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Current Electricity – Complete Formula, Laws & PYQ Profiling

Current Electricity – Complete Formula, Laws & PYQ Profiling (JEE Main Only) 1. Electric Current & Drift Velocity Electric current: I = Q / t Current density: J = nqv d Drift velocity: v d = eEτ / m Relation: I = nAev d Mobility: μ = v d / E Conductivity: σ = nqμ Resistivity: ρ = 1 / σ JEE Trap: Drift velocity is extremely small, but electrical signal propagates almost at speed of light. 2. Ohm’s Law & Resistance Ohm’s law: V = IR Resistance: R = ρL / A Temperature dependence: R = R₀(1 + αΔT) Combination of resistors: Series: R eq = R₁ + R₂ + … Parallel: 1/R eq = 1/R₁ + 1/R₂ + … PYQ Trap: For same material & volume, R ∝ L² (since A ∝ 1/L). 3. Electric Power & Heating Effect P = VI = I²R = V² / R Electrical energy: E = Pt Joule’s law of heating: H = I²Rt 4. EMF & Internal Resistance Terminal voltage (discharging): V = E − Ir Terminal voltage (charging): V = E + Ir Current: I = E / (R + r) M...
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Capacitors – Complete Formula, Traps & Question Profiling

Capacitors – Complete Formula, Traps & Question Profiling (JEE Main Only) 1. Basic Concept of Capacitor Capacitor: Device to store electric charge Consists of two conductors separated by dielectric C = Q / V SI unit → Farad (F) 1 μF = 10⁻⁶ F 2. Parallel Plate Capacitor C = ε₀ A / d A → area of plates d → separation With dielectric (k): C = k ε₀ A / d 3. Effect of Dielectric Capacitance increases k times Electric field reduces: E = E₀ / k Potential reduces: V = V₀ / k Dielectric constant: k = ε / ε₀ 4. Series & Parallel Combination Series: 1/C eq = 1/C₁ + 1/C₂ + ... Charge same on each capacitor V distributes Parallel: C eq = C₁ + C₂ + ... Potential same Charge distributes 5. Energy Stored in Capacitor U = ½ C V² U = Q² / (2C) U = ½ QV Energy density: u = ½ ε E² 6. Capacitor with Battery Connected / Disconnected Battery connected: V constant Q increases with dielectric Energy increas...
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Oscillations – Complete Formula & Question Profiling

Oscillations – Complete Formula & Question Profiling (JEE Main Only) 1. Periodic & Oscillatory Motion Periodic motion: Repeats itself after equal intervals of time Oscillatory motion: To-and-fro about mean position All oscillatory motions are periodic (not vice-versa) 2. Simple Harmonic Motion (SHM) Defining condition: a ∝ −x a = −ω²x Restoring force always towards mean position 3. SHM Kinematics Displacement: x = A sin(ωt + φ) Velocity: v = ω√(A² − x²) Acceleration: a = −ω²x Maximum values: v max = ωA a max = ω²A 4. Time Period & Frequency T = 2π / ω f = 1 / T Independent of amplitude (for SHM) 5. Mass–Spring System ω = √(k / m) T = 2π√(m / k) Horizontal and vertical springs → same T Extension due to gravity does not affect T 6. Simple Pendulum T = 2π√(l / g) Valid for small angular displacement Independent of mass Effective length change: In lift accelerating upward → g' = g + ...
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Mechanical Properties of Fluids – Complete Formula Sheet physics

Mechanical Properties of Fluids – Complete Formula Sheet (JEE Main Only) 1. Basic Definitions Fluid: Substance that can flow (liquids + gases) Density (ρ): Mass / Volume Relative density: Density of substance / Density of water ρ = m / V 2. Pressure in Fluids Pressure: P = F / A Pressure at depth h: P = P₀ + ρgh Independent of container shape Same at same depth 3. Pascal’s Law Pressure applied to confined fluid is transmitted equally Hydraulic lift: F₂ / F₁ = A₂ / A₁ 4. Buoyancy & Archimedes’ Principle Buoyant force: F B = ρ fluid g V displaced Acts vertically upward Independent of depth 5. Floatation Conditions Floating body: Weight = Buoyant force Fraction submerged = ρ body / ρ fluid Apparent weight: W apparent = mg − F B 6. Continuity Equation A₁v₁ = A₂v₂ Valid for incompressible fluids Velocity ↑ when area ↓ 7. Bernoulli’s Theorem P + ½ρv² + ρgh = constant Valid for steady, incompressi...
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Thermal Properties of Matter – Complete Formula Sheet

Thermal Properties of Matter – Complete Formula Sheet (JEE Main Only) 1. Temperature & Heat Temperature: Measure of degree of hotness Heat: Energy transferred due to temperature difference Heat always flows: Higher T → Lower T SI unit of heat: Joule (J) 2. Temperature Scales K = °C + 273 °C = (5/9)(°F − 32) Zero points: 0 K → Absolute zero Triple point of water = 273.16 K 3. Thermal Expansion (a) Linear Expansion ΔL = α L ΔT (b) Areal Expansion ΔA = β A ΔT    (β = 2α) (c) Volume Expansion ΔV = γ V ΔT    (γ = 3α) 4. Expansion of Solids – PYQ Traps Hole expands as if material absent α is same in all directions (isotropic solid) If expansion prevented → thermal stress develops Thermal stress: σ = Y α ΔT 5. Calorimetry Heat absorbed/released: Q = m c ΔT c → specific heat capacity Water has maximum specific heat Principle: Heat lost = Heat gained 6. Latent Heat Q = m L L → latent heat Temper...
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Mechanical Properties of Solids – Complete Formula Sheet

Mechanical Properties of Solids – Complete Formula Sheet (JEE Main Only) 1. Elasticity – Basic Terms Stress (σ) = Force / Area Strain (ε) = Change / Original dimension Elastic limit → Max stress up to which Hooke’s law holds Plastic region → Permanent deformation σ = F / A ε = ΔL / L 2. Types of Stress & Strain Longitudinal stress (Tensile / Compressive) Shearing stress Bulk stress Longitudinal strain = ΔL / L Shear strain = θ (radian) Volumetric strain = ΔV / V 3. Hooke’s Law Stress ∝ Strain σ = Yε τ = Gθ P = K(ΔV / V) 4. Elastic Moduli Young’s Modulus: Y = (FL) / (AΔL) Bulk Modulus: K = −P / (ΔV / V) Shear Modulus: G = τ / θ 5. Poisson’s Ratio μ = Lateral strain / Longitudinal strain −1 ≤ μ ≤ 0.5 Rubber → μ ≈ 0.5 6. Relations between Elastic Constants Y = 2G(1 + μ) Y = 3K(1 − 2μ) G = Y / [2(1 + μ)] K = Y / [3(1 − 2μ)] 7. Stress–Strain Curve Proportional limit Elastic limit Yield point Ultimate tensile stress ...
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50 Most Repeated Physics MCQs: Class 12 CBSE

  50 Most Repeated Physics MCQs: Class 12 CBSE Solved & Optimized for Board Exams 2026 प्रबंधक की सूचना (Manager's Note): All questions follow the latest CBSE MCQ pattern. Click the "Solution" dropdown to check your accuracy. Unit 1: Electrostatics & Current Electricity Q1. A dipole is placed in a uniform electric field. It experiences: (a) Force only (b) Torque only (c) Both force and torque (d) Neither force nor torque उत्तर (Solution) Ans: (b) Torque only. In a uniform field, net force is zero ($qE - qE$), but since the forces act at different points, they produce torque. Q2. If the distance between two charges is doubled, the electrostatic force becomes: (a) 1/2 times (b) 2 times (c) 1/4 times (d) 4 times उत्तर (Solution) Ans: (c) 1/4 times. $F \propto 1/r^2$. So, doubling $r$ makes $F$ one-fourth. Q3. Which of th...
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CBSE Class 12 Science: 3-Year Weightage & Trend Analysis (2024-2026)

  CBSE Class 12 Science: 3-Year Weightage & Trend Analysis (2024-2026) A Detailed Comparison of Physics, Chemistry, Biology & Maths Marking Schemes सामग्री की तालिका (Table of Contents): 1. प्रमुख रुझान और परिवर्तन (Key Trends & Changes) 2. भौतिकी: 3-वर्षीय तुलना (Physics Comparison) 3. रसायन विज्ञान डेटा (Chemistry Data) 4. परीक्षा पैटर्न में बदलाव (Exam Pattern Shift) 1. The Strategic Shift: 2024 vs 2026 Over the last three years, CBSE has moved away from rote memorization. In 2024 , direct questions and derivations dominated. By 2026 , "Competency-Based Questions" (Case Studies and MCQs) have increased to 50% of the total weightage. This means students must now focus on application rather than just definitions. 2. Physics (Theory - 70 Marks): 3-Year Mark Distribution Unit Name ...
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