Electromagnetic Induction
Complete Formula Sheet & Shortcut Bible · BITSAT 2026
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Faraday's Law & Magnetic Flux
Magnetic Flux (Φ)
Φ = B ⋅ A
Φ = BA cos(θ)
Φ = BA cos(θ)
θ is the angle between the magnetic field B and the area vector A.
Faraday's Law (EMF)
ε = -N (dΦ/dt)
N = number of turns. The negative sign indicates Lenz's Law.
Motional EMF
ε = Bℓv
For a conductor of length ℓ moving with velocity v perpendicular to field B.
Lenz's Law
Concept Card
The induced current flows in a direction that opposes the change in magnetic flux that produced it.
Eddy Currents
Concept Card
Induced circulating currents in a bulk conductor when the magnetic flux changes. Cause energy loss.
Self & Mutual Inductance
Self-Inductance (L)
Φ = LI
L = μ₀n²Aℓ
L = μ₀n²Aℓ
The second formula is for a long solenoid (n=turns/length).
EMF in an Inductor
ε = -L (dI/dt)
This is the 'back EMF' that opposes the change in current.
Mutual Inductance (M)
Φ₂ = MI₁
ε₂ = -M (dI₁/dt)
ε₂ = -M (dI₁/dt)
Flux in coil 2 due to current in coil 1. M depends on geometry and orientation.
Energy in Inductor
U = ½ LI²
Energy stored in the magnetic field of the inductor.
AC Fundamentals: Peak & RMS
Instantaneous Voltage
V = V₀ sin(ωt)
V₀ is the peak or maximum voltage.
Instantaneous Current
I = I₀ sin(ωt + φ)
I₀ is peak current, φ is phase difference.
RMS Voltage
Vᵣₘₛ = V₀ / √2
Effective value, ~0.707 V₀. Standard household voltage is RMS.
RMS Current
Iᵣₘₛ = I₀ / √2
Effective current, ~0.707 I₀.
Angular Frequency
ω = 2πf = 2π/T
ω in rad/s, f in Hz.
AC Circuits: LCR Components
Inductive Reactance (Xₗ)
Xₗ = ωL = 2πfL
Opposition to current by an inductor. Proportional to frequency.
Capacitive Reactance (X꜀)
X꜀ = 1 / (ωC)
Opposition to current by a capacitor. Inversely proportional to frequency.
Impedance (Z) of LCR
Z = √[R² + (Xₗ - X꜀)²]
Total opposition in an AC circuit. Ohm's law for AC: Vᵣₘₛ = Iᵣₘₛ Z.
Phase Angle (φ)
tan(φ) = (Xₗ - X꜀) / R
Phase difference between voltage and current in an LCR circuit.
BITSAT Speed Tricks
Remember 'ELI the ICE man': In an Inductor (L), Voltage (E) leads Current (I). In a Capacitor (C), Current (I) leads Voltage (E).
For resonance, Xₗ = X꜀. This means Z = R (minimum impedance), so current is maximum.
Power factor (cos φ = R/Z) is 1 at resonance. This means maximum power transfer.
In DC circuits (f=0), an inductor is a short circuit (Xₗ=0) and a capacitor is an open circuit (X꜀=∞).
Quickly find the direction of induced current using Fleming's Right-Hand Rule (for generators/motional EMF).
Resonance & Power
Resonant Frequency (ω₀)
ω₀ = 1 / √(LC)
f₀ = ω₀ / 2π
f₀ = ω₀ / 2π
Frequency at which Xₗ = X꜀ and current is maximum.
Quality Factor (Q)
Q = ω₀L / R = 1 / (ω₀CR)
Measures the sharpness of resonance. High Q = sharp peak.
Average Power
Pₐᵥ = Vᵣₘₛ Iᵣₘₛ cos(φ)
cos(φ) is the power factor. Power is only dissipated in the resistor.
Wattless Current
Iᵣₘₛ sin(φ)
Component of current that consumes no average power (in pure L or C circuits).
Transformers & Generators
Transformer Equation
V₂/V₁ = N₂/N₁ = I₁/I₂
For an ideal transformer. V=voltage, N=turns, I=current. 1=primary, 2=secondary.
Transformer Efficiency (η)
η = (Power out / Power in)
η = (V₂I₂ / V₁I₁)
η = (V₂I₂ / V₁I₁)
For real transformers, η is always < 100% due to losses.
AC Generator EMF
ε = NBAω sin(ωt)
ε₀ = NBAω
ε₀ = NBAω
ε₀ is the peak EMF. N=turns, B=field, A=area, ω=angular velocity.
AC Circuit Component Behavior
| Component | Reactance/Resistance | Phase (Voltage vs Current) | Frequency Dependence |
|---|---|---|---|
Resistor (R) | R | In Phase (φ = 0°) | Independent of f |
Inductor (L) | Xₗ = ωL | Voltage leads by 90° (π/2) | Xₗ ∝ f (High f → Open Ckt) |
Capacitor (C) | X꜀ = 1/(ωC) | Current leads by 90° (π/2) | X꜀ ∝ 1/f (High f → Short Ckt) |