EMI/AC formulas

Every formula JEE Advanced expects you to know for EMI/AC, with the variables spelled out. Free, no sign-up. Read it before a mock, not during one.

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Formulas: 36
Subject: Physics
Exam: JEE Advanced
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EMI/AC, every formula

36 formulas, typeset and free. Print it, or keep it open beside your practice.

Magnetic flux
$ϕ = B \cdot A = B A cos θ$
Faraday's law
$ε = - N \frac{d ϕ}{d t}$
Motional EMF
$ε = B v l$
Induced current (rod)
$I = \frac{B v l}{R}$
Force on a moving rod
$F = \frac{B ^{2} l ^{2} v}{R}$
Power dissipated (rod)
$P = \frac{B ^{2} l ^{2} v ^{2}}{R}$
EMF of a rotating rod
$ε = \frac{1}{2} B ω l^{2}$
Self inductance
$L = \frac{N ϕ}{I}$
EMF in an inductor
$ε = - L \frac{d I}{d t}$
Solenoid inductance
$L = μ_{0} n^{2} A l$
Mutual inductance
$M = \frac{N _{2} ϕ _{2}}{I _{1}}$
Coupling coefficient
$k = \frac{M}{L _{1} L _{2}}$
Energy stored in an inductor
$U = \frac{1}{2} L I^{2}$
Magnetic energy density
$u = \frac{B ^{2}}{2 μ _{0}}$
Inductors in series
$L = L_{1} + L_{2} \pm 2 M$
Inductors in parallel
$\frac{1}{L} = \frac{1}{L _{1}} + \frac{1}{L _{2}}$
no coupling
L–R growth of current
$I = \frac{ε}{R} (1 - e^{- R t / L})$
L–R decay of current
$I = I_{0} e^{- R t / L}$
L–R time constant
$τ = \frac{L}{R}$
LC oscillation frequency
$ω = \frac{1}{L C}$
RMS current
$I_{r m s} = \frac{I _{0}}{2}$
RMS voltage
$V_{r m s} = \frac{V _{0}}{2}$
Inductive reactance
$X_{L} = ω L$
Capacitive reactance
$X_{C} = \frac{1}{ω C}$
Impedance (series RLC)
$Z = R^{2} + (X_{L} - X_{C})^{2}$
Phase angle
$ϕ = tan^{- 1} (\frac{X _{L} - X _{C}}{R})$
Average power
$P = V_{r m s} I_{r m s} cos ϕ$
Power factor
$cos ϕ = \frac{R}{Z}$
Purely inductive circuit
$I lags V by 9 0^{\circ}, P = 0$
Purely capacitive circuit
$I leads V by 9 0^{\circ}, P = 0$
Resonant frequency
$ω_{0} = \frac{1}{L C}$
At resonance
$X_{L} = X_{C}, Z = R, I = max$
Quality factor
$Q = \frac{ω _{0}}{Δ ω} = \frac{1}{R} \frac{L}{C}$
Transformer relation
$\frac{ε _{s}}{ε _{p}} = \frac{N _{s}}{N _{p}} = \frac{I _{p}}{I _{s}}$
Wattless current
$I sin ϕ$
power = 0
Transformer efficiency
$η = \frac{P _{o u t}}{P _{in}}$

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EMI/AC formulas

EMI/AC, every formula

Magnetic flux

Faraday's law

Motional EMF

Induced current (rod)

Force on a moving rod

Power dissipated (rod)

EMF of a rotating rod

Self inductance

EMF in an inductor

Solenoid inductance

Mutual inductance

Coupling coefficient

Energy stored in an inductor

Magnetic energy density

Inductors in series

Inductors in parallel

L–R growth of current

L–R decay of current

L–R time constant

LC oscillation frequency

RMS current

RMS voltage

Inductive reactance

Capacitive reactance

Impedance (series RLC)

Phase angle

Average power

Power factor

Purely inductive circuit

Purely capacitive circuit

Resonant frequency

At resonance

Quality factor

Transformer relation

Wattless current

Transformer efficiency

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