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TGBIE · 2nd Year · MPC & BiPC

Physics — Formula Sheet

Key formulas for TS Intermediate 2nd Year Physics — all 16 chapters as per the TGBIE Annual Plan 2025-26. Most-tested chapters shown with fuller formula sets. Paper: 60 marks · 3 hours.

1.

Waves

  • v = fλ — wave speed, frequency, wavelength relationship
  • T = 1/f — time period
  • Doppler effect (source moving): f′ = f(v ± v_observer)/(v ∓ v_source)
  • Standing wave: y = 2A sin(kx) cos(ωt)
  • Fundamental frequency (string): f = (1/2L)√(T/μ)
  • Beat frequency = |f₁ − f₂|
2.

Ray Optics & Optical Instruments

  • Mirror formula: 1/f = 1/v + 1/u
  • Magnification (mirror): m = −v/u = h′/h
  • Snell's law: n₁ sin i = n₂ sin r; μ = sin i / sin r
  • Lens formula: 1/f = 1/v − 1/u
  • Lens maker's equation: 1/f = (n−1)[1/R₁ − 1/R₂]
  • Prism: n = sin[(A+δₘ)/2] / sin(A/2)
  • Microscope magnification: m = L/f_o × D/f_e
  • Telescope magnification: m = f_o/f_e
3.

Wave Optics

  • Young's double slit — fringe width: β = λD/d
  • Path difference for bright fringe: Δ = nλ (n = 0, ±1, ±2, …)
  • Path difference for dark fringe: Δ = (2n−1)λ/2
  • Diffraction — first minimum: d sin θ = λ
  • Brewster's angle: tan(θ_B) = n
4.

Electrostatics

  • Coulomb's law: F = kq₁q₂/r² where k = 1/(4πε₀) = 9×10⁹ N m²/C²
  • Electric field: E = F/q = kQ/r²
  • Gauss's law: ∮ E·dA = q_enc/ε₀
  • Electric potential: V = kQ/r; potential energy U = kq₁q₂/r
  • Capacitance: C = Q/V; parallel plate: C = ε₀A/d
  • Energy stored: U = ½CV² = Q²/2C
  • Capacitors in series: 1/C = 1/C₁ + 1/C₂ + …
  • Capacitors in parallel: C = C₁ + C₂ + …
6.

Current Electricity

  • Ohm's law: V = IR; Resistivity: R = ρL/A
  • Kirchhoff's laws: ΣI = 0 (junction), ΣV = 0 (loop)
  • Wheatstone bridge balanced: P/Q = R/S
  • Cells in series: E = E₁+E₂, r = r₁+r₂
  • Cells in parallel: 1/r = 1/r₁+1/r₂; E_eff = (E₁/r₁+E₂/r₂)/(1/r₁+1/r₂)
  • Potentiometer: E₁/E₂ = l₁/l₂
7.

Magnetic Effects of Current

  • Biot-Savart law: dB = μ₀I dl sin θ / (4πr²)
  • Field at centre of circular coil: B = μ₀nI / (2R)
  • Straight wire: B = μ₀I / (2πr)
  • Solenoid: B = μ₀nI (n = turns per unit length)
  • Force on current: F = BIL sin θ
  • Lorentz force: F = q(v × B)
  • Radius in magnetic field: r = mv/(qB)
  • Galvanometer to ammeter: S = Ig/(I−Ig) × G
9.

Electromagnetic Induction

  • Faraday's law: ε = −dΦ/dt; Φ = B·A·cos θ
  • Motional EMF: ε = Bvl
  • Self-inductance: ε = −L(dI/dt); L for solenoid = μ₀n²Al
  • Mutual inductance: ε₂ = −M(dI₁/dt)
10.

Alternating Current

  • RMS values: V_rms = V₀/√2; I_rms = I₀/√2
  • Inductive reactance: X_L = ωL; Capacitive reactance: X_C = 1/(ωC)
  • Impedance: Z = √(R² + (X_L−X_C)²)
  • Resonance: ω₀ = 1/√(LC); Q = ω₀L/R
  • Power factor: cos φ = R/Z; P = V_rms I_rms cos φ
  • Transformer: V₁/V₂ = N₁/N₂; I₁/I₂ = N₂/N₁
12.

Dual Nature of Radiation & Matter

  • Photoelectric effect: hν = φ + (½mv²_max)
  • Work function: φ = hν₀ (threshold frequency)
  • de Broglie wavelength: λ = h/mv = h/p
  • Energy of photon: E = hν = hc/λ
  • Stopping potential: eV₀ = ½mv²_max
13.

Atoms & Nuclei

  • Bohr: rₙ = n²a₀ (a₀ = 0.529 Å); Eₙ = −13.6/n² eV
  • Transition energy: ΔE = E_higher − E_lower = hν
  • Hydrogen spectra (Rydberg): 1/λ = R[1/n₁² − 1/n₂²]
  • Mass-energy: E = mc²; Binding energy = Δm × 931.5 MeV/u
  • Radioactive decay: N = N₀e^(−λt); T₁/₂ = 0.693/λ
  • Activity: A = λN
15.

Semiconductor Electronics

  • p-n junction: V₀ = barrier potential (~0.7 V for Si)
  • Transistor: I_E = I_B + I_C; α = I_C/I_E; β = I_C/I_B
  • β = α/(1−α); Voltage gain = β × R_C/R_B
  • Rectifier: V_DC = V_m/π (half-wave); V_DC = 2V_m/π (full-wave)
  • NAND: output = A̅·B̅; NOR: output = A̅+B̅
Important Derivations →All 2nd Year Formula Sheets →