PhysicsPHY 09
EMI & Alternating Currents
Faraday's law, inductance, LCR resonance, power factor, transformer
NCERT XII Ch.6–7
NCERT Ref
Concept Core
Essential theory — everything NCERT tests on EMI & Alternating Currents
FARADAY'S LAWS OF EMI
1st Law: Changing magnetic flux induces EMF. 2nd Law: EMF = −dΦ/dt (magnitude = rate of flux change). Negative sign = Lenz's law (opposes change).
Motional EMF: ε = Bvl. EMF in rotating coil: ε = NBAω sin(ωt) → εmax = NBAω.
INDUCTANCE
Self-inductance: L = NΦ/I. EMF = −L(dI/dt). Solenoid: L = μ₀n²Al.
Mutual inductance: M = NΦ₂/I₁. EMF₂ = −M(dI₁/dt). Transformer principle: M between coils.
Energy stored in inductor: U = ½LI².
AC CIRCUITS
V = V₀ sinωt, I = I₀ sin(ωt − φ). RMS values: Vrms = V₀/√2. Irms = I₀/√2.
Reactances: XL = ωL. XC = 1/(ωC). Impedance Z = √(R² + (XL−XC)²).
Resonance: XL = XC → ω₀ = 1/√(LC). Z = R (minimum). I = maximum.
POWER & TRANSFORMER
Power: P = VrmsIrms cosφ. cosφ = power factor. Pure L or C: cosφ = 0 (wattless circuit). Pure R: cosφ = 1.
Transformer: Vs/Vp = Ns/Np = Ip/Is. Ideal transformer: 100% efficiency. Step-up: Ns>Np. Step-down: Ns<Np.
Fact & Formula Vault
High-yield facts, numbers, and formulas
EMI Formulae
EMF = −NdΦ/dt
Motional EMF = Bvl
ε_max = NBAω
L = μ₀n²Al (solenoid)
AC Values
V_rms = V₀/√2
I_rms = I₀/√2
XL = ωL (inductive reactance)
XC = 1/ωC (capacitive reactance)
Resonance & Power
ω₀ = 1/√LC (resonance)
At resonance: Z=R (min), I=max
P = V_rms·I_rms·cosφ
Transformer: Vs/Vp = Ns/Np
Worked Examples
NEET-style questions solved step-by-step
EASYIn an AC circuit with pure inductor, the phase difference between V and I is:▾
In an AC circuit with pure inductor, the phase difference between V and I is:
V leads I by 90° (π/2). In pure inductor: I lags V. Power factor cosφ = cos90° = 0. No power consumed.
MEDIUMAn LCR circuit resonates at 50 Hz. At resonance, what happens to impedance?▾
An LCR circuit resonates at 50 Hz. At resonance, what happens to impedance?
At resonance: X_L = X_C → Z = √(R² + 0) = R (minimum). Current is maximum. Power factor = 1.
HARDA step-up transformer has 100 primary turns and 1000 secondary turns. If primary voltage = 220V, secondary voltage and current ratio?▾
A step-up transformer has 100 primary turns and 1000 secondary turns. If primary voltage = 220V, secondary voltage and current ratio?
Vs/Vp = Ns/Np → Vs = 220 × 1000/100 = 2200V. Current ratio: Is/Ip = Np/Ns = 100/1000 = 1:10 (secondary current lower).
Mistake DNA
Common NEET traps for this chapter
⚠ Power factor in pure L or C
Pure inductor or capacitor has power factor = 0 (cosφ = 0). They consume no power — just store and release energy.
✓ Fix: L and C: wattless. R: max power (cosφ=1).
⚠ Transformer current direction
Step-up transformer: voltage increases, current DECREASES. V×I = constant (conservation). V_s > V_p → I_s < I_p.
✓ Fix: Step-up: V↑, I↓. Step-down: V↓, I↑. Power conserved.
⚠ Resonance condition
At resonance: X_L = X_C, Z = R (min), I = max, cosφ = 1. NOT that Z = 0.
✓ Fix: Z_min = R at resonance (not zero, unless R=0)
Chapter Intelligence
Exam data and last-minute strategy
NEET Frequency
2–3 Q/year. Faraday's law applications, resonance condition, transformer ratio, power factor, rms values are standard.
High-Yield
ε = −NdΦ/dt. V_rms = V₀/√2. Resonance: ω₀ = 1/√LC, Z=R. Power factor = cosφ. Transformer: Vs/Vp = Ns/Np = Ip/Is.
Strategy
Transformer ratio problems: practice Vs/Vp = Ns/Np. LCR resonance: identify condition and what's maximum/minimum. Rms = peak/√2.
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