This chapter answers the question the previous two chapters set up without quite asking — if a current creates a magnetic field, can a changing magnetic field create a current in return? The answer is yes, and it is the single physical principle behind every generator and transformer in use today.
Faraday's law quantifies how much EMF a changing magnetic flux induces; Lenz's law tells you which direction that induced current flows, and it does so through energy conservation — the induced current always opposes the very change that created it, since anything else would create energy from nothing. Self and mutual inductance then describe how a changing current in one coil affects itself or a neighbouring coil, setting up the language needed for AC circuits, where current and voltage no longer stay in step with one another the way they do in a simple DC circuit.
Core EMI and AC formulae
| Quantity | Formula |
|---|---|
| Faraday's law of induction | ε = −dΦ/dt |
| Motional EMF | ε = Bvl |
| Self inductance (EMF) | ε = −L(dI/dt) |
| Mutual inductance (EMF) | ε₂ = −M(dI₁/dt) |
| Inductive reactance | XL = ωL |
| Capacitive reactance | XC = 1/ωC |
| Impedance of a series LCR circuit | Z = √(R² + (XL−XC)²) |
| Resonant frequency of an LCR circuit | ω₀ = 1/√(LC) |
| Transformer relation | Vs/Vp = Ns/Np |
Topics covered
- Magnetic flux — the quantity whose rate of change drives every induction phenomenon in this chapter
- Faraday's law of electromagnetic induction — and how induced EMF relates directly to the rate of flux change
- Lenz's law — the direction rule grounded in energy conservation
- Motional EMF — induction produced specifically by a conductor moving through a magnetic field
- Self inductance and mutual inductance — how a changing current induces an opposing EMF in itself or a neighbouring circuit
- Alternating current basics — peak, RMS and average values, and why RMS is the value used in practical ratings
- AC through a resistor, inductor and capacitor — phase relationships between current and voltage in each individual case
- Series LCR circuit — impedance, phase angle, and resonance
- Transformer — step-up and step-down operation, and why AC (not DC) makes transformers possible at all
Why this chapter matters
In NEET and JEE, Lenz's law conceptual questions and LCR circuit impedance-and-resonance numericals are consistently among the highest-frequency topics in this section, since they combine cleanly with the previous two chapters' concepts. Transformer efficiency and turns-ratio numericals are a reliable, quick-scoring question type.
For Class 12 boards, expect a derivation of motional EMF or self-inductance and a numerical on series LCR circuit impedance or resonant frequency.
Mistakes students make in this chapter
- Forgetting the negative sign in Faraday's and Lenz's law is not optional. It specifically encodes the direction of opposition described by Lenz's law — dropping it in a derivation loses the physical meaning, even if the magnitude comes out correct.
- Believing RMS value and peak value are the same thing. For a sinusoidal AC, RMS value equals peak value divided by √2, and mixing the two up gives answers off by that factor in power calculations.
- Assuming current and voltage are always in phase in an AC circuit. They're in phase only across a pure resistor; across an inductor voltage leads current by 90°, and across a capacitor current leads voltage by 90° — the LCR combination sits somewhere between these extremes.
- Believing a transformer works with DC input. A transformer specifically requires a continuously changing flux to induce EMF in the secondary coil — a steady DC current produces no changing flux and therefore induces nothing.
- Confusing resonance in an LCR circuit with maximum impedance. At resonance, impedance is actually at its minimum (equal to just R, since XL and XC cancel), which is exactly why current is maximum at resonance.
Worked example: a series LCR circuit that is not quite at resonance
- Find both reactances at the supply frequency. With ω = 2πf = 2π(50) ≈ 314 rad/s:X_L = ωL = 314 × 0.5 ≈ 157 ΩX_C = 1/ωC = 1/(314 × 25×10⁻⁶) ≈ 127 Ω
- Combine them into the impedance. The reactances oppose each other, so they subtract before the Pythagorean step:Z = √[R² + (X_L − X_C)²] = √[900 + (30)²] ≈ 42.3 Ω
- Find the current from the rms voltage:I = V/Z = 200 / 42.3 ≈ 4.7 A
- Find the power factor. Only the resistive part of the impedance dissipates energy:cos φ = R/Z = 30 / 42.3 ≈ 0.71
- Find the average power. Using P = VI cos φ, or equivalently I²R, which avoids the rounding in cos φ:P = I²R = (4.7)² × 30 ≈ 670 W
What the notes contain
The PDF derives motional EMF and self/mutual inductance from Faraday's law, works through phase relationships for R, L and C individually before combining them into the full LCR circuit analysis, and includes a transformer efficiency numerical alongside a resonance-condition derivation.
How to use this: build the concept from these notes first, then do one quick NCERT pass before the exam for exact wording and diagram labels, and spend whatever time is left on previous year questions.
Questions
Why does Lenz's law say the induced current opposes the change that caused it?
If the induced current instead reinforced the change, the resulting flux increase would induce even more current, which would increase the flux further, in an unstoppable runaway loop that would violate energy conservation. The PDF explains this reasoning directly.
Why is RMS value used for AC ratings instead of peak value?
RMS value is the equivalent steady DC value that would deliver the same average power, which is why appliances are rated using it rather than the peak value, which is always higher by a factor of √2.
Why doesn't a transformer work with a DC supply?
A transformer relies on a continuously changing magnetic flux linking the primary and secondary coils to induce EMF. A steady DC current produces a constant flux with no rate of change, and Faraday's law gives zero induced EMF when dΦ/dt is zero.
Does this cover the phase relationship in R, L and C circuits separately?
Yes, each case (pure resistor, pure inductor, pure capacitor) is worked through individually with phasor diagrams before combining them into the full series LCR analysis.
All other chapters
Every chapter of Class 11 and Class 12 Physics, Chemistry and Biology — each with its own notes and PDF.