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EMI/AC formulas

Master EMI/AC through 36 JEE Advanced-level formulas, systematically structured with every variable spelled out. Revise concept-wise, identify the areas where you need improvement, and focus your preparation with greater precision.

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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
$ε = - N \frac{d ϕ}{d t}$
Q1MCQFaraday's law
The induced EMF equals:
- A
  $-N\dfrac{d\phi}{dt}$
- B
  $N\phi$
- C
  $-N\phi t$
- D
  $\dfrac{d\phi}{dt^{2}}$
Motional EMF
$ε = B v l$
Induced current (rod)
$I = \frac{B v l}{R}$
Force on a moving rod
$F = \frac{B ^{2} l ^{2} v}{R}$
Q1MCQForce on rod
The retarding force on a rod moving in a field is:
- A
  $\dfrac{B^{2}l^{2}v}{R}$
- B
  $Bvl$
- C
  $\dfrac{Bvl}{R}$
- D
  $B^{2}l^{2}v$
Power dissipated (rod)
$P = \frac{B ^{2} l ^{2} v ^{2}}{R}$
Q1MCQPower dissipated
The power to keep the rod moving is:
- A
  $\dfrac{B^{2}l^{2}v^{2}}{R}$
- B
  $\dfrac{B^{2}l^{2}v}{R}$
- C
  $Bvl$
- D
  $\dfrac{Bvl}{R}$
EMF of a rotating rod
$ε = \frac{1}{2} B ω l^{2}$
Q1MCQRotating rod EMF
The EMF of a rod rotating about one end is:
- A
  $\tfrac12 B\omega l^{2}$
- B
  $B\omega l^{2}$
- C
  $B\omega l$
- D
  $\tfrac12 B\omega l$
Self inductance
$L = \frac{N ϕ}{I}$
Q1MCQSelf inductance
Self inductance is defined as:
- A
  $\dfrac{N\phi}{I}$
- B
  $\dfrac{I}{N\phi}$
- C
  $N\phi I$
- D
  $\dfrac{\phi}{N}$
EMF in an inductor
$ε = - L \frac{d I}{d t}$
Q1MCQInductor EMF
The back-EMF of an inductor is:
- A
  $-L\dfrac{dI}{dt}$
- B
  $-L I$
- C
  $LI$
- D
  $-\dfrac{dI}{dt}$
Solenoid inductance
$L = μ_{0} n^{2} A l$
Q1MCQSolenoid inductance
The self inductance of a long solenoid is:
- A
  $\mu_0 n^{2}Al$
- B
  $\mu_0 nAl$
- C
  $\mu_0 n^{2}A$
- D
  $\mu_0 n^{2}l$
Mutual inductance
$M = \frac{N _{2} ϕ _{2}}{I _{1}}$
Q1MCQMutual inductance
Mutual inductance $M$ is:
- A
  $\dfrac{N_2\phi_2}{I_1}$
- B
  $\dfrac{I_1}{N_2\phi_2}$
- C
  $N_2\phi_2 I_1$
- D
  $\dfrac{\phi_2}{I_1}$
Coupling coefficient
$k = \frac{M}{L _{1} L _{2}}$
Q1MCQCoupling coefficient
The coupling coefficient is:
- A
  $\dfrac{M}{\sqrt{L_1 L_2}}$
- B
  $\dfrac{\sqrt{L_1 L_2}}{M}$
- C
  $M L_1 L_2$
- D
  $\dfrac{M}{L_1+L_2}$
Energy stored in an inductor
$U = \frac{1}{2} L I^{2}$
Magnetic energy density
$u = \frac{B ^{2}}{2 μ _{0}}$
Q1MCQEnergy density
The magnetic energy density is:
- A
  $\dfrac{B^{2}}{2\mu_0}$
- B
  $\dfrac{B^{2}}{\mu_0}$
- C
  $\tfrac12\mu_0 B^{2}$
- D
  $\dfrac{B}{2\mu_0}$
Inductors in series
$L = L_{1} + L_{2} \pm 2 M$
Q1MCQInductors series
Two inductors (same winding sense, coupled) in series give:
- A
  $L_1+L_2+2M$
- B
  $L_1+L_2$
- C
  $L_1+L_2-2M$
- D
  $L_1 L_2$
Inductors in parallel
$\frac{1}{L} = \frac{1}{L _{1}} + \frac{1}{L _{2}}$
no coupling
L–R growth of current
$I = \frac{ε}{R} (1 - e^{- R t / L})$
Q1MCQLR growth
The current growth in an L–R circuit is:
- A
  $\dfrac{\varepsilon}{R}(1-e^{-Rt/L})$
- B
  $\dfrac{\varepsilon}{R}e^{-Rt/L}$
- C
  $\dfrac{\varepsilon}{R}$
- D
  $\varepsilon t$
L–R decay of current
$I = I_{0} e^{- R t / L}$
Q1MCQLR decay
The current decay in an L–R circuit is:
- A
  $I_0 e^{-Rt/L}$
- B
  $I_0(1-e^{-Rt/L})$
- C
  $I_0$
- D
  $0$
L–R time constant
$τ = \frac{L}{R}$
LC oscillation frequency
$ω = \frac{1}{L C}$
Q1MCQLC frequency
The angular frequency of an LC oscillator is:
- A
  $\dfrac{1}{\sqrt{LC}}$
- B
  $\sqrt{LC}$
- C
  $\dfrac{1}{LC}$
- D
  $LC$
RMS current
$I_{r m s} = \frac{I _{0}}{2}$
RMS voltage
$V_{r m s} = \frac{V _{0}}{2}$
Q1MCQRMS voltage
The rms value of an AC voltage of peak $V_0$ is:
- A
  $\dfrac{V_0}{\sqrt2}$
- B
  $V_0\sqrt2$
- C
  $\dfrac{V_0}{2}$
- D
  $V_0$
Inductive reactance
$X_{L} = ω L$
Q1MCQInductive reactance
The inductive reactance is:
- A
  $\omega L$
- B
  $\dfrac{1}{\omega L}$
- C
  $\dfrac{L}{\omega}$
- D
  $\omega^{2}L$
Capacitive reactance
$X_{C} = \frac{1}{ω C}$
Q1MCQCapacitive reactance
The capacitive reactance is:
- A
  $\dfrac{1}{\omega C}$
- B
  $\omega C$
- C
  $\dfrac{C}{\omega}$
- D
  $\omega^{2}C$
Impedance (series RLC)
$Z = R^{2} + (X_{L} - X_{C})^{2}$
Phase angle
$ϕ = tan^{- 1} (\frac{X _{L} - X _{C}}{R})$
Q1MCQPhase angle
The phase angle in a series RLC circuit is:
- A
  $\tan^{-1}\!\left(\dfrac{X_L-X_C}{R}\right)$
- B
  $\tan^{-1}\!\left(\dfrac{R}{X_L-X_C}\right)$
- C
  $\dfrac{X_L-X_C}{R}$
- D
  $0$
Average power
$P = V_{r m s} I_{r m s} cos ϕ$
Q1MCQAverage power
The average power in an AC circuit is:
- A
  $V_{rms}I_{rms}\cos\phi$
- B
  $V_{rms}I_{rms}$
- C
  $V_{rms}I_{rms}\sin\phi$
- D
  $V_0 I_0$
Power factor
$cos ϕ = \frac{R}{Z}$
Q1MCQPower factor
The power factor of an AC circuit is:
- A
  $\dfrac{R}{Z}$
- B
  $\dfrac{Z}{R}$
- C
  $\dfrac{X_L}{Z}$
- D
  $RZ$
Purely inductive circuit
$I lags V by 9 0^{\circ}, P = 0$
Q1MCQPurely inductive
In a purely inductive circuit, the current:
- A
  lags the voltage by $90^{\circ}$
- B
  leads by $90^{\circ}$
- C
  is in phase
- D
  is zero
Purely capacitive circuit
$I leads V by 9 0^{\circ}, P = 0$
Q1MCQPurely capacitive
In a purely capacitive circuit, the current:
- A
  leads the voltage by $90^{\circ}$
- B
  lags by $90^{\circ}$
- C
  is in phase
- D
  is zero
Resonant frequency
$ω_{0} = \frac{1}{L C}$
Q1MCQResonant frequency
The resonant frequency of a series RLC circuit is:
- A
  $\dfrac{1}{\sqrt{LC}}$
- B
  $\sqrt{LC}$
- C
  $\dfrac{1}{LC}$
- D
  $\dfrac{R}{L}$
At resonance
$X_{L} = X_{C}, Z = R, I = max$
Q1MCQAt resonance
At resonance in a series RLC circuit:
- A
  $Z=R$ and current is maximum
- B
  $Z$ is maximum
- C
  current is zero
- D
  $\cos\phi=0$
Quality factor
$Q = \frac{ω _{0}}{Δ ω} = \frac{1}{R} \frac{L}{C}$
Q1MCQQuality factor
The quality factor of a series resonant circuit is:
- A
  $\dfrac{1}{R}\sqrt{\dfrac{L}{C}}$
- B
  $R\sqrt{\dfrac{C}{L}}$
- C
  $\sqrt{LC}$
- D
  $\dfrac{R}{\sqrt{LC}}$
Transformer relation
$\frac{ε _{s}}{ε _{p}} = \frac{N _{s}}{N _{p}} = \frac{I _{p}}{I _{s}}$
Q1MCQTransformer
For an ideal transformer:
- A
  $\dfrac{\varepsilon_s}{\varepsilon_p}=\dfrac{N_s}{N_p}$
- B
  $\dfrac{\varepsilon_s}{\varepsilon_p}=\dfrac{N_p}{N_s}$
- C
  $\varepsilon_s=\varepsilon_p$
- D
  $N_s=N_p$
Wattless current
$I sin ϕ$
power = 0
Q1MCQWattless current
The component of AC current that dissipates no power is:
- A
  $I\sin\phi$
- B
  $I\cos\phi$
- C
  $I$
- D
  $0$
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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