CBSE · Class 12 · Physics

Physics Formula Sheet

97 formulas across 14 chapters — with variables explained and exam tips where needed.

Ch 1Electric Charges and Fields(8 formulas)

Coulomb's Law

F = kq₁q₂/r²

k = 9×10⁹ N·m²/C², q = charge (C), r = distance (m)

Electric Field due to point charge

N/C or V/m

E = kq/r²

q = source charge, r = distance

Electric Flux

N·m²/C

Φ = E·A·cosθ = ∮E·dA

Gauss's Law

N·m²/C

Φ = q_enc/ε₀

ε₀ = 8.85×10⁻¹² C²/N·m²

Electric field of infinite line charge

N/C

E = λ/2πε₀r

λ = linear charge density

Electric field of infinite plane sheet

N/C

E = σ/2ε₀

σ = surface charge density

Electric dipole moment

C·m

p = q × 2l

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Direction: negative to positive charge

Torque on dipole in uniform field

N·m

τ = pE sinθ

Ch 2Electrostatic Potential and Capacitance(9 formulas)

Electric Potential due to point charge

V (Volt)

V = kq/r

Potential energy of system of charges

U = kq₁q₂/r

Work done in moving charge

W = q(V_A − V_B)

Capacitance

F (Farad)

C = Q/V

Capacitance of parallel plate capacitor

C = ε₀A/d

A = plate area, d = plate separation

Capacitors in series

1/C = 1/C₁ + 1/C₂ + 1/C₃

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Total capacitance < smallest individual capacitance

Capacitors in parallel

C = C₁ + C₂ + C₃

Energy stored in capacitor

U = ½CV² = Q²/2C = QV/2

Effect of dielectric on capacitance

C' = KC₀

K = dielectric constant

Ch 3Current Electricity(10 formulas)

Ohm's Law

V = IR

V = voltage (V), I = current (A), R = resistance (Ω)

Resistance

R = ρL/A

ρ = resistivity, L = length, A = area

Resistors in series

R = R₁ + R₂ + R₃

Resistors in parallel

1/R = 1/R₁ + 1/R₂ + 1/R₃

Electric Power

W (Watt)

P = VI = I²R = V²/R

EMF and terminal voltage

V = E − Ir

E = EMF, r = internal resistance, I = current

Kirchhoff's Current Law (KCL)

ΣI_in = ΣI_out (at a junction)

Kirchhoff's Voltage Law (KVL)

ΣV = 0 (around a closed loop)

Wheatstone bridge (balanced)

P/Q = R/S

💡

No current through galvanometer when balanced

Drift velocity

v_d = I/neA

n = number density of electrons, e = 1.6×10⁻¹⁹ C

Ch 4Moving Charges and Magnetism(8 formulas)

Magnetic force on charge (Lorentz)

F = qvB sinθ

Magnetic force on current-carrying wire

F = BIL sinθ

Biot-Savart Law

dB = (μ₀/4π) × Idl sinθ/r²

μ₀ = 4π×10⁻⁷ T·m/A

Magnetic field at centre of circular loop

B = μ₀I/2R

Ampere's Law

∮B·dl = μ₀I_enc

Magnetic field inside solenoid

B = μ₀nI

n = turns per unit length

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Remember: uniform field inside solenoid

Torque on current loop in magnetic field

τ = NIAB sinθ = MB sinθ

M = NIA = magnetic moment

Radius of circular motion in magnetic field

r = mv/qB

Ch 5Magnetism and Matter(6 formulas)

Magnetic dipole moment

A·m²

M = m × 2l

m = pole strength, 2l = magnetic length

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Direction: S-pole to N-pole inside magnet

Torque on magnetic dipole

N·m

τ = MB sinθ

M = magnetic moment, B = external field, θ = angle between M and B

Potential energy of dipole

U = −MB cosθ

Axial field of bar magnet (short magnet)

B_axial = (μ₀/4π) × 2M/r³

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Qualitative treatment only in exam — direction along M

Equatorial field of bar magnet (short magnet)

B_eq = (μ₀/4π) × M/r³

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Direction opposite to M

Curie's Law

χ_m = C/T

C = Curie constant, T = absolute temperature

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For paramagnetic materials only; ferromagnetics lose magnetism above Curie temperature

Ch 6Electromagnetic Induction(6 formulas)

Magnetic Flux

Weber (Wb)

Φ = BA cosθ

Faraday's Law of EMF

ε = −dΦ/dt = −N(dΦ/dt)

Motional EMF

ε = Blv

B = field, l = length, v = velocity

Self-inductance

H (Henry)

ε = −L(dI/dt)

Mutual inductance

ε₂ = −M(dI₁/dt)

Energy stored in inductor

U = ½LI²

Ch 7Alternating Current(7 formulas)

RMS value of AC

I_rms = I₀/√2 | V_rms = V₀/√2

Inductive reactance

X_L = ωL = 2πfL

Capacitive reactance

X_C = 1/ωC = 1/2πfC

Impedance of LCR circuit

Z = √(R² + (X_L − X_C)²)

Resonant frequency

f₀ = 1/2π√(LC)

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At resonance: Z = R (minimum impedance)

Power in AC circuit

P = V_rms × I_rms × cosφ

cosφ = power factor

Transformer voltage ratio

V_s/V_p = N_s/N_p = I_p/I_s

Ch 8Electromagnetic Waves(4 formulas)

Speed of EM wave in vacuum

c = 1/√(μ₀ε₀) = 3×10⁸ m/s

Relationship: wavelength, frequency, speed

c = fλ

f = frequency, λ = wavelength

Displacement current

I_d = ε₀ × dΦ_E/dt

Φ_E = electric flux

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Maxwell added this to make Ampere's law consistent

EM spectrum order (increasing frequency)

Radio → Microwave → IR → Visible → UV → X-ray → γ-ray

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Visible range: 400 nm (violet) to 700 nm (red)

Ch 9Ray Optics(9 formulas)

Snell's Law

n₁ sinθ₁ = n₂ sinθ₂

Mirror Formula

1/f = 1/v + 1/u

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Use sign convention: distances measured from pole

Magnification (mirror)

m = −v/u = h'/h

Lens Formula

1/f = 1/v − 1/u

Lens Maker's Formula

1/f = (n−1)[1/R₁ − 1/R₂]

Magnification (lens)

m = v/u

Power of lens

Dioptre (D)

P = 1/f (in metres)

Critical angle

sinθ_c = n₂/n₁ = 1/n (if n₂ = 1)

Prism formula

n = sin[(A+δ_m)/2] / sin(A/2)

A = prism angle, δ_m = minimum deviation

Ch 10Wave Optics(4 formulas)

Condition for bright fringes (YDSE)

y_n = nλD/d

D = screen distance, d = slit separation

Fringe width

β = λD/d

Condition for dark fringes

y_n = (2n−1)λD/2d

Resolving power of telescope

θ = 1.22λ/D

D = aperture diameter

Ch 11Dual Nature of Radiation and Matter(4 formulas)

Photoelectric equation (Einstein)

KE_max = hf − φ = hf − hf₀

h = 6.626×10⁻³⁴ J·s, φ = work function

de Broglie wavelength

λ = h/mv = h/p

p = momentum

Threshold frequency

f₀ = φ/h

Stopping potential

eV₀ = KE_max = hf − φ

Ch 12Atoms(5 formulas)

Bohr's quantisation condition

mvr_n = nh/2π

n = orbit number, h = 6.626×10⁻³⁴ J·s

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Angular momentum is quantised in multiples of h/2π

Radius of Bohr orbit

r_n = n²a₀/Z

a₀ = 0.529 Å, Z = atomic number, n = orbit number

Energy of Bohr orbit (Hydrogen)

E_n = −13.6/n² eV

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Total energy is negative (bound state); KE = |E_n|, PE = 2E_n

Wavelength of spectral line (Rydberg)

1/λ = R[1/n₁² − 1/n₂²]

R = 1.097×10⁷ m⁻¹, n₂ > n₁

Distance of closest approach (α-scattering)

r₀ = k·(2e)(Ze)/KE_α = 2kZe²/(½mv²)

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All KE of α-particle converts to electrostatic PE at this point

Ch 13Nuclei(9 formulas)

Nuclear radius

R = R₀A^(1/3)

R₀ = 1.2×10⁻¹⁵ m = 1.2 fm, A = mass number

Mass defect

Δm = [Z·m_p + (A−Z)·m_n] − M_nucleus

Binding energy

BE = Δm × 931.5 MeV (when Δm in u)

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Higher BE/A → more stable nucleus; Fe-56 has highest BE/A ≈ 8.8 MeV

Binding energy per nucleon

BE/A = Δm × 931.5/A MeV per nucleon

Mass-energy equivalence

E = mc²

1 u = 931.5 MeV/c²

Radioactive decay law

N = N₀e^(−λt)

λ = decay constant (s⁻¹)

Activity

Becquerel (Bq) = 1 decay/s; 1 Curie = 3.7×10¹⁰ Bq

A = λN = A₀e^(−λt)

Half-life

T₁/₂ = 0.693/λ

Mean life

τ = 1/λ = 1.44 T₁/₂

Ch 14Semiconductor Electronics(8 formulas)

Mass action law

n_e × n_h = nᵢ²

nᵢ = intrinsic carrier concentration

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n-type: n_e >> n_h (electrons majority); p-type: n_h >> n_e (holes majority)

Half-wave rectifier output

V_dc = V_m/π | I_dc = I_m/π

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Only one half cycle used; efficiency ≈ 40.6%

Full-wave rectifier output

V_dc = 2V_m/π | I_dc = 2I_m/π

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Both half cycles used; efficiency ≈ 81.2%

Transistor current relation

I_E = I_B + I_C

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Emitter current splits into base and collector currents

Current gain α (common base)

α = I_C/I_E

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α < 1 (typically 0.95–0.99)

Current gain β (common emitter)

β = I_C/I_B

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β >> 1 (typically 20–200); most common transistor configuration

Relation between α and β

β = α/(1−α) | α = β/(1+β)

Voltage gain (CE amplifier)

A_V = −β(R_C/R_in)

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Negative sign indicates 180° phase inversion in CE configuration

More for CBSE Class 12

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Physics Formula Sheet — Class 12