NCERT Physics Laws & Equations | Class 10 to 12

📘 How to use this page

This reference organizes important Physics laws, principles, rules and equations generally encountered in NCERT Physics from Class 10 through Class 12.

Use the search box to quickly find a law or formula. The Class buttons can be used to filter the content.

📚 Chapter Navigation

Class 10 — Electricity Class 10 — Magnetic Effects Class 10 — Light Class 11 — Motion Class 11 — Laws of Motion Class 11 — Work & Energy Class 11 — Gravitation Class 11 — Thermodynamics Class 11 — Waves Class 12 — Electrostatics Class 12 — Current Electricity Class 12 — Magnetism Class 12 — Electromagnetic Induction Class 12 — Alternating Current Class 12 — Optics Class 12 — Dual Nature Class 12 — Atoms Class 12 — Nuclei

Electricity Class 10

1. Ohm's Law

At constant temperature, the potential difference across a conductor is directly proportional to the current through it.

V = IR

V = potential difference, I = current, R = resistance

2. Resistance of a Uniform Conductor

R = ρL/A

ρ = resistivity, L = length, A = cross-sectional area

3. Series Combination of Resistances

R = R₁ + R₂ + R₃ + ...

The same current flows through each resistance in series.

4. Parallel Combination of Resistances

1/R = 1/R₁ + 1/R₂ + 1/R₃ + ...

5. Electric Power

P = VI = I²R = V²/R

6. Electrical Energy

W = Pt = VIt

7. Joule's Law of Heating

The heat produced in a resistor is proportional to the square of current, resistance and time.

H = I²Rt

Magnetic Effects of Electric Current Class 10

8. Right-Hand Thumb Rule

If a straight current-carrying conductor is held in the right hand with the thumb pointing in the direction of current, the curled fingers indicate the direction of the magnetic field.

9. Fleming's Left-Hand Rule

It gives the direction of force acting on a current-carrying conductor placed in a magnetic field.

F = BIL sin θ

10. Fleming's Right-Hand Rule

It gives the direction of induced current in a conductor moving through a magnetic field.

11. Force on a Current-Carrying Conductor

F = BIL sin θ

B = magnetic field, I = current, L = length of conductor

Light — Reflection & Refraction Class 10

12. Laws of Reflection

1. The angle of incidence is equal to the angle of reflection.

∠i = ∠r

2. The incident ray, reflected ray and normal lie in the same plane.

13. Mirror Formula

1/f = 1/v + 1/u

14. Magnification of Mirror

m = hᵢ/hₒ = -v/u

15. Snell's Law of Refraction

n₁ sin i = n₂ sin r

16. Refractive Index

n = c/v

17. Lens Formula

1/f = 1/v - 1/u

18. Magnification of Lens

m = hᵢ/hₒ = v/u

19. Power of Lens

P = 1/f

f must be expressed in metres. Unit of power = dioptre (D).

Motion Class 11

20. First Equation of Motion

v = u + at

21. Second Equation of Motion

s = ut + ½at²

22. Third Equation of Motion

v² = u² + 2as

23. Average Velocity

v_avg = Total displacement / Total time

Laws of Motion Class 11

24. Newton's First Law

An object remains at rest or in uniform motion in a straight line unless acted upon by an external unbalanced force.

ΣF = 0 → constant velocity

25. Newton's Second Law

F = dp/dt

For constant mass:

F = ma

26. Newton's Third Law

For every action there is an equal and opposite reaction.

F₁₂ = -F₂₁

27. Conservation of Linear Momentum

p_total = constant

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

28. Friction

f ≤ μN

For limiting friction:

f_max = μN

Work, Energy & Power Class 11

29. Work Done by a Constant Force

W = Fs cos θ

30. Kinetic Energy

K = ½mv²

31. Work-Energy Theorem

W_net = ΔK

32. Gravitational Potential Energy

U = mgh

33. Mechanical Energy

E = K + U

34. Conservation of Mechanical Energy

K₁ + U₁ = K₂ + U₂

35. Power

P = W/t

Instantaneous power:

P = F · v

Gravitation Class 11

36. Newton's Universal Law of Gravitation

Every two masses attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

F = Gm₁m₂/r²

37. Acceleration Due to Gravity

g = GM/R²

38. Gravitational Potential Energy

U = -GMm/r

39. Escape Velocity

vₑ = √(2GM/R)

Near Earth's surface:

vₑ = √(2gR)

40. Orbital Velocity

vₒ = √(GM/r)

41. Kepler's Third Law

T² ∝ r³

Thermodynamics Class 11

42. Zeroth Law of Thermodynamics

If two systems are separately in thermal equilibrium with a third system, they are in thermal equilibrium with each other.

43. First Law of Thermodynamics

ΔQ = ΔU + ΔW

Heat supplied = increase in internal energy + work done by the system.

44. Work Done by an Ideal Gas

W = ∫P dV

45. Ideal Gas Equation

PV = nRT

46. Boyle's Law

PV = constant

47. Charles' Law

V/T = constant

48. Gay-Lussac's Law

P/T = constant

Oscillations & Waves Class 11

49. Simple Harmonic Motion

a = -ω²x

50. Time Period of Simple Pendulum

T = 2π√(l/g)

51. Wave Equation

v = fλ

52. Superposition Principle

When waves overlap, the resultant displacement is the algebraic sum of the individual displacements.

y = y₁ + y₂

Electrostatics Class 12

53. Coulomb's Law

The electrostatic force between two point charges is proportional to the product of their charges and inversely proportional to the square of their separation.

F = (1/4πε₀) q₁q₂/r²

54. Electric Field

E = F/q

55. Electric Field of a Point Charge

E = (1/4πε₀) q/r²

56. Electric Potential

V = W/q

57. Potential Due to a Point Charge

V = (1/4πε₀) q/r

58. Gauss's Law

Φ_E = q_enclosed/ε₀

In integral form:

∮ E · dA = q/ε₀

59. Capacitance

C = Q/V

60. Parallel Plate Capacitor

C = ε₀A/d

61. Energy Stored in a Capacitor

U = ½CV² = ½QV = Q²/2C

Current Electricity Class 12

62. Current

I = Q/t

63. Ohm's Law

V = IR

64. Drift Current

I = neAv_d

65. Resistivity

R = ρL/A

66. Kirchhoff's Junction Rule

The algebraic sum of currents at a junction is zero.

ΣI = 0

67. Kirchhoff's Loop Rule

The algebraic sum of potential changes around a closed loop is zero.

ΣV = 0

68. Wheatstone Bridge Balance Condition

P/Q = R/S

69. Electric Power

P = VI = I²R = V²/R

70. Electrical Energy

E = VIt

Moving Charges & Magnetism Class 12

71. Lorentz Force

F = q(E + v × B)

72. Magnetic Force on a Moving Charge

F = qvB sin θ

73. Biot-Savart Law

dB = (μ₀/4π) I(dl × r̂)/r²

74. Ampere's Circuital Law

∮B · dl = μ₀I

75. Magnetic Field Near a Straight Current-Carrying Wire

B = μ₀I/(2πr)

76. Magnetic Field at Centre of Circular Coil

B = μ₀NI/(2R)

77. Force Between Parallel Current-Carrying Conductors

F/L = μ₀I₁I₂/(2πd)

78. Torque on Current Loop

τ = NIAB sin θ

Electromagnetic Induction Class 12

79. Faraday's First Law

An emf is induced in a circuit whenever the magnetic flux linked with the circuit changes.

80. Faraday's Second Law

ε = -dΦ_B/dt

For N turns:

ε = -N dΦ_B/dt

81. Lenz's Law

The direction of induced current is such that it opposes the change in magnetic flux that produces it.

82. Magnetic Flux

Φ_B = BA cos θ

83. Motional EMF

ε = Blv

Alternating Current Class 12

84. AC Voltage

V = V₀ sin ωt

85. RMS Voltage

V_rms = V₀/√2

86. RMS Current

I_rms = I₀/√2

87. Inductive Reactance

X_L = ωL

88. Capacitive Reactance

X_C = 1/(ωC)

89. Impedance of Series LCR Circuit

Z = √[R² + (X_L - X_C)²]

90. Resonance in LCR Circuit

X_L = X_C

ω₀ = 1/√LC

91. AC Power

P = V_rms I_rms cos φ

Ray & Wave Optics Class 12

92. Laws of Reflection

i = r

93. Snell's Law

n₁ sin i = n₂ sin r

94. Lens Maker's Formula

1/f = (n - 1)(1/R₁ - 1/R₂)

95. Thin Lens Formula

1/f = 1/v - 1/u

96. Power of Lens

P = 1/f

97. Young's Double-Slit Experiment

β = λD/d

β = fringe width.

98. Brewster's Law

μ = tan i_p

99. Malus' Law

I = I₀ cos²θ

Dual Nature of Matter & Radiation Class 12

100. Planck's Quantum Relation

E = hν

101. Einstein's Photoelectric Equation

hν = φ + K_max

K_max = hν - φ

102. de Broglie Wavelength

λ = h/p

For a non-relativistic particle:

λ = h/mv

103. Photoelectric Work Function

φ = hν₀

Atoms Class 12

104. Bohr's Quantization Condition

mvr = nh/2π

105. Bohr Energy of Hydrogen Atom

E_n = -13.6/n² eV

106. Rydberg Formula

1/λ = R(1/n₁² - 1/n₂²)

Nuclei Class 12

107. Mass-Energy Equivalence

E = mc²

108. Radioactive Decay Law

N = N₀e^(-λt)

109. Activity

A = λN

110. Half-Life

T₁/₂ = ln2/λ

111. Mean Life

τ = 1/λ

112. Binding Energy

BE = Δmc²

Quick Formula Reference

⚡ Electricity

V = IR | P = VI | P = I²R | P = V²/R

🚀 Mechanics

F = ma | p = mv | K = ½mv² | W = Fs cosθ

🌍 Gravitation

F = Gm₁m₂/r² | g = GM/R²

🌊 Waves