Electromagnetic Induction and Alternating Currents - Important Formulas Table

 Electromagnetic Induction and Alternating Currents - Important Formulas Table

S.No.	Concept / Quantity	Formula	Key Notes
1	Magnetic Flux	$\phi = \vec{B} \cdot \vec{A} = BA \cos\theta$	Unit: Weber (Wb)
2	Faraday’s Law of Induction	$\mathcal{E} = -\frac{d\phi}{dt}$	Induced EMF
3	Induced EMF in a Coil	$\mathcal{E} = -N \frac{d\phi}{dt}$	N = number of turns
4	Lenz’s Law	Induced current opposes the change in flux	Direction rule
5	Motional EMF (Rod moving in B-field)	$\mathcal{E} = B l v$ (when v ⊥ B and l)	Straight conductor
6	Motional EMF (Rotating Rod)	$\mathcal{E} = \frac{1}{2} B \omega l^2$	-
7	Self-Inductance	$\mathcal{E} = -L \frac{dI}{dt}$	L = coefficient of self-inductance
8	Self-Inductance of Solenoid	$L = \mu_0 n^2 A l$	-
9	Mutual Inductance	$\mathcal{E}_2 = -M \frac{dI_1}{dt}$	M = coefficient of mutual inductance
10	Mutual Inductance (Two Coils)	$M = \frac{\mu_0 N_1 N_2 A}{l}$	-
11	Energy Stored in Inductor	$U = \frac{1}{2} L I^2$	-
12	Energy Density in Magnetic Field	$u = \frac{B^2}{2\mu_0}$	-
13	Eddy Current Loss	Power loss ∝ $B^2 f^2 t^2$	Laminations reduce it
14	Instantaneous AC Voltage	$v = V_0 \sin(\omega t)$ or $V_0 \cos(\omega t)$	-
15	Instantaneous AC Current	$i = I_0 \sin(\omega t + \phi)$	-
16	RMS Value (Voltage)	$V_{rms} = \frac{V_0}{\sqrt{2}}$	Effective value
17	RMS Value (Current)	$I_{rms} = \frac{I_0}{\sqrt{2}}$	-
18	Average Value (Half Cycle)	$V_{avg} = \frac{2V_0}{\pi}$	-
19	Inductive Reactance	$X_L = \omega L = 2\pi f L$	-
20	Capacitive Reactance	$X_C = \frac{1}{\omega C} = \frac{1}{2\pi f C}$	-
21	Impedance in LCR Series Circuit	$Z = \sqrt{R^2 + (X_L - X_C)^2}$	-
22	Phase Angle in LCR Circuit	$\tan\phi = \frac{X_L - X_C}{R}$	-
23	Power Factor	$\cos\phi = \frac{R}{Z}$	-
24	Average Power in AC Circuit	$P_{avg} = V_{rms} I_{rms} \cos\phi$	Real power
25	Resonance in LCR Series Circuit	$\omega_0 = \frac{1}{\sqrt{LC}}$, $f_0 = \frac{1}{2\pi\sqrt{LC}}$	X_L = X_C
26	Quality Factor (Q-factor)	$Q = \frac{\omega_0 L}{R} = \frac{1}{\omega_0 C R} = \frac{X_L}{R}$	Sharpness of resonance
27	Bandwidth of Resonance	$\Delta \omega = \frac{R}{L}$	-
28	Transformer (Voltage Ratio)	$\frac{V_s}{V_p} = \frac{N_s}{N_p}$	Ideal transformer
29	Transformer (Current Ratio)	$\frac{I_s}{I_p} = \frac{N_p}{N_s}$	-
30	Transformer Efficiency	$\eta = \frac{\text{Output Power}}{\text{Input Power}} \times 100\%$	-
31	LC Oscillations	$\omega = \frac{1}{\sqrt{LC}}$, $T = 2\pi \sqrt{LC}$	-
32	Charging of Capacitor through Inductor	$q = Q_0 (1 - \cos\omega t)$	-
33	Peak Current in Pure Inductor	$I_0 = \frac{V_0}{X_L}$	Current lags by 90°
34	Peak Current in Pure Capacitor	$I_0 = \frac{V_0}{X_C}$	Current leads by 90°
35	AC Generator (Induced EMF)	$\mathcal{E} = NBA\omega \sin(\omega t)$	-

Important Constants & Relations

• $\omega = 2\pi f$
• $\mu_0 = 4\pi \times 10^{-7}$ T m/A
• In ideal transformer: $V_p I_p = V_s I_s$

Note: All formulas are in SI units. This table covers the complete chapter for Class 12 Board Exams, JEE Main, JEE Advanced, and NEET.