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NEET Physics Formulas
Complete Formula Sheet

All Chapters Covered — NEET 2026 | 200+ Formulas | MathJax Rendered

📐 Physical Constants 🏃 Kinematics ⚡ Electrostatics 🌡️ Thermodynamics ⚛️ Modern Physics 💡 Optics 🧲 Magnetism 🌊 Waves
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Table of Contents

1
Physical Constants
2
Kinematics
3
Laws of Motion & Friction
4
Work, Power & Energy
5
Centre of Mass & Collision
6
Rotational Motion
7
Gravitation
8
Simple Harmonic Motion
9
Properties of Matter
10
Thermodynamics
11
Kinetic Theory of Gases
12
Waves & Sound
13
Ray Optics
14
Wave Optics
15
Electrostatics
16
Current Electricity
17
Magnetism & Magnetic Field
18
EMI & AC Circuits
19
Dual Nature of Radiation
20
Atoms & Nuclei
🔬

1. Physical Constants

18 Constants
Important Physical Constants
ConstantSymbolValue
Speed of light\(c\)\(3 \times 10^8\) m/s
Planck's constant\(h\)\(6.626 \times 10^{-34}\) J·s
Gravitational constant\(G\)\(6.67 \times 10^{-11}\) N·m²/kg²
Boltzmann constant\(k_B\)\(1.38 \times 10^{-23}\) J/K
Molar gas constant\(R\)8.314 J/mol·K
Avogadro's number\(N_A\)\(6.023 \times 10^{23}\) mol⁻¹
Charge of electron\(e\)\(1.602 \times 10^{-19}\) C
Mass of electron\(m_e\)\(9.1 \times 10^{-31}\) kg
Mass of proton\(m_p\)\(1.6726 \times 10^{-27}\) kg
Mass of neutron\(m_n\)\(1.6749 \times 10^{-27}\) kg
Atomic mass unit\(u\)\(1.66 \times 10^{-27}\) kg = 931.5 MeV/c²
Coulomb constant\(k = \frac{1}{4\pi\epsilon_0}\)\(9 \times 10^9\) N·m²/C²
Permittivity of vacuum\(\epsilon_0\)\(8.85 \times 10^{-12}\) F/m
Permeability of vacuum\(\mu_0\)\(4\pi \times 10^{-7}\) N/A²
Stefan–Boltzmann constant\(\sigma\)\(5.67 \times 10^{-8}\) W/m²K⁴
Rydberg constant\(R_\infty\)\(1.097 \times 10^7\) m⁻¹
Bohr radius\(a_0\)\(0.529 \times 10^{-10}\) m
hc (useful product)\(hc\)1242 eV·nm
🏃

2. Kinematics

14 Formulas
Important
Equations of Motion (Uniform Acceleration)
\[ v = u + at \] \[ s = ut + \tfrac{1}{2}at^2 \] \[ v^2 = u^2 + 2as \]
Key
Average Velocity & Acceleration
\[ v_{avg} = \frac{\Delta r}{\Delta t},\quad a_{avg} = \frac{\Delta v}{\Delta t} \]
Relative Velocity
\[ \vec{v}_{A/B} = \vec{v}_A - \vec{v}_B \]
NEET Freq.
Projectile – Time of Flight
\[ T = \frac{2u\sin\theta}{g} \]
NEET Freq.
Projectile – Horizontal Range
\[ R = \frac{u^2 \sin 2\theta}{g} \]
Maximum range at θ = 45°
NEET Freq.
Projectile – Maximum Height
\[ H = \frac{u^2 \sin^2\theta}{2g} \]
Projectile – Trajectory Equation
\[ y = x\tan\theta - \frac{gx^2}{2u^2\cos^2\theta} \]
nth Second of Motion
\[ s_n = u + \frac{a}{2}(2n-1) \]
Velocity Components (Projectile)
\[ v_x = u\cos\theta,\quad v_y = u\sin\theta - gt \]
⚖️

3. Laws of Motion & Friction

12 Formulas
Important
Newton's Second Law
\[ \vec{F} = m\vec{a} = \frac{d\vec{p}}{dt} \]
Linear Momentum
\[ \vec{p} = m\vec{v} \]
Newton's Third Law
\[ \vec{F}_{AB} = -\vec{F}_{BA} \]
NEET Freq.
Friction Forces
\[ f_{static,max} = \mu_s N \] \[ f_{kinetic} = \mu_k N \]
Always: μ_k < μ_s
NEET Freq.
Centripetal Force
\[ F_c = \frac{mv^2}{r} = mr\omega^2 \]
Banking of Roads
\[ \tan\theta = \frac{v^2}{rg} \]
With friction: \(v_{max} = \sqrt{rg\frac{\mu+\tan\theta}{1-\mu\tan\theta}}\)
Vertical Circular Motion – Min. Speed
\[ v_{min,top} = \sqrt{gR} \] \[ v_{min,bottom} = \sqrt{5gR} \]
Conical Pendulum – Time Period
\[ T = 2\pi\sqrt{\frac{l\cos\theta}{g}} \]
Pseudo Force (Non-inertial Frame)
\[ \vec{F}_{pseudo} = -m\vec{a}_0 \]
⚡

4. Work, Power & Energy

10 Formulas
Important
Work Done
\[ W = \vec{F}\cdot\vec{s} = Fs\cos\theta = \int \vec{F}\cdot d\vec{s} \]
Important
Kinetic Energy
\[ K = \frac{1}{2}mv^2 = \frac{p^2}{2m} \]
Potential Energy
\[ U_{grav} = mgh \] \[ U_{spring} = \frac{1}{2}kx^2 \]
NEET Freq.
Work–Energy Theorem
\[ W_{net} = \Delta K = K_f - K_i \]
Conservative Force & PE
\[ F = -\frac{dU}{dx} \]
Work by conservative forces is path independent
Power
\[ P_{avg} = \frac{W}{\Delta t},\quad P_{inst} = \vec{F}\cdot\vec{v} \]
Mechanical Energy Conservation
\[ E = K + U = \text{constant} \]
(when only conservative forces act)
🎯

5. Centre of Mass & Collision

14 Formulas
Important
Centre of Mass
\[ x_{cm} = \frac{\sum m_i x_i}{\sum m_i} = \frac{\int x\,dm}{\int dm} \]
CM of Common Shapes
ShapeCM Position
Triangle (from base)\(y_c = h/3\)
Semi-circular ring (from centre)\(y_c = 2r/\pi\)
Semi-circular disc (from centre)\(y_c = 4r/3\pi\)
Hemispherical shell (from centre)\(y_c = r/2\)
Solid hemisphere (from centre)\(y_c = 3r/8\)
Solid cone (from base)\(h/4\)
Hollow cone (from base)\(h/3\)
Impulse
\[ \vec{J} = \int \vec{F}\,dt = \Delta\vec{p} \]
NEET Freq.
Momentum Conservation (Collision)
\[ m_1v_1 + m_2v_2 = m_1v_1' + m_2v_2' \]
Coefficient of Restitution
\[ e = \frac{v_2' - v_1'}{v_1 - v_2} \]
e=1: perfectly elastic; e=0: perfectly inelastic
NEET Freq.
Elastic Collision (Equal Masses, v₂=0)
\[ v_1' = 0,\quad v_2' = v_1 \]
Velocities exchange completely
🌀

6. Rotational Motion

16 Formulas
Important
Angular Kinematics
\[ \omega = \omega_0 + \alpha t \] \[ \theta = \omega_0 t + \tfrac{1}{2}\alpha t^2 \] \[ \omega^2 = \omega_0^2 + 2\alpha\theta \]
Moment of Inertia
\[ I = \sum m_i r_i^2 = \int r^2\,dm \]
NEET Freq.
Moment of Inertia – Common Bodies
BodyAxisI
Solid cylinder / DiscOwn axis\(\frac{1}{2}MR^2\)
Ring / Hollow cylinderOwn axis\(MR^2\)
Solid sphereDiameter\(\frac{2}{5}MR^2\)
Hollow sphereDiameter\(\frac{2}{3}MR^2\)
Thin rodCentre, ⊥\(\frac{ML^2}{12}\)
Thin rodEnd, ⊥\(\frac{ML^2}{3}\)
Disc / RingDiameter\(\frac{1}{2}MR^2 / \frac{MR^2}{2}\)
Parallel Axis Theorem
\[ I = I_{cm} + Md^2 \]
Perpendicular Axis Theorem
\[ I_z = I_x + I_y \]
(for laminar bodies only)
Torque
\[ \vec{\tau} = \vec{r}\times\vec{F} = I\alpha \]
Angular Momentum
\[ \vec{L} = \vec{r}\times\vec{p} = I\vec{\omega} \]
NEET Freq.
Conservation of Angular Momentum
\[ \tau_{ext} = 0 \Rightarrow I_1\omega_1 = I_2\omega_2 \]
Rolling Without Slipping
\[ v_{cm} = R\omega \] \[ KE_{total} = \frac{1}{2}mv^2\left(1+\frac{k^2}{R^2}\right) \]
Rotational KE
\[ K_{rot} = \frac{1}{2}I\omega^2 \]
🪐

7. Gravitation

12 Formulas
Important
Newton's Law of Gravitation
\[ F = G\frac{m_1 m_2}{r^2} \]
Gravitational Field Intensity
\[ g = \frac{GM}{R^2} \]
Gravitational Potential Energy
\[ U = -\frac{GMm}{r} \]
NEET Freq.
Variation of g with Depth
\[ g_d = g\left(1 - \frac{d}{R}\right) \]
g = 0 at centre of Earth
NEET Freq.
Variation of g with Height
\[ g_h = g\left(1 - \frac{2h}{R}\right) \approx g\frac{R^2}{(R+h)^2} \]
Effect of Earth's Rotation on g
\[ g' = g - \omega^2 R\cos^2\lambda \]
λ = latitude; g max at poles, min at equator
Important
Orbital Velocity of Satellite
\[ v_0 = \sqrt{\frac{GM}{R+h}} \approx \sqrt{gR} \text{ (near surface)} \]
Important
Escape Velocity
\[ v_e = \sqrt{\frac{2GM}{R}} = \sqrt{2gR} \approx 11.2\text{ km/s} \]
Time Period of Satellite
\[ T = 2\pi\sqrt{\frac{(R+h)^3}{GM}} \]
NEET Freq.
Kepler's Third Law
\[ T^2 \propto a^3,\quad T^2 = \frac{4\pi^2}{GM}a^3 \]
a = semi-major axis of ellipse
Total Energy of Satellite
\[ E = -\frac{GMm}{2(R+h)} \]
KE = |E|, PE = 2E (negative means bound)
🔄

8. Simple Harmonic Motion

14 Formulas
Important
SHM Condition (Hooke's Law)
\[ F = -kx,\quad a = -\omega^2 x \]
Important
Time Period
\[ T = \frac{2\pi}{\omega} = 2\pi\sqrt{\frac{m}{k}} \]
Displacement
\[ x = A\sin(\omega t + \phi) \]
NEET Freq.
Velocity in SHM
\[ v = \omega\sqrt{A^2 - x^2} \]
v_max = Aω (at x = 0)
Acceleration in SHM
\[ a = -\omega^2 x \]
a_max = Aω² (at x = ±A)
Energies in SHM
\[ KE = \frac{1}{2}m\omega^2(A^2-x^2) \] \[ PE = \frac{1}{2}m\omega^2 x^2 \] \[ E_{total} = \frac{1}{2}m\omega^2 A^2 \]
NEET Freq.
Simple Pendulum
\[ T = 2\pi\sqrt{\frac{l}{g}} \]
Valid for small oscillations (θ < 5°)
Physical Pendulum
\[ T = 2\pi\sqrt{\frac{I}{mgl}} \]
Spring Combinations
\[ \text{Series: } \frac{1}{k_{eq}} = \frac{1}{k_1} + \frac{1}{k_2} \] \[ \text{Parallel: } k_{eq} = k_1 + k_2 \]
🧱

9. Properties of Matter

16 Formulas
Important
Young's Modulus
\[ Y = \frac{F/A}{\Delta L/L} = \frac{\text{Stress}}{\text{Strain}} \]
Bulk Modulus & Compressibility
\[ B = -V\frac{\Delta P}{\Delta V} \] \[ K = \frac{1}{B} \]
Poisson's Ratio
\[ \sigma = \frac{\text{Lateral strain}}{\text{Longitudinal strain}} = \frac{\Delta D/D}{\Delta L/L} \]
Elastic Potential Energy
\[ U = \frac{1}{2} \times \text{stress} \times \text{strain} \times \text{volume} \]
NEET Freq.
Surface Tension
\[ S = \frac{F}{l} \]
NEET Freq.
Excess Pressure in Bubbles
\[ \Delta P_{air} = \frac{2S}{R} \] \[ \Delta P_{soap} = \frac{4S}{R} \]
Soap bubble has 2 surfaces
Capillary Rise
\[ h = \frac{2S\cos\theta}{r\rho g} \]
Hydrostatic Pressure
\[ P = P_0 + \rho g h \]
Important
Buoyant Force (Archimedes)
\[ F_B = \rho_{liquid} V g = \text{Weight of displaced liquid} \]
Equation of Continuity
\[ A_1 v_1 = A_2 v_2 \]
NEET Freq.
Bernoulli's Equation
\[ P + \frac{1}{2}\rho v^2 + \rho g h = \text{constant} \]
Torricelli's Theorem (Efflux)
\[ v_{efflux} = \sqrt{2gh} \]
Stokes' Law
\[ F = 6\pi\eta r v \]
Terminal Velocity
\[ v_t = \frac{2r^2(\rho-\sigma)g}{9\eta} \]
Poiseuille's Equation
\[ Q = \frac{\pi P r^4}{8\eta l} \]
🌡️

10. Thermodynamics

18 Formulas
Temperature Scales
\[ K = C + 273.16,\quad F = \frac{9}{5}C + 32 \]
Important
Ideal Gas Equation
\[ PV = nRT \]
n = moles, R = 8.314 J/mol·K
Thermal Expansion
\[ L = L_0(1+\alpha\Delta T) \] \[ A = A_0(1+\beta\Delta T),\quad V = V_0(1+\gamma\Delta T) \] \[ \gamma = 2\beta = 3\alpha \]
Important
First Law of Thermodynamics
\[ \Delta Q = \Delta U + \Delta W \]
NEET Freq.
Thermodynamic Processes
ProcessConditionWork Done W\(\Delta U\)
IsothermalT = const\(nRT\ln(V_2/V_1)\)0
IsobaricP = const\(P(V_2-V_1)\)\(nC_v\Delta T\)
IsochoricV = const0\(\Delta Q\)
Adiabatic\(\Delta Q = 0\)\(\frac{P_1V_1-P_2V_2}{\gamma-1}\)\(-W\)
NEET Freq.
Efficiency of Heat Engine
\[ \eta = 1 - \frac{Q_2}{Q_1} = 1 - \frac{T_2}{T_1} \text{ (Carnot)} \]
COP of Refrigerator
\[ \text{COP} = \frac{Q_2}{W} = \frac{Q_2}{Q_1-Q_2} = \frac{T_2}{T_1-T_2} \]
Specific Heat Relations
\[ C_p - C_v = R,\quad \gamma = \frac{C_p}{C_v} \]
Monatomic: γ=5/3; Diatomic: γ=7/5
Conduction – Heat Transfer
\[ \frac{\Delta Q}{\Delta t} = KA\frac{\Delta T}{x} \]
Stefan–Boltzmann Law
\[ \frac{\Delta Q}{\Delta t} = \sigma e A T^4 \]
Wien's Displacement Law
\[ \lambda_m T = b = 2.9\times 10^{-3} \text{ m·K} \]
Newton's Law of Cooling
\[ \frac{dT}{dt} = -bA(T-T_0) \]
💨

11. Kinetic Theory of Gases

10 Formulas
Important
RMS Speed
\[ v_{rms} = \sqrt{\frac{3RT}{M}} = \sqrt{\frac{3kT}{m}} \]
Average Speed
\[ \bar{v} = \sqrt{\frac{8RT}{\pi M}} = \sqrt{\frac{8kT}{\pi m}} \]
Most Probable Speed
\[ v_p = \sqrt{\frac{2RT}{M}} = \sqrt{\frac{2kT}{m}} \]
Speed Comparison
\[ v_p : \bar{v} : v_{rms} = 1 : 1.128 : 1.225 \]
Pressure of Gas
\[ P = \frac{1}{3}\rho v_{rms}^2 \]
NEET Freq.
Equipartition of Energy
\[ E = \frac{1}{2}kT \text{ per degree of freedom} \]
Monatomic: f=3; Diatomic: f=5 (at room T)
Internal Energy
\[ U = \frac{f}{2}nRT \]
Van der Waals Equation
\[ \left(P + \frac{a}{V^2}\right)(V-b) = nRT \]
🌊

12. Waves & Sound

18 Formulas
Important
Wave Equation & Notation
\[ y = A\sin(kx - \omega t) \] \[ T = \frac{1}{\nu},\quad v = \nu\lambda,\quad k = \frac{2\pi}{\lambda} \]
Speed of Wave on String
\[ v = \sqrt{\frac{T}{\mu}} \]
T = tension, μ = linear mass density
Speed of Sound
\[ v_{gas} = \sqrt{\frac{\gamma P}{\rho}},\quad v_{liquid} = \sqrt{\frac{B}{\rho}} \] \[ v \approx 331 + 0.6\,T_C \text{ m/s in air} \]
NEET Freq.
Standing Waves – String & Organ Pipes
SystemFundamental Freq.Harmonics Present
String (both ends fixed)\(\nu_0 = \frac{1}{2L}\sqrt{\frac{T}{\mu}}\)All (1st, 2nd, 3rd…)
Closed pipe (one end)\(\nu_0 = \frac{v}{4L}\)Odd only (1st, 3rd, 5th…)
Open pipe (both ends)\(\nu_0 = \frac{v}{2L}\)All (1st, 2nd, 3rd…)
Interference Conditions
\[ \Delta x = n\lambda \text{ (constructive)} \] \[ \Delta x = (2n-1)\frac{\lambda}{2} \text{ (destructive)} \]
NEET Freq.
Beat Frequency
\[ \nu_{beat} = |\nu_1 - \nu_2| \]
NEET Freq.
Doppler Effect
\[ \nu' = \nu\left(\frac{v \pm v_0}{v \mp v_s}\right) \]
+v₀: observer moving towards source; −vₛ: source moving towards observer
Sound Intensity & Level
\[ I = \frac{P}{4\pi r^2} \] \[ \beta = 10\log_{10}\left(\frac{I}{I_0}\right) \text{ dB} \]
I₀ = 10⁻¹² W/m²
Resonance Column
\[ l_1 + d = \frac{\lambda}{4},\quad l_2 + d = \frac{3\lambda}{4} \] \[ v = 2(l_2 - l_1)\nu \]
🔭

13. Ray Optics

18 Formulas
Important
Snell's Law
\[ \mu_1\sin i = \mu_2\sin r,\quad \mu = \frac{c}{v} \]
Critical Angle (TIR)
\[ \sin\theta_c = \frac{1}{\mu} \]
TIR occurs when i > θ_c
Apparent Depth
\[ \mu = \frac{\text{real depth}}{\text{apparent depth}} = \frac{d}{d'} \]
NEET Freq.
Mirror Formula
\[ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} = \frac{2}{R} \] \[ m = -\frac{v}{u} \]
Important
Lens Formula
\[ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \] \[ m = \frac{v}{u} \]
Important
Lens Maker's Formula
\[ \frac{1}{f} = (\mu-1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) \]
Power of Lens
\[ P = \frac{1}{f\text{ (in m)}} \text{ dioptre} \]
Combination of Lenses
\[ P_{eq} = P_1 + P_2 - dP_1P_2 \] \[ \frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2} - \frac{d}{f_1 f_2} \]
NEET Freq.
Prism – Minimum Deviation
\[ \mu = \frac{\sin\!\left(\frac{A+\delta_m}{2}\right)}{\sin\!\left(\frac{A}{2}\right)} \]
Prism Deviation (Small Angle)
\[ \delta = (\mu-1)A \]
Simple Microscope
\[ m = 1 + \frac{D}{f} \text{ (with image at D)} \]
D = 25 cm (least distance of distinct vision)
NEET Freq.
Compound Microscope Magnification
\[ m = \frac{L}{f_o}\times\frac{D}{f_e} \]
Astronomical Telescope
\[ m = -\frac{f_o}{f_e},\quad L = f_o + f_e \]
💡

14. Wave Optics

14 Formulas
Important
Young's Double Slit – Path Difference
\[ \Delta x = \frac{yd}{D} \]
d = slit separation, D = screen distance, y = fringe position
NEET Freq.
Fringe Width (YDSE)
\[ \beta = \frac{\lambda D}{d} \]
Bright & Dark Fringes
\[ \Delta x = n\lambda \text{ (bright)} \] \[ \Delta x = (2n-1)\frac{\lambda}{2} \text{ (dark)} \]
Resultant Intensity (Interference)
\[ I = I_1 + I_2 + 2\sqrt{I_1 I_2}\cos\delta \] \[ I_{max} = (\sqrt{I_1}+\sqrt{I_2})^2,\quad I_{min} = (\sqrt{I_1}-\sqrt{I_2})^2 \]
For Equal Intensities (I₁=I₂=I₀)
\[ I = 4I_0\cos^2\!\left(\frac{\delta}{2}\right) \] \[ I_{max} = 4I_0,\quad I_{min} = 0 \]
Phase & Path Difference
\[ \delta = \frac{2\pi}{\lambda}\Delta x \]
Thin Film Interference (Reflected)
\[ 2\mu t = n\lambda \text{ (destructive)} \] \[ 2\mu t = (2n-1)\frac{\lambda}{2} \text{ (constructive)} \]
Single Slit Diffraction – Minima
\[ b\sin\theta = n\lambda \]
b = slit width
Resolving Power (Telescope)
\[ \sin\theta_{min} = \frac{1.22\lambda}{D} \]
Law of Malus (Polarisation)
\[ I = I_0\cos^2\theta \]
⚡

15. Electrostatics

20 Formulas
Important
Coulomb's Law
\[ F = \frac{1}{4\pi\epsilon_0}\frac{q_1 q_2}{r^2} \]
Electric Field
\[ E = \frac{1}{4\pi\epsilon_0}\frac{q}{r^2} \]
Electrostatic Potential
\[ V = \frac{1}{4\pi\epsilon_0}\frac{q}{r} \]
Relation E and V
\[ E = -\frac{dV}{dr},\quad V = -\int E\,dr \]
Electric Dipole Moment
\[ \vec{p} = q\vec{d} \]
Dipole – Potential & Field
\[ V = \frac{p\cos\theta}{4\pi\epsilon_0 r^2} \] \[ E_{axial} = \frac{2p}{4\pi\epsilon_0 r^3},\quad E_{equator} = \frac{p}{4\pi\epsilon_0 r^3} \]
Torque on Dipole
\[ \tau = pE\sin\theta = \vec{p}\times\vec{E} \]
Gauss's Law
\[ \oint \vec{E}\cdot d\vec{S} = \frac{q_{in}}{\epsilon_0} \]
NEET Freq.
Electric Field – Special Cases
ConfigurationElectric Field E
Infinite line charge (λ)\(E = \frac{\lambda}{2\pi\epsilon_0 r}\)
Infinite sheet (σ)\(E = \frac{\sigma}{2\epsilon_0}\)
Conductor surface (σ)\(E = \frac{\sigma}{\epsilon_0}\)
Uniformly charged sphere (inside)\(E = \frac{Qr}{4\pi\epsilon_0 R^3}\)
Uniformly charged sphere (outside)\(E = \frac{Q}{4\pi\epsilon_0 r^2}\)
Spherical shell (inside)\(E = 0\)
Important
Capacitance
\[ C = \frac{q}{V} \]
Parallel Plate Capacitor
\[ C = \frac{\epsilon_0 A}{d},\quad C = \frac{K\epsilon_0 A}{d} \text{ (with dielectric)} \]
Capacitor Combinations
\[ \text{Series: } \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} \] \[ \text{Parallel: } C_{eq} = C_1 + C_2 \]
NEET Freq.
Energy Stored in Capacitor
\[ U = \frac{1}{2}CV^2 = \frac{Q^2}{2C} = \frac{QV}{2} \]
Energy Density in Electric Field
\[ u = \frac{U}{V} = \frac{1}{2}\epsilon_0 E^2 \]
🔋

16. Current Electricity

18 Formulas
Important
Ohm's Law & Resistance
\[ V = iR,\quad R = \frac{\rho l}{A} \] \[ R = R_0(1+\alpha\Delta T) \]
Current Density & Drift Speed
\[ j = \frac{i}{A} = \sigma E \] \[ v_d = \frac{i}{neA} \]
Kirchhoff's Laws
\[ \text{KCL: } \sum I = 0 \text{ (at junction)} \] \[ \text{KVL: } \sum \Delta V = 0 \text{ (closed loop)} \]
Resistance Combinations
\[ R_{series} = R_1 + R_2 \] \[ \frac{1}{R_{parallel}} = \frac{1}{R_1} + \frac{1}{R_2} \]
Electric Power
\[ P = VI = I^2R = \frac{V^2}{R} \]
NEET Freq.
Cell EMF & Internal Resistance
\[ V = \varepsilon - Ir \] \[ I = \frac{\varepsilon}{R+r} \]
Wheatstone Bridge (Balanced)
\[ \frac{P}{Q} = \frac{R}{S} \Rightarrow \text{no current through galvanometer} \]
Meter Bridge (Slide Wire Bridge)
\[ \frac{R}{S} = \frac{l}{100-l} \]
Charging of Capacitor (RC)
\[ q(t) = CV\left(1 - e^{-t/RC}\right) \] \[ \tau = RC \]
Discharging of Capacitor
\[ q(t) = q_0\,e^{-t/RC} \]
Galvanometer → Ammeter
\[ i_g G = (i - i_g)S \Rightarrow S = \frac{i_g G}{i-i_g} \]
Galvanometer → Voltmeter
\[ V = i_g(G + R) \Rightarrow R = \frac{V}{i_g} - G \]
🧲

17. Magnetism & Magnetic Field

18 Formulas
Important
Lorentz Force
\[ \vec{F} = q(\vec{v}\times\vec{B}) + q\vec{E} \]
NEET Freq.
Charged Particle in Magnetic Field
\[ r = \frac{mv}{qB},\quad T = \frac{2\pi m}{qB} \]
Circular motion; r independent of v for fixed m/q
Force on Current-Carrying Wire
\[ \vec{F} = i\vec{l}\times\vec{B} = BiL\sin\theta \]
Biot–Savart Law
\[ d\vec{B} = \frac{\mu_0}{4\pi}\frac{id\vec{l}\times\hat{r}}{r^2} \]
NEET Freq.
Magnetic Field – Special Cases
ConfigurationMagnetic Field B
Infinite straight wire\(B = \frac{\mu_0 i}{2\pi d}\)
Centre of circular loop\(B = \frac{\mu_0 i}{2R}\)
Axis of circular loop\(B = \frac{\mu_0 i R^2}{2(R^2+x^2)^{3/2}}\)
Inside solenoid\(B = \mu_0 ni\) (n = turns/m)
Inside toroid\(B = \frac{\mu_0 Ni}{2\pi r}\)
Centre of arc (angle θ)\(B = \frac{\mu_0 i\theta}{4\pi R}\)
Ampere's Law
\[ \oint \vec{B}\cdot d\vec{l} = \mu_0 I_{enc} \]
Force Between Parallel Wires
\[ \frac{F}{l} = \frac{\mu_0 i_1 i_2}{2\pi d} \]
Attractive for same direction currents
Magnetic Dipole Moment
\[ \vec{m} = i\vec{A} = NiA \]
Torque on Magnetic Dipole
\[ \tau = mB\sin\theta = \vec{m}\times\vec{B} \]
Moving Coil Galvanometer
\[ NiAB = k\theta \Rightarrow i = \frac{k\theta}{NAB} \]
Angle of Dip
\[ \tan\delta = \frac{B_v}{B_h} \]
δ = 0° at equator; 90° at poles
🔌

18. Electromagnetic Induction & AC Circuits

20 Formulas
Important
Faraday's Law
\[ e = -\frac{d\Phi}{dt},\quad \Phi = \int \vec{B}\cdot d\vec{S} \]
Motional EMF
\[ e = Bvl\sin\theta \]
Self Inductance
\[ \Phi = Li,\quad e = -L\frac{di}{dt} \] \[ L_{solenoid} = \mu_0 n^2 \pi r^2 l \]
Mutual Inductance
\[ \Phi = Mi,\quad e = -M\frac{di}{dt} \]
Energy in Inductor
\[ U = \frac{1}{2}Li^2,\quad u = \frac{B^2}{2\mu_0} \]
Growth of Current (LR Circuit)
\[ i(t) = \frac{e}{R}\left(1-e^{-t/\tau}\right),\quad \tau = \frac{L}{R} \]
NEET Freq.
EMF of Rotating Coil
\[ e = NBA\omega\sin\omega t = e_0\sin\omega t \]
RMS & Peak Values
\[ i_{rms} = \frac{i_0}{\sqrt{2}},\quad V_{rms} = \frac{V_0}{\sqrt{2}} \]
Reactances
\[ X_L = \omega L,\quad X_C = \frac{1}{\omega C} \]
Important
LCR Circuit Impedance
\[ Z = \sqrt{R^2 + (X_L-X_C)^2} \] \[ \tan\phi = \frac{X_L-X_C}{R} \]
NEET Freq.
Resonance Frequency (LCR)
\[ f_0 = \frac{1}{2\pi\sqrt{LC}},\quad Z_{min} = R \text{ at resonance} \]
Average Power in AC
\[ P = V_{rms}I_{rms}\cos\phi \]
cos φ = power factor; P=0 for pure L or C
NEET Freq.
Transformer
\[ \frac{N_1}{N_2} = \frac{V_1}{V_2} = \frac{I_2}{I_1} \]
Step-up: N₂>N₁; Step-down: N₂<N₁
Speed of EM Waves
\[ c = \frac{1}{\sqrt{\mu_0\epsilon_0}} = 3\times10^8 \text{ m/s} \]
🌟

19. Dual Nature of Radiation & Matter

12 Formulas
Important
Photon Energy & Momentum
\[ E = hf = \frac{hc}{\lambda},\quad p = \frac{h}{\lambda} = \frac{E}{c} \]
Important
Photoelectric Effect (Einstein)
\[ K_{max} = hf - \phi = hf - hf_0 \]
φ = work function, f₀ = threshold frequency
Stopping Potential
\[ eV_0 = K_{max} = hf - \phi \]
Threshold Wavelength
\[ \lambda_0 = \frac{hc}{\phi} \]
No emission if λ > λ₀
NEET Freq.
de Broglie Wavelength
\[ \lambda = \frac{h}{p} = \frac{h}{mv} = \frac{h}{\sqrt{2mK}} \]
de Broglie (Accelerated Electron)
\[ \lambda = \frac{h}{\sqrt{2meV}} = \frac{1.227}{\sqrt{V}}\text{ nm} \]
Heisenberg Uncertainty Principle
\[ \Delta x\cdot\Delta p \geq \frac{h}{4\pi} \]
Einstein's Photoelectric Equation
\[ hf = \phi + \frac{1}{2}mv_{max}^2 \]
⚛️

20. Atoms & Nuclei

20 Formulas
Important
Bohr's Radius (Hydrogen)
\[ r_n = \frac{0.529\,n^2}{Z}\text{ Å} \]
Important
Energy of Electron (Bohr Model)
\[ E_n = -\frac{13.6\,Z^2}{n^2}\text{ eV} \]
NEET Freq.
Wavelength of Emitted Photon
\[ \frac{1}{\lambda} = RZ^2\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right) \]
R = 1.097 × 10⁷ m⁻¹ (Rydberg constant)
NEET Freq.
Hydrogen Spectral Series
Seriesn₁n₂Region
Lyman12,3,4…UV
Balmer23,4,5…Visible
Paschen34,5,6…IR
Brackett45,6,7…IR (Far)
Pfund56,7,8…Far IR
Bohr's Velocity & Angular Momentum
\[ v_n = \frac{Ze^2}{2\epsilon_0 hn} \] \[ L = mvr = \frac{nh}{2\pi} \]
Nuclear Radius
\[ R = R_0 A^{1/3},\quad R_0 = 1.2\times10^{-15}\text{ m} \]
Mass Defect & Binding Energy
\[ \Delta m = [Zm_p + Nm_n] - M_{nucleus} \] \[ BE = \Delta m \cdot c^2 \]
Mass–Energy Equivalence
\[ E = mc^2,\quad 1\text{ u} = 931.5\text{ MeV}/c^2 \]
Important
Radioactive Decay Law
\[ N = N_0\,e^{-\lambda t},\quad A = \lambda N = A_0\,e^{-\lambda t} \]
NEET Freq.
Half-Life
\[ t_{1/2} = \frac{\ln 2}{\lambda} = \frac{0.693}{\lambda} \]
Mean Life (Average Life)
\[ \tau = \frac{1}{\lambda} = \frac{t_{1/2}}{0.693} = 1.443\,t_{1/2} \]
Remaining Nuclei After n Half-Lives
\[ N = N_0\left(\frac{1}{2}\right)^n = \frac{N_0}{2^n} \]
Alpha Decay
\[ {}^A_Z X \rightarrow {}^{A-4}_{Z-2}Y + {}^4_2\text{He} \]
Beta Decay
\[ \beta^-: {}^A_Z X \rightarrow {}^A_{Z+1}Y + e^- + \bar{\nu}_e \] \[ \beta^+: {}^A_Z X \rightarrow {}^A_{Z-1}Y + e^+ + \nu_e \]