CBSE · Class 12 · Physics

Physics Formula Sheet

72 formulas across 10 chapters — with variables explained and exam tips where needed.

1. Electric Charges and Fields 2. Electrostatic Potential and Capacitance 3. Current Electricity 4. Moving Charges and Magnetism 6. Electromagnetic Induction 7. Alternating Current 9. Ray Optics 10. Wave Optics 11. Dual Nature of Radiation and Matter 12. Atoms and Nuclei

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

💡

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

💡

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

💡

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 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)

💡

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 9Ray Optics(9 formulas)

Snell's Law

n₁ sinθ₁ = n₂ sinθ₂

Mirror Formula

1/f = 1/v + 1/u

💡

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 and Nuclei(7 formulas)

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

Wavelength of spectral line (Rydberg)

1/λ = R[1/n₁² − 1/n₂²]

R = 1.097×10⁷ m⁻¹

Mass-energy equivalence

E = mc²

Radioactive decay law

N = N₀e^(−λt)

λ = decay constant

Half-life

T₁/₂ = 0.693/λ

Binding energy per nucleon

BE/A = Δm × 931.5 MeV/A

Δm = mass defect in u

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