Samacheer Kalvi 12th Physics Chapter 4 Exercise Solutions

Chapter 4 — Exercise Solutions

This chapter has both conceptual laws and AC numerical problems. Keep RMS and peak values separate.

How to Use This Page

• Read the Key Concepts table first to refresh definitions before attempting questions.
• Work through MCQs and fill-in-the-blanks to test recall, then move to short and detailed answers.
• Use the Formula Recap section as a quick reference while solving numericals.
• Check the Common Mistakes to Avoid section before exams to catch frequent errors.
• Tick off items in the Exam Checklist once you are confident about each point.

Formula Recap

Key Concepts (Quick Recap)

AC Circuit Pattern

1. Identify R, L, C values. 2. Calculate XL and XC. 3. Find impedance if needed. 4. Use Ohm law for AC: Vrms = Irms Z. 5. Check phase relation.

Short Answer Points

• Lenz law follows conservation of energy.
• Eddy currents are induced currents in bulk conductors.
• Transformer works on mutual induction.
• AC can be stepped up or stepped down using transformer.

I. Choose the Best Answer (MCQs)

1. The direction of induced current is given by: (a) Fleming's left-hand rule   (b) Fleming's right-hand rule   (c) Ampere's rule   (d) Biot-Savart law

2. The SI unit of magnetic flux is: (a) Henry   (b) Weber   (c) Tesla   (d) Volt

3. The coefficient of self-induction is measured in: (a) Ohm   (b) Farad   (c) Henry   (d) Weber

4. In a pure inductive AC circuit, the current: (a) Leads voltage by 90 degrees   (b) Lags voltage by 90 degrees   (c) Is in phase with voltage   (d) Lags by 45 degrees

5. At resonance in an LCR circuit, the impedance is equal to: (a) XL   (b) XC   (c) R   (d) Z

6. A step-up transformer increases: (a) Current   (b) Voltage   (c) Power   (d) Frequency

7. The RMS value of an AC with peak value I0 is: (a) I0   (b) I0 / 2   (c) I0 / sqrt(2)   (d) 2 I0

8. Eddy currents are reduced by using: (a) Thick conductors   (b) Laminated core   (c) Air core   (d) Increasing frequency

9. The power factor of a pure resistive circuit is: (a) 0   (b) 0.5   (c) 1   (d) Infinity

10. The phenomenon of production of EMF in a coil due to change in current in the same coil is: (a) Mutual induction   (b) Electromagnetic induction   (c) Self-induction   (d) Eddy current

II. Fill in the Blanks

1. The unit of self-inductance is ______. Answer: henry

2. According to Lenz's law, the induced current always ______ the change that causes it. Answer: opposes

3. The impedance of a pure capacitive circuit is called ______. Answer: capacitive reactance

4. The average power in a pure inductive circuit is ______. Answer: zero

5. In a step-up transformer, the number of turns in the secondary coil is ______ than in the primary coil. Answer: more (greater)

6. The relation between peak value and RMS value of voltage is Vrms = ______. Answer: V0 / sqrt(2)

7. At resonance, the current in an LCR circuit is ______. Answer: maximum

8. The core of a transformer is laminated to reduce ______ losses. Answer: eddy current

III. True or False (with Corrections)

1. Statement: Lenz's law is a consequence of the law of conservation of energy. Answer: True

2. Statement: In a pure capacitor circuit, current lags the voltage by 90 degrees. Answer: False. In a pure capacitor circuit, current leads the voltage by 90 degrees.

3. Statement: The RMS value of AC is equal to its peak value. Answer: False. The RMS value of AC is I0 / sqrt(2), which is approximately 0.707 times the peak value.

4. Statement: A transformer can step up DC voltage. Answer: False. A transformer works only on AC (changing current) because mutual induction requires a time-varying current.

5. Statement: Eddy currents are always undesirable. Answer: False. Eddy currents are used in induction furnaces, electromagnetic braking, and speedometers.

6. Statement: At resonance, the impedance of an LCR circuit is maximum. Answer: False. At resonance, the impedance is minimum and equal to R.

7. Statement: The self-inductance of a coil depends on the current flowing through it. Answer: False. Self-inductance depends on the geometry of the coil (number of turns, area, length) and the core material, not on the current.

IV. Match the Following

V. Answer Briefly (2-mark)

1. State Faraday's first law of electromagnetic induction. Whenever the magnetic flux linked with a closed circuit changes, an EMF is induced in the circuit. The induced EMF lasts only as long as the change in flux continues. This is the basis of all electromagnetic induction phenomena.

2. What is the significance of Lenz's law? Lenz's law gives the direction of the induced EMF and current. It states that the induced current flows in such a direction that it opposes the change in magnetic flux that produced it. This law is a consequence of the law of conservation of energy.

3. Define self-inductance of a coil. Self-inductance of a coil is defined as the property by virtue of which the coil opposes any change in the current flowing through it. It is numerically equal to the magnetic flux linkage per unit current. Its SI unit is henry (H).

4. Why is the core of a transformer laminated? The core of a transformer is laminated to reduce eddy current losses. Eddy currents are circulating currents induced in the bulk iron core by the changing magnetic flux. Lamination increases the resistance of the path of eddy currents, thereby reducing their magnitude and the resulting energy loss as heat.

5. What is the power factor of an LCR circuit at resonance? At resonance, XL = XC, so the impedance Z = R and the phase angle phi = 0. Therefore, the power factor cos phi = cos 0 = 1. This means the entire power supplied is consumed as true power, and there is no wattless component of current.

Worked Examples

Example 1 — Induced EMF

A coil of 200 turns has its flux change from 0.01 Wb to 0.05 Wb in 0.2 s. Find the induced EMF.

Example 2 — RMS value

The peak value of an AC current is 10 A. Find its RMS value.

Example 3 — Transformer

A step-down transformer has 1000 primary turns and 100 secondary turns. If the primary voltage is 230 V, find the secondary voltage.

VI. Answer in Detail (5-mark)

1. State and explain Faraday's laws of electromagnetic induction. Faraday's first law states that whenever the magnetic flux linked with a closed circuit changes, an EMF is induced in the circuit and it lasts only as long as the change in flux continues. Faraday's second law states that the magnitude of the induced EMF is equal to the rate of change of magnetic flux linkage. Mathematically, emf = -N dPhi/dt, where N is the number of turns and dPhi/dt is the rate of change of flux. The negative sign indicates the direction of the induced EMF as given by Lenz's law. This law can be demonstrated by moving a magnet towards or away from a coil, or by changing the current in a nearby coil. The induced EMF is proportional to the speed of the magnet; faster movement produces a larger EMF. Faraday's laws form the foundation for generators, transformers, and many other electrical devices.

2. Explain Lenz's law and show that it is in accordance with the law of conservation of energy. Lenz's law states that the direction of the induced current is such that it always opposes the change in magnetic flux that produced it. When the north pole of a magnet approaches a coil, the induced current flows in a direction that creates a north pole on the face nearest the magnet, repelling it. When the magnet is withdrawn, the induced current reverses, creating a south pole that attracts the magnet. In both cases, mechanical work must be done to move the magnet against this opposing force. This mechanical work is converted into electrical energy in the circuit. If the induced current aided the change instead of opposing it, a small displacement would produce current that further accelerates the magnet, creating energy from nothing, which violates conservation of energy. Thus Lenz's law ensures energy is conserved in the process of electromagnetic induction.

3. Derive an expression for the current in an LCR series circuit connected to an AC source and discuss resonance. Consider an LCR series circuit with resistance R, inductance L, and capacitance C connected to an AC source V = V0 sin(omega t). The voltage across the resistor VR is in phase with current, the voltage across the inductor VL leads the current by 90 degrees, and the voltage across the capacitor VC lags the current by 90 degrees. By phasor diagram, the total voltage V = sqrt(VR^2 + (VL - VC)^2). The impedance Z = sqrt(R^2 + (XL - XC)^2), where XL = omega L and XC = 1/(omega C). The current I = V / Z, and the phase angle is given by tan phi = (XL - XC) / R. At resonance, XL = XC, so omega L = 1/(omega C), giving the resonant frequency f = 1 / (2 pi sqrt(LC)). At resonance, Z = R (minimum), current is maximum, and the circuit behaves as purely resistive. The power factor becomes unity, meaning all supplied power is consumed.

4. Explain the principle, construction, and working of a transformer. A transformer works on the principle of mutual induction. When an alternating current flows through the primary coil, it produces a changing magnetic flux that links with the secondary coil and induces an EMF in it. A transformer consists of a laminated core made of soft iron, a primary coil with Np turns, and a secondary coil with Ns turns, both wound on the core. The primary coil is connected to the AC input and the secondary to the load. By Faraday's law, the EMF induced in the secondary is Es = -Ns dPhi/dt, and the EMF in the primary is Ep = -Np dPhi/dt. Since the same flux links both coils, Es/Ep = Ns/Np. For a step-up transformer, Ns > Np and voltage increases; for a step-down transformer, Ns < Np and voltage decreases. The efficiency of an ideal transformer is 100%, but real transformers have losses due to copper loss (I^2 R), eddy current loss, hysteresis loss, and flux leakage.

Common Mistakes to Avoid

• ❌ Using peak values where RMS values are required → ✅ Always convert: Irms = I0 / sqrt(2), Vrms = V0 / sqrt(2).
• ❌ Ignoring the angular frequency omega when calculating reactance → ✅ Use XL = omega L = 2 pi f L and XC = 1 / (omega C) = 1 / (2 pi f C).
• ❌ Swapping Ns and Np in the transformer formula → ✅ Remember: Vs/Vp = Ns/Np; secondary on top, primary on bottom.
• ❌ Saying "Lenz's law gives the magnitude of induced EMF" → ✅ Lenz's law gives the direction; Faraday's law gives the magnitude.
• ❌ Treating impedance as a simple sum of R, XL, and XC → ✅ Impedance is Z = sqrt(R^2 + (XL - XC)^2); it is a phasor sum, not an arithmetic sum.
• ❌ Assuming transformer works on DC → ✅ Transformer requires changing flux (AC); a DC input produces no secondary EMF after the initial transient.

Exam Checklist

• Can you state Faraday's two laws and write the formula emf = -N dPhi/dt?
• Can you explain Lenz's law and relate it to conservation of energy?
• Can you derive motional EMF using e = Blv and identify the direction?
• Do you know the difference between self-induction and mutual induction?
• Can you calculate RMS values from peak values and vice versa?
• Can you compute inductive reactance (XL), capacitive reactance (XC), and impedance (Z)?
• Can you draw the phasor diagram for an LCR series circuit?
• Can you derive the resonant frequency formula f = 1 / (2 pi sqrt(LC))?
• Can you explain transformer principle and write the turns ratio formula?
• Can you list and explain the energy losses in a transformer?

Additional Numerical Practice

Example 4 — Motional EMF

A conducting rod of length 0.5 m moves at 4 m/s perpendicular to a 0.3 T magnetic field. Find the induced EMF.

Example 5 — Self-inductance

A coil has a self-inductance of 2 H. If the current through it changes from 5 A to 2 A in 0.01 s, find the induced EMF.

Example 6 — LCR impedance

An LCR series circuit has R = 30 Ω, L = 0.1 H, C = 100 μF connected to a 50 Hz AC supply. Find the impedance.

Example 7 — Power in AC circuit

An AC circuit has Vrms = 220 V, Irms = 5 A and power factor 0.8. Find the power consumed.