Coulomb
F = (1/(4πε₀)) (q₁ q₂ / r²)
One sheet · NCERT · Board revision
Class 12 Physics Formula Sheet
76 formulas from Mathematics and Science, chapter by chapter. Search, filter, copy, or print. This is a revision sheet — not a replacement for the textbook derivation.
Practice questions aligned to NCERT topics used in CBSE classrooms. These are original exam-oriented questions for revision — not official CBSE board papers and not a guarantee of any exam question. Always match the textbook issued by your school and the latest PDFs on ncert.nic.in and cbseacademic.nic.in.
⚛️ Class 12 · Physics
Electric Charges and Fields
1/(4πε₀)
9 × 10⁹ N m² C⁻²
Electric field
E = F / q₀ = (1/(4πε₀)) (q / r²)
Dipole field (axial)
E = (1/(4πε₀)) (2p / r³)
Dipole field (equatorial)
E = (1/(4πε₀)) (p / r³)
Torque on dipole
τ = p E sin θ
Gauss’s law
∮ E · dA = Q_enclosed / ε₀
Infinite sheet
E = σ / (2ε₀)
From chapter list
F=q1q2/(4πε0 r²)
⚛️ Class 12 · Physics
Electrostatic Potential and Capacitance
Potential
V = W / q₀ = (1/(4πε₀)) (q / r)
Relation
E = −dV/dr (radial)
Capacitance
C = Q / V
Parallel-plate
C = ε₀ A / d
Series
1/C = 1/C₁ + 1/C₂
Parallel
C = C₁ + C₂
Energy
U = ½ C V² = Q² / (2C)
From chapter list
U=½CV²
⚛️ Class 12 · Physics
Current Electricity
Current
I = q / t = n e v_d A
Ohm (microscopic)
J = σ E
Resistance
R = ρ l / A
EMF and internal r
ε = I (R + r), V = ε − I r
Kirchhoff junction
Σ I = 0
Kirchhoff loop
Σ ε = Σ I R
Wheatstone
P/Q = R/S (balanced)
From chapter list
ε=I(R+r)
⚛️ Class 12 · Physics
Moving Charges and Magnetism
Lorentz force
F = q (v × B) + q E
Force on wire
F = I l B sin θ
Biot–Savart (wire idea)
dB = (μ₀ / 4π) (I dl sinθ / r²)
Long straight wire
B = μ₀ I / (2π r)
Centre of loop
B = μ₀ I / (2R)
Solenoid
B = μ₀ n I
Cyclotron frequency
f = qB / (2π m)
⚛️ Class 12 · Physics
Magnetism and Matter
Bar magnet dipole
B_axial = (μ₀ / 4π) (2M / r³)
Torque
τ = m B sin θ
⚛️ Class 12 · Physics
Electromagnetic Induction
Faraday–Lenz
ε = − dφ_B / dt
Motional emf
ε = B l v (rod on rails)
Self inductance
ε = −L dI/dt, φ = L I
Energy in inductor
U = ½ L I²
From chapter list
ε=−dφB/dt
⚛️ Class 12 · Physics
Alternating Current
RMS
I_rms = I₀ / √2, V_rms = V₀ / √2
Inductive reactance
X_L = ω L = 2π f L
Capacitive reactance
X_C = 1 / (ω C)
Series LCR impedance
Z = √[R² + (X_L − X_C)²]
Resonance
ω₀ = 1 / √(LC)
Power
P = V_rms I_rms cos φ
Transformer
Vₛ / Vₚ = Nₛ / Nₚ = Iₚ / Iₛ (ideal)
From chapter list
XL=ωL; XC=1/ωC
⚛️ Class 12 · Physics
Electromagnetic Waves
Speed
c = 1 / √(μ₀ ε₀) = 3 × 10⁸ m/s
c and fields
c = E₀ / B₀
⚛️ Class 12 · Physics
Ray Optics and Optical Instruments
Mirror / lens formula
1/v − 1/u = 1/f (lens sign convention)
Refraction at spherical surface
n₂/v − n₁/u = (n₂ − n₁)/R
Lens maker
1/f = (n−1)(1/R₁ − 1/R₂)
Prism
μ = sin[(A+δ_m)/2] / sin(A/2)
TIR
i > i_c, sin i_c = 1/μ
Simple microscope
m = 1 + D/f
Telescope (normal)
m = f_o / f_e
From chapter list
1/v−1/u=1/f
⚛️ Class 12 · Physics
Wave Optics
YDSE fringe
β = λ D / d
Path difference (bright)
d sinθ = n λ
Brewster
μ = tan i_p
⚛️ Class 12 · Physics
Dual Nature of Radiation and Matter
Photon energy
E = h ν = hc / λ
Photoelectric
K_max = hν − φ
de Broglie
λ = h / p = h / (mv)
From chapter list
Kmax=hν−φ
⚛️ Class 12 · Physics
Atoms
Bohr radius
rₙ = n² a₀, a₀ ≈ 0.53 Å
Energy levels
Eₙ = −13.6 / n² eV (H-atom)
Wave number
1/λ = R (1/n₁² − 1/n₂²)
From chapter list
En=−13.6/n² eV
⚛️ Class 12 · Physics
Nuclei
Decay law
N = N₀ e^{−λ t}
Half-life
T½ = 0.693 / λ
Mean life
τ = 1 / λ
Mass–energy
E = Δm c²
From chapter list
N=N0 e^{−λt}
⚛️ Class 12 · Physics
Semiconductor Electronics: Materials, Devices and Simple Circuits
NAND / NOR
Universal gates
AND, OR, NOT
Basic Boolean operations as in NCERT truth tables
From chapter list
NAND is universal
Also open
FAQs
Are these all official board formulas?
They are the standard NCERT relations used in CBSE Maths and Science papers. Always match the edition issued by your school.
Why are some Biology items short?
Biology is mostly definitions. Only equations and standard ratios (photosynthesis, Hardy–Weinberg, growth models) sit on this sheet.
Will a formula come as-is in the exam?
Often the paper asks you to use a formula, not recite it. Practise a numerical or a derivation after you memorise the line.