Electromagnetic Induction and Alternating Current – Class 12 Physics Guide

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📌 Introduction

Electromagnetic Induction (EMI) and Alternating Current (AC) are two of the most crucial topics in Class 12 Physics. Understanding these principles is essential for excelling in board exams and competitive tests like WBJEE, JEE, and NEET. This guide covers Faraday’s laws, Lenz’s law, self and mutual induction, AC circuits, transformers, and resonance, along with 30+ exam-relevant MCQs.

Scroll down for MCQs  ↓  ↓  ↓ 

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⚡ Electromagnetic Induction (EMI)

🔹 Faraday’s Laws of Electromagnetic Induction

1. First Law: Whenever there is a change in magnetic flux linked with a coil, an induced electromotive force (EMF) is generated.
2. Second Law: The magnitude of induced EMF is proportional to the rate of change of magnetic flux: $$E = -\frac{d\Phi}{dt}$$The negative sign follows Lenz’s Law, which states that the induced current opposes the cause that produces it.

🔹 Self and Mutual Induction

• Self-Induction (L): When the current in a coil changes, it induces an EMF in the same coil. $$E=-L\frac{dI}{d\mathrm{t}}$$
• Mutual Induction (M): When the current in one coil changes, it induces an EMF in a nearby coil: $$E=-M\frac{dI}{d\mathrm{t}}$$

🔹 Applications of EMI

✅ Transformers
✅ Induction motors
✅ Generators
✅ Eddy current brakes

Scroll down for MCQs  ↓  ↓  ↓ 

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🔄 Alternating Current (AC) – Concepts & Equations

🔹 AC vs. DC

Feature	Direct Current (DC)	Alternating Current (AC)
Flow Direction	Unidirectional	Changes periodically
Source	Battery, Solar Cell	Alternators, Power Plants
Transmission	High loss	Low loss (HVAC used)

🔹 AC Voltage and Current Equations

1. Instantaneous Voltage: $$V=V_0\sin (\omega t)$$
2. Root Mean Square (RMS) Value: $$I_{rms}=\frac{I_0}{\sqrt{2}},V_{rms}=\frac{V_0}{\sqrt{\mathrm{2}}}$$
3. Power in AC Circuits: $$P = VI \cos \phi$$

🔹 Reactance and Impedance in AC Circuits

• Inductive Reactance: $X_L = \omega L$
• Capacitive Reactance: $X_C = \frac{1}{\omega C}$
• Total Impedance: $$Z=\sqrt{R^2+(X_L-X_C{)}^2}$$

Scroll down for MCQs  ↓  ↓  ↓ 

🔹 Resonance in AC Circuits

• Resonance occurs when: $$X_L=X_C\Rightarrow {\omega }_{0}L=\frac{1}{{\omega }_0\mathrm{C}}$$
• At resonance, the circuit allows maximum current flow.

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🔍 30+ Most Important MCQs for WB Higher Secondary Exam

🟢 Electromagnetic Induction (EMI) MCQs

1. The SI unit of magnetic flux is:
   a) Weber ✔
   b) Tesla
   c) Henry
   d) Gauss

2. Lenz’s law is based on:
   a) Law of inertia
   b) Law of conservation of energy ✔
   c) Newton’s law
   d) Kirchhoff’s Law

3. Mutual inductance depends on:
   a) Distance between coils ✔
   b) Wire resistance
   c) Battery voltage
   d) Air pressure

4. The SI unit of inductance is:
   a) Farad
   b) Henry ✔
   c) Tesla
   d) Coulomb

5. The device that works on mutual induction is:
   a) Generator
   b) Transformer ✔
   c) Battery
   d) Voltmeter

6. A moving conductor in a magnetic field experiences:
   a) Mechanical force
   b) Induced EMF ✔
   c) Heat
   d) No effect

🔵 Alternating Current (AC) MCQs

7. The average value of AC over a complete cycle is:
   a) Zero ✔
   b) Maximum
   c) Half of peak value
   d) Infinity

8. The phase difference between voltage and current in a pure inductive circuit is:
   a) 0°
   b) 90° ✔
   c) 180°
   d) 270°

9. A capacitor in an AC circuit causes current to:
   a) Lead voltage ✔
   b) Lag voltage
   c) Be in phase
   d) Be zero

10. In a purely resistive circuit, power factor is:
    a) 0
    b) 1 ✔
    c) -1
    d) 0.5

11. The efficiency of an ideal transformer is:
    a) 100% ✔
    b) 75%
    c) 50%
    d) 25%

12. A step-up transformer increases:
    a) Power
    b) Current
    c) Voltage ✔
    d) Resistance

13. What happens in a series LCR circuit at resonance?
    a) $X_L = X_C$ ✔
    b) $X_L > X_C$
    c) $X_C > X_L$
    d) $R = X_C$

14. The power factor of a purely inductive circuit is:
    a) 1
    b) 0 ✔
    c) -1
    d) 0.5

15. Transformers work on the principle of:
    a) Ohm’s Law
    b) Faraday’s Law ✔
    c) Kirchhoff’s Law
    d) Lenz’s Law

🟢 Electromagnetic Induction (EMI) – MCQs

Basic Concepts of Electromagnetic Induction

16. The phenomenon of electromagnetic induction was discovered by:
    a) Newton
    b) Michael Faraday ✔
    c) Coulomb
    d) Maxwell

17. The device that converts mechanical energy to electrical energy using EMI is:
    a) Motor
    b) Generator ✔
    c) Transformer
    d) Capacitor

18. Lenz’s law ensures that the induced current:
    a) Opposes the cause producing it ✔
    b) Increases the magnetic field
    c) Produces high voltage
    d) Remains constant

19. A current-carrying coil produces:
    a) Heat
    b) Magnetic field ✔
    c) Capacitance
    d) Electric charge

20. Eddy currents are used in:
    a) Electric motors
    b) Magnetic braking systems ✔
    c) AC circuits
    d) Superconductors

Self-Induction and Mutual Induction

21. The property of a coil that opposes the change in its own current is called:
    a) Resistance
    b) Self-induction ✔
    c) Capacitance
    d) Impedance

22. Mutual induction occurs when:
    a) Two coils are placed close to each other ✔
    b) Current changes in a single coil
    c) Voltage remains constant
    d) Magnetic field is absent

23. Inductance is measured in:
    a) Weber
    b) Henry ✔
    c) Tesla
    d) Farad

24. The formula for energy stored in an inductor is:

$$a) W = \frac{1}{2} L I^2 \quad \textbf{✔}$$

         b) $W = \frac{1}{2} C V^2$
         c) $W = qV$
         d) $W=I{R}^2$

25. A coil with high self-inductance:
    a) Increases current
    b) Opposes current change ✔
    c) Reduces resistance
    d) Stores electric charge

26. Mutual induction is used in:
    a) Generators
    b) Motors
    c) Transformers ✔
    d) Resistors

27. In a step-up transformer, mutual inductance:
    a) Decreases
    b) Increases ✔
    c) Remains constant
    d) Becomes zero

Faraday’s Law and Applications

28. According to Faraday’s law, the magnitude of induced EMF is:
    a) Proportional to magnetic flux
    b) Proportional to the rate of change of flux ✔
    c) Proportional to resistance
    d) Constant

29. If the number of turns in a coil is doubled, its induced EMF:
    a) Doubles ✔
    b) Becomes half
    c) Remains unchanged
    d) Becomes zero

30. The working principle of an electric generator is based on:
    a) Lenz’s law
    b) Faraday’s law ✔
    c) Coulomb’s law
    d) Ohm’s law

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🔵 Alternating Current (AC) – MCQs

AC Basics and RMS Values

31. AC current reverses its direction:
    a) Once per second
    b) Periodically ✔
    c) Only when resistance is present
    d) Never

32. The SI unit of frequency is:
    a) Hertz ✔
    b) Weber
    c) Henry
    d) Tesla

33. The average value of AC over a complete cycle is:
    a) Maximum value
    b) Zero ✔
    c) Half of the peak value
    d) Infinite

34. The RMS value of AC is:
    a) $I_0$
    b) $\frac{I_0}{\sqrt{2}}$ ✔
    c) $2I_0$
    d) $I_0^2$

AC Circuits & Impedance

35. In a purely inductive circuit, the phase difference between voltage and current is:
    a) 0°
    b) 90° ✔
    c) 180°
    d) 270°

36. In a purely capacitive circuit, the phase difference between voltage and current is:
    a) 0°
    b) 90° ✔
    c) 180°
    d) 270°

37. The impedance in an LCR circuit is given by:

$$Z = \sqrt{R^2 + (X_L - X_C)^2}$$

a) True ✔

b) False

38. If frequency increases, inductive reactance:
    a) Increases ✔
    b) Decreases
    c) Remains the same
    d) Becomes zero

39. The power factor of an ideal inductor is:
    a) 1
    b) 0 ✔
    c) -1
    d) Infinity

Transformers & Resonance

40. Transformers work on the principle of:
    a) Mutual induction ✔
    b) Self-induction
    c) Kirchhoff’s Law
    d) Ohm’s Law

41. In an ideal transformer, the efficiency is:
    a) 100% ✔
    b) 80%
    c) 60%
    d) 0%

42. A step-up transformer increases:
    a) Power
    b) Voltage ✔
    c) Current
    d) Resistance

43. If primary turns > secondary turns, the transformer is:
    a) Step-up
    b) Step-down ✔
    c) Ideal
    d) Open circuit

44. The resonant frequency of an LCR circuit is:

$$\omega_0 = \frac{1}{\sqrt{LC}}$$

a) True ✔

b) False

45. The condition for maximum power transfer in an AC circuit is:
    a) $R = X_L$
    b) $X_L = X_C$✔
    c) $R = X_C$
    d) $X_L+X_C=\mathrm{0<span\; class="base"></span>}$

Here are 25 additional WBJEE & NEET-oriented MCQs based on Electromagnetic Induction (EMI) and Alternating Current (AC). These questions are designed to test your conceptual understanding and problem-solving skills in Class 12 Physics.

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🔹 WBJEE & NEET-Oriented MCQs on Electromagnetic Induction & AC

📌 Electromagnetic Induction – Advanced MCQs

Faraday’s Law & Lenz’s Law

1. A rectangular loop is moving with velocity $v$ towards a long straight current-carrying wire. The induced EMF in the loop is:
a) Proportional to $v$ ✔
b) Inversely proportional to $v$
c) Zero
d) Depends on resistance

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2. Which of the following statements is true for Lenz’s law?
a) It follows the conservation of momentum
b) It follows the conservation of charge
c) It follows the conservation of energy ✔
d) It follows the conservation of mass

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3. The magnitude of the induced EMF does not depend on:
a) Rate of change of magnetic flux
b) Resistance of the coil ✔
c) Number of turns in the coil
d) Strength of the magnetic field

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4. A metal rod is moved in a uniform magnetic field with velocity $v$. The induced EMF across the ends of the rod is given by:
a) $Bvl$ ✔
b) $\frac{Bvl}{2}$
c) $B^2vl$
d) $\frac{B}{vl}$

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Self & Mutual Induction

5. The self-inductance of a solenoid is given by:

$$L = \frac{\mu_0 N^2 A}{l}$$

a) True ✔
b) False

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6. If the self-inductance of a coil is 1 Henry, what does it mean?
a) A 1V EMF is induced when the current changes by 1A in 1s ✔
b) A 1A EMF is induced when current changes by 1V
c) The coil does not resist the change in current
d) The coil has zero resistance

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7. If the current in a coil changes from 5A to 10A in 0.2s, and the self-inductance of the coil is 2H, what is the induced EMF?
a) 25V
b) 50V ✔
c) 100V
d) 10V

🔹 Solution:

$$E = L \frac{dI}{dt} = 2 \times \frac{(10 - 5)}{0.2} = 50V$$

8. If the number of turns in a coil is tripled, its self-inductance:
a) Remains the same
b) Doubles
c) Triples
d) Becomes 9 times ✔

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📌 Alternating Current – WBJEE & NEET MCQs

AC Fundamentals & Phasors

9. The average power dissipated in an AC circuit is given by:

$$P = V_{rms} I_{rms} \cos \phi$$

a) True ✔
b) False

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10. The peak value of AC voltage is 325V. The RMS value is:
a) 230V ✔
b) 162.5V
c) 200V
d) 100V

🔹 Solution:

$$V_{rms}=\frac{V_0}{\sqrt{2}}=\frac{325}{\sqrt{2}}=230V$$

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AC Circuits & Resonance

11. In a purely resistive AC circuit, the power factor is:
a) 0
b) 1 ✔
c) -1

d) Infinity12. The power factor in a purely capacitive circuit is:

a) 1
b) 0 ✔
c) -1
d) 0.5

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AC Circuits & Resonance

13. The impedance of an LCR circuit is given by:

$$Z = \sqrt{R^2 + (X_L - X_C)^2}$$a) True ✔

b) False

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14. In a series LCR circuit at resonance, the impedance is:
a) Maximum
b) Minimum ✔
c) Infinity
d) Zero

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15. At resonance, the current in a series LCR circuit is:
a) Maximum ✔
b) Minimum
c) Zero
d) Constant

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16. The resonant frequency of an LCR circuit is given by:

$$f_0=\frac{1}{2\pi \sqrt{L\mathrm{C}}}$$

a) True ✔
b) False

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17. The reactance of an inductor in an AC circuit is given by:

$$X_L=\omega L$$

a) True ✔
b) False

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18. In an ideal transformer, the efficiency is:
a) 100% ✔
b) 90%
c) 80%
d) 50%

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19. In a step-up transformer, which quantity increases?
a) Voltage ✔
b) Current
c) Power
d) Resistance

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20. A transformer works on the principle of:
a) Faraday’s Law ✔
b) Lenz’s Law
c) Ohm’s Law
d) Kirchhoff’s Law

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AC Power & Applications

21. The power dissipated in an AC circuit is:

$$P = VI \cos \phi$$

a) True ✔
b) False

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22. In a purely resistive AC circuit, the power factor is:
a) 0
b) 1 ✔
c) -1
d) 0.5

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23. If frequency increases, inductive reactance:
a) Increases ✔
b) Decreases
c) Remains the same
d) Becomes zero

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24. The power loss in a transformer is mainly due to:
a) Resistance in the windings
b) Eddy currents
c) Hysteresis loss
d) All of the above ✔

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25. The advantage of AC over DC in power transmission is:
a) AC can be easily stepped up/down using transformers ✔
b) AC is cheaper
c) AC needs no resistance
d) AC has higher frequency

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📝 Conclusion

Understanding Electromagnetic Induction and Alternating Current is essential for WB Higher Secondary students. Mastering Faraday’s Laws, Lenz’s Law, AC circuits, and transformers will help you score high in exams. Regular practice of MCQs and numericals will strengthen your concepts.

📚 For more exam-focused physics notes, visit MightyKnowledge. 🚀