Chapter-Wise Key Concepts

Physics - Class 12th Key Concepts

⚡

Electric Charges and Fields

Fundamental concepts of electrostatics

📋 Essential Formulas

F = kq₁q₂/r² (Coulomb's Law)
E = F/q = kQ/r² (Electric Field)
k = 9 × 10⁹ Nm²/C²
ε₀ = 8.85 × 10⁻¹² C²/Nm²
E (dipole, axial) = 2kp/r³

💡 Important Points

✓ Like charges repel, unlike charges attract
✓ Electric field is a vector quantity
✓ Field lines never intersect
✓ Charge is quantized: q = ne
✓ Inside conductor: E = 0
✓ Gauss's Law: φ = q/ε₀

🔌

Electrostatic Potential and Capacitance

Potential energy and capacitors

📋 Essential Formulas

V = kQ/r (Potential)
W = q(V₂ - V₁) (Work Done)
C = Q/V (Capacitance)
C = ε₀A/d (Parallel Plate)
U = ½CV² = ½QV (Energy)

💡 Important Points

✓ Potential is scalar (no direction)
✓ V at infinity = 0 (reference)
✓ Series: 1/C = 1/C₁ + 1/C₂
✓ Parallel: C = C₁ + C₂
✓ Dielectric increases capacitance
✓ Energy density: u = ½ε₀E²

🧲

Current Electricity

Ohm's law, circuits, and resistance

📋 Essential Formulas

V = IR (Ohm's Law)
R = ρL/A (Resistance)
P = VI = I²R = V²/R (Power)
Series: R = R₁ + R₂ + ...
Parallel: 1/R = 1/R₁ + 1/R₂

💡 Important Points

✓ Current: I = Q/t (charge flow)
✓ Drift velocity: v_d = I/(neA)
✓ Kirchhoff's Current Law: ΣI = 0
✓ Kirchhoff's Voltage Law: ΣV = 0
✓ Internal resistance: V = E - Ir
✓ Wheatstone bridge condition

Chemistry - Class 12th Key Concepts

🧪

Solutions

Concentration, colligative properties

📋 Essential Formulas

M = moles/L (Molarity)
m = moles/kg (Molality)
P = P°χ (Raoult's Law)
ΔT_b = iK_b m (Boiling Point)
π = iCRT (Osmotic Pressure)

💡 Important Points

✓ Mole fraction: χ = n/(n_total)
✓ van't Hoff factor: i = actual/formula
✓ Ideal solution: ΔH_mix = 0
✓ Henry's Law: p = K_H × χ
✓ Freezing point depression
✓ Reverse osmosis for purification

⚗️

Electrochemistry

Cells, electrolysis, and conductance

📋 Essential Formulas

E°_cell = E°_cathode - E°_anode
E = E° - (0.059/n)log Q (Nernst)
ΔG° = -nFE° (Gibbs energy)
m = ZIt = (M×I×t)/(nF) (Faraday)
κ = 1/ρ (Conductivity)

💡 Important Points

✓ SHE: Standard Hydrogen Electrode = 0V
✓ Anode: oxidation, Cathode: reduction
✓ F = 96500 C/mol (Faraday constant)
✓ Salt bridge maintains neutrality
✓ Kohlrausch's Law for Λ°_m
✓ Batteries: Primary vs Secondary

Mathematics - Class 12th Key Concepts

📊

Relations and Functions

Types of functions and their properties

📋 Essential Formulas

f: A → B (function notation)
Domain, Codomain, Range
Composite: (fog)(x) = f(g(x))
Inverse: f⁻¹(f(x)) = x
Binary operations properties

💡 Important Points

✓ One-One (Injective) function
✓ Onto (Surjective) function
✓ Bijective = One-One + Onto
✓ Equivalence relation properties
✓ Identity and inverse elements
✓ Function types: polynomial, trig, etc.

📈

Calculus - Differentiation

Derivatives, rates of change, maxima-minima

📋 Essential Formulas

d/dx(xⁿ) = nxⁿ⁻¹
d/dx(sin x) = cos x
d/dx(eˣ) = eˣ
d/dx(ln x) = 1/x
Product: (uv)' = u'v + uv'

💡 Important Points

✓ Chain Rule: dy/dx = (dy/du)(du/dx)
✓ Quotient Rule: (u/v)' = (u'v-uv')/v²
✓ Critical points: f'(x) = 0
✓ Maxima: f'(x)=0, f''(x) < 0
✓ Minima: f'(x)=0, f''(x) > 0
✓ Mean Value Theorem

∫

Calculus - Integration

Indefinite and definite integrals

📋 Essential Formulas

∫xⁿdx = xⁿ⁺¹/(n+1) + C
∫cos x dx = sin x + C
∫eˣdx = eˣ + C
∫1/x dx = ln|x| + C
By Parts: ∫udv = uv - ∫vdu

💡 Important Points

✓ ILATE rule for integration by parts
✓ Substitution method: put t = g(x)
✓ Definite: ∫ₐᵇf(x)dx = F(b) - F(a)
✓ Property: ∫₀ᵃf(x)dx = ∫₀ᵃf(a-x)dx
✓ Area under curve formula
✓ Volume by rotation