing flux after the initial transient.

3. 2-Mark Important Questions

Q21 · 2 marks

Differentiate between peak value and RMS value of a sinusoidal current.

Answer: Peak value I₀ is the maximum instantaneous current. RMS value is the effective DC-equivalent current for the same heating effect in a resistor. For a sine wave, I_rms = I₀/√2.

Q22 · 2 marks

A sinusoidal AC current has peak value 14.14 A. Find its RMS value.

Solution: I_rms = 14.14/√2 = 10 A.

Q23 · 2 marks

Explain why an ideal inductor consumes zero average power in an AC circuit.

Answer: In a pure inductor, current and voltage differ in phase by 90°, so cosφ = 0. Hence P_avg = V_rmsI_rmscosφ = 0. The inductor temporarily stores and returns energy.

Q24 · 2 marks

Explain why an ideal capacitor consumes zero average power in an AC circuit.

Answer: In a pure capacitor, |φ| = 90°, so cosφ = 0. Thus average power over a complete cycle is zero because energy stored in the electric field is returned to the circuit.

Q25 · 2 marks

How do inductive and capacitive reactances change when the frequency of AC is doubled?

Answer: X_L = 2πfL, so X_L doubles. X_C = 1/(2πfC), so X_C becomes half.

Q26 · 2 marks

A series LCR circuit has R = 8 Ω, X_L = 6 Ω and X_C = 2 Ω. Find its impedance.

Solution: Net reactance = 4 Ω. Z = √(8² + 4²) = √80 ≈ 8.94 Ω.

Q27 · 2 marks

What are two consequences of series resonance in an LCR circuit?

Answer: X_L = X_C, so Z = R is minimum. For fixed V_rms, current is maximum and power factor becomes unity.

Q28 · 2 marks

State two differences between an AC generator and a transformer.

Answer: An AC generator converts mechanical energy into electrical energy and uses a rotating coil. A transformer transfers AC electrical energy between circuits by mutual induction and normally has stationary coils on a magnetic core.

Q29 · 2 marks

An ideal transformer has N_p = 500 and N_s = 1000. If V_p = 110 V, find V_s and identify the transformer.

Solution: V_s/110 = 1000/500 = 2. Hence V_s = 220 V. It is a step-up transformer.

Q30 · 2 marks

Why is the RMS value more useful than the peak value for power calculations in AC circuits?

Answer: RMS values directly correspond to the equivalent DC heating effect. Average AC power is conveniently expressed as P = V_rmsI_rmscosφ.

4. 3-Mark Important Questions

Q31 · 3 marks

For a series LCR circuit, explain the phasor relationship among V_R, V_L and V_C, and obtain the expression for the applied voltage.

Answer: Taking current as reference, V_R is in phase with I, V_L leads I by 90° and V_C lags I by 90°. Hence the net reactive voltage is V_L − V_C. Therefore V = √[V_R² + (V_L − V_C)²].

Q32 · 3 marks

Derive the expression for impedance of a series LCR circuit using the phasor relationship.

Solution: Since V_R = IR, V_L = IX_L, and V_C = IX_C, divide the voltage relation by I: Z = √[R² + (X_L − X_C)²].

Q33 · 3 marks

A 220 V RMS source of frequency 50 Hz is connected to a pure inductor of 0.70 H. Find its inductive reactance and RMS current.

Solution: X_L = 2πfL = 2π(50)(0.70) ≈ 220 Ω. Thus I_rms = V_rms/X_L ≈ 1 A.

Q34 · 3 marks

A 220 V RMS, 50 Hz source is connected to a capacitor of 20 μF. Find X_C and the RMS current.

Solution: X_C = 1/(2πfC) ≈ 159.2 Ω. Therefore I_rms = 220/159.2 ≈ 1.38 A.

Q35 · 3 marks

A series LCR circuit has R = 30 Ω, X_L = 50 Ω and X_C = 10 Ω. Find Z, power factor and state whether current leads or lags.

Solution: Z = √(30² + 40²) = 50 Ω. Power factor = R/Z = 0.6. Since X_L > X_C, the circuit is inductive and current lags voltage.

Q36 · 3 marks

Explain resonance in a series LCR circuit and write the resonant frequency.

Answer: At resonance X_L = X_C. Thus ωL = 1/(ωC), giving ω₀ = 1/√(LC) and f₀ = 1/(2π√LC). At resonance Z = R and current is maximum for a fixed source voltage.

Q37 · 3 marks

An AC circuit has V_rms = 200 V, I_rms = 5 A and power factor 0.6. Find average power. What is the wattless-current component?

Solution: P = 200 × 5 × 0.6 = 600 W. Since cosφ = 0.6, sinφ = 0.8. I_w = 5 × 0.8 = 4 A.

Q38 · 3 marks

An AC generator has N = 200 turns, area A = 0.02 m², magnetic field B = 0.5 T and angular speed 100 rad s⁻¹. Find its peak EMF.

Solution: E₀ = NBAω = 200 × 0.02 × 0.5 × 100 = 200 V.

Q39 · 3 marks

An ideal transformer changes 220 V to 1100 V. If the primary current is 5 A, find the secondary current.

Solution: For an ideal transformer, V_pI_p = V_sI_s. Thus I_s = (220 × 5)/1100 = 1 A.

Q40 · 3 marks

Explain three important causes of energy loss in a real transformer and one method of reducing each.

Answer: Copper loss: reduced using suitable low-resistance windings. Eddy-current loss: reduced using a laminated core. Hysteresis loss: reduced by using suitable magnetic material. Flux leakage can also occur and is reduced by improving magnetic coupling/core design.

5. 4-Mark Competency / Case-Style Questions

Case 1 · 4 marks

A student connects a series LCR circuit to an AC source and varies frequency. At a certain frequency, current becomes maximum and voltage and current are in phase.

(a) Identify the condition. (b) What is the relation between X_L and X_C? (c) What happens to impedance? (d) What is the power factor?

Answers: (a) Series resonance. (b) X_L = X_C. (c) Z becomes minimum and equals R. (d) Power factor = 1.

Case 2 · 4 marks

An AC source has voltage v = 311 sin(100πt) V. A student is asked to determine its peak voltage, frequency, RMS voltage and time period.

Answers: Peak voltage V₀ = 311 V. Angular frequency ω = 100π rad s⁻¹, so f = ω/(2π) = 50 Hz. V_rms = 311/√2 ≈ 220 V. T = 1/f = 0.02 s.

Case 3 · 4 marks

A transformer has 100 primary turns and 500 secondary turns. The primary is connected to 200 V AC. Assume it is ideal.

(a) Is it step-up or step-down? (b) Find secondary voltage. (c) If primary current is 2 A, find secondary current. (d) State why DC is unsuitable.

Answers: (a) Step-up. (b) V_s = 200 × 5 = 1000 V. (c) I_s = (200×2)/1000 = 0.4 A. (d) Transformer action requires changing magnetic flux; steady DC cannot provide continuous changing flux.

Case 4 · 4 marks

A series LCR circuit has R = 40 Ω, X_L = 30 Ω and X_C = 70 Ω and is connected to a 200 V RMS source.

(a) Find net reactance. (b) Find impedance. (c) Find RMS current. (d) State whether current leads or lags.

Answers: (a) X_L − X_C = −40 Ω. (b) Z = √(40²+40²) ≈ 56.6 Ω. (c) I_rms ≈ 200/56.6 = 3.54 A. (d) Net capacitive, so current leads voltage.

6. 5-Mark Important Questions

Q41 · 5 marks

For a series LCR circuit connected to an AC source, draw/describe the phasor relationship and obtain expressions for impedance and phase angle. State the condition for resonance.

Answer outline: Take current I as reference. V_R is in phase with I; V_L is +90° and V_C is −90°. Hence V² = V_R² + (V_L−V_C)². Using V_R=IR, V_L=IX_L, V_C=IX_C, obtain Z = √[R²+(X_L−X_C)²] and tanφ=(X_L−X_C)/R. Resonance occurs when X_L=X_C.

Q42 · 5 marks

Discuss resonance in a series LCR circuit. Obtain the expression for resonant frequency and explain the behaviour of impedance, current and power factor at resonance.

Answer outline: Set X_L=X_C: ωL=1/(ωC), hence ω₀=1/√LC and f₀=1/(2π√LC). At resonance net reactance is zero, Z=R, current is maximum for fixed V_rms, φ=0 and power factor is unity.

Q43 · 5 marks

Describe the principle, construction and working of an AC generator and obtain the expression for instantaneous induced EMF.

Answer outline: Principle: electromagnetic induction. A coil of N turns and area A rotates in field B with angular speed ω. The changing flux produces induced EMF. In the ideal sinusoidal model, e=E₀sinωt, where E₀=NBAω. Mention armature, field magnet, slip rings and brushes, and explain why the output alternates.

Q44 · 5 marks

Describe the construction and working of a transformer and obtain the relation between primary and secondary voltage and number of turns. Mention important losses.

Answer outline: Explain primary, secondary and magnetic core; changing primary current produces changing core flux and induces secondary EMF. For an ideal transformer, V_s/V_p=N_s/N_p. Also V_pI_p=V_sI_s. Discuss copper, eddy-current, hysteresis and flux-leakage losses.

Q45 · 5 marks

An AC source v = 140 sin(100πt) V is connected to a series LCR circuit having R = 400 Ω, L = 5/π H and C = 50/π μF. Find impedance and RMS current. Also state the power factor.

Solution: ω=100π. X_L=ωL=500 Ω. X_C=1/(ωC)=200 Ω. Therefore Z=√(400²+300²)=500 Ω. V_rms=140/√2≈99 V. I_rms≈99/500≈0.20 A. Power factor = R/Z = 0.8; circuit is inductive.

7. Higher-Order and “What Happens If?” Questions

Q46

In a series LCR circuit, the frequency is increased from below resonance to above resonance. Describe how the nature of the circuit changes.

Answer: Below resonance X_C > X_L, so the circuit is capacitive and current leads voltage. At resonance X_L=X_C. Above resonance X_L > X_C, so the circuit becomes inductive and current lags voltage.

Q47

Two ideal capacitors have the same capacitance but are used at different AC frequencies. Which one offers greater capacitive reactance?

Answer: The capacitor connected to the lower frequency, because X_C is inversely proportional to frequency.

Q48

A series LCR circuit has power factor 0.8 and is inductive. What can you say about the phase angle?

Answer: cosφ=0.8, so |φ|≈36.9°. Since the circuit is inductive, φ is positive in the usual convention and current lags voltage.

Q49

At resonance, the voltages across L and C need not be zero. Explain.

Answer: At resonance X_L=X_C, so V_L=IX_L and V_C=IX_C can both be non-zero. They are equal in magnitude and opposite in phase, so their net contribution to the supply-voltage phasor is zero.

Q50

An ideal transformer is used to increase voltage. What happens to secondary current if input power remains equal to output power?

Answer: Secondary current decreases because V_pI_p=V_sI_s. Increasing voltage requires a corresponding decrease in current in the ideal model.

8. Common Exam Traps

Trap 1: Full-cycle average of a sine wave is zero; half-cycle average magnitude is 2I₀/π.

Trap 2: RMS is not the same as average value.

Trap 3: Pure L: current lags voltage. Pure C: current leads voltage.

Trap 4: X_L rises with frequency; X_C falls.

Trap 5: Series-LCR impedance is not R+X_L+X_C.

Trap 6: At resonance, Z=R—not zero.

Trap 7: Zero average power in a pure reactive circuit does not mean zero current.

Trap 8: Ideal transformer voltage ratio follows turns ratio; current ratio is inverse.

Trap 9: AC generator uses slip rings; do not confuse them with the split-ring commutator of a DC generator.

Trap 10: The current CBSE syllabus says LCR series circuit phasors only; avoid unnecessary advanced phasor mathematics.

9. How to Write Board Answers

Numerical
Write given data → formula → substitution → unit → final answer.

Derivation
State the principle, define symbols, show the key steps, and box the final relation.

Phase question
State lead/lag explicitly and give the phase angle.

Transformer/generator
Include principle + labelled construction points + working + equation wherever asked.

10. Priority Revision Map

Area	Must be able to do	Practice focus
Peak/RMS/average	Convert values and interpret waveform	1–2 mark + numerical
Pure R/L/C	Phase, reactance and power	Concept + comparison
Series LCR	Phasor relation, Z, φ and I	3–5 mark
Resonance	Condition, frequency, minimum Z and maximum I	MCQ + numerical + explanation
AC power	P, cosφ and wattless current	Numerical + reasoning
AC generator	Principle, construction, working, EMF	Long answer
Transformer	Turns ratio, current relation, losses	Numerical + long answer

11. Recommended Practice Sequence

Step 1: Revise the Chapter 7 Notes.

Step 2: Solve Q1–Q20 without looking at answers.

Step 3: Attempt Q21–Q40 with full working.

Step 4: Practise Q41–Q50 as board-style higher-mark/application questions.

Step 5: Revisit mistakes and then continue to the forthcoming Chapter 7 MCQs, Numericals, Case-Based Questions, Assertion–Reason, PYQs, Formula Sheet and Chapter Test once those resources are published.

12. Frequently Asked Questions — Alternating Current

What is the RMS value of a sinusoidal AC?

For a sinusoidal current, I_rms = I₀/√2. For voltage, V_rms = V₀/√2.

What is the condition for resonance in a series LCR circuit?

Resonance occurs when X_L = X_C. Then Z = R, current is maximum for a fixed source voltage and the power factor is unity.

What is the difference between inductive and capacitive reactance?

Inductive reactance is X_L = ωL and increases with frequency. Capacitive reactance is X_C = 1/(ωC) and decreases with frequency.

What is power factor in an AC circuit?

Power factor is cosφ, where φ is the phase difference between voltage and current. For a series LCR circuit, cosφ = R/Z.

Why is a transformer used with AC rather than steady DC?

Transformer action requires changing magnetic flux. A steady DC supply does not maintain the required changing flux after the initial transient.

Which Chapter 7 topics should a student practise?

Practise RMS and average values, pure R/L/C circuits, reactance, series LCR phasors and impedance, resonance, AC power and power factor, wattless current, AC generator and transformer.

13. Chapter 6 → Chapter 7 Connection

Chapter 6 established Faraday's law and electromagnetic induction. Chapter 7 applies that foundation to the AC generator and connects changing magnetic flux to the operation of a transformer. Read Chapter 6 — Electromagnetic Induction Notes.

14. Final Self-Check

✓ I can distinguish peak, average and RMS values.

✓ I know the phase relation in pure R, L and C circuits.

✓ I can calculate X_L, X_C, Z and power factor.

✓ I can explain series resonance and calculate f₀.

✓ I can solve AC-power and wattless-current questions.

✓ I can explain an AC generator and obtain E₀.

✓ I can solve transformer turns/current/voltage questions.

✓ I can handle multi-step competency-style questions without mixing peak and RMS values.

Research note: Recent board-question compilations repeatedly feature RMS/phase relations, series LCR impedance and resonance, power factor/wattless current, AC generator and transformer questions. These patterns informed the coverage here, but they should be used for practice planning rather than treated as predictions.