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Alternating Current (AC) – Complete Formula Framework (JEE Mains) Phasors | Impedance | Resonance | Power | PYQ Mapping 1️⃣ AC Basics Alternating current: \[ i = I_0 \sin \omega t \] Peak current = \( I_0 \) Angular frequency = \( \omega = 2\pi f \) Time period = \( T = \frac{2\pi}{\omega} \) RMS value: \[ I_{rms} = \frac{I_0}{\sqrt{2}} \] \[ V_{rms} = \frac{V_0}{\sqrt{2}} \] ⚠ Mains Trap: Household voltage is RMS, not peak. 2️⃣ AC through Pure Resistor Voltage & current in phase \[ V = IR \] Power: \[ P = V_{rms} I_{rms} \] Phase angle: \[ \phi = 0 \] 3️⃣ AC through Pure Inductor Inductive reactance: \[ X_L = \omega L \] Current: \[ I = \frac{V}{X_L} \] Phase: \[ \phi = +90^\circ \] Voltage leads current. 4️⃣ AC through Pure Capacitor Capacitive reactance: \[ X_C = \frac{1}{\omega C} \] Current: \[ I = \frac{V}{X_C} \] Phase: \[ \phi = -90^\circ \] Current leads voltage. 5️⃣ RLC Series Circuit Imped...

Waves – Complete Formula Revision          (JEE Mains) Every Formula | Every Trap | PYQ Mapping 1️⃣ Basic Wave Parameters Wave equation: \[ y(x,t) = A \sin(kx - \omega t + \phi) \] Amplitude = \( A \) Angular frequency = \( \omega = 2\pi f \) Wave number = \( k = \frac{2\pi}{\lambda} \) Wave speed = \( v = \frac{\omega}{k} \) Also: \( v = f\lambda \) ⚠ Trap: Sign in wave equation decides direction. 2️⃣ Speed of Transverse Wave on String \[ v = \sqrt{\frac{T}{\mu}} \] T = tension \( \mu = \frac{m}{L} \) (linear density) ⚠ Increasing tension increases speed, but frequency remains constant. 3️⃣ Longitudinal Sound Waves Speed in medium: \[ v = \sqrt{\frac{B}{\rho}} \] B = Bulk modulus \( \rho \) = density For gas: \[ v = \sqrt{\frac{\gamma P}{\rho}} \] ⚠ Trap: Speed independent of frequency. 4️⃣ Principle of Superposition Resultant displacement: \[ y = y_1 + y_2 \] Resultant amplitude: ...

GRAVITATION — Complete JEE Mains Revision.  Every Formula | Every Trap | Every Mains Question Type 1. Universal Law of Gravitation Newton’s Law: $$ F = G \frac{m_1 m_2}{r^2} $$ G = $6.67 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2$ Key Results Force ∝ product of masses Force ∝ 1 / r² (inverse square) Force always attractive Vector Form: $$ \vec{F} = - G \frac{m_1 m_2}{r^2} \hat{r} $$ Mains Trap: Distance is center-to-center, NOT surface distance. 2. Gravitational Field & Acceleration Due to Gravity Field Definition: $$ g = \frac{F}{m} $$ For planet of mass M: $$ g = \frac{GM}{R^2} $$ Variation with height (h): $$ g_h = \frac{GM}{(R+h)^2} $$ For small h: $$ g_h = g \left(1 - \frac{2h}{R}\right) $$ Variation with depth (d): $$ g_d = g \left(1 - \frac{d}{R}\right) $$ Mains Trap: g decreases linearly with depth but inverse square with height. 3. Gravitational Potential & Potential Energy Potential: $$ V = -\frac{...

Moving Charges & Magnetism — StudyBeacon 1️⃣ Magnetic Force on a Moving Charge Lorentz Force: $$\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$$ In pure magnetic field: $$F = qvB\sin\theta$$ Special Cases: θ = 0° → F = 0 θ = 90° → F = qvB (maximum) Circular Motion: $$qvB = \frac{mv^2}{r}$$ $$r = \frac{mv}{qB}$$ $$T = \frac{2\pi m}{qB}$$ $$f = \frac{qB}{2\pi m}$$ ⚠ Trap: Frequency is independent of velocity. --- 2️⃣ Helical Motion If velocity has components: $$v_\parallel = v\cos\theta$$ $$v_\perp = v\sin\theta$$ Radius: $$r = \frac{mv_\perp}{qB}$$ Pitch: $$p = v_\parallel T$$ --- 3️⃣ Magnetic Force on Current Carrying Conductor $$\vec{F} = I \vec{L} \times \vec{B}$$ Magnitude: $$F = ILB\sin\theta$$ For parallel wires: $$\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d}$$ ⚠ Same direction currents → Attraction ⚠ Opposite → Repulsion --- 4️⃣ Biot–Savart Law $$dB = \frac{\mu_0}{4\pi}\frac{Idl\sin\theta}{r^2}$$ Circular loo...

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...

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...

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...

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...

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 ...

  Electrochemistry – Complete Formula Sheet (JEE Main Only) 1. Electrochemical (Galvanic) Cell Oxidation → Anode (−) Reduction → Cathode (+) Electron flow: Anode → Cathode Cell Representation: Anode | Anode electrolyte || Cathode electrolyte | Cathode Zn | Zn²⁺ || Cu²⁺ | Cu 2. Electrode Potential & Electrochemical Series Standard Hydrogen Electrode (SHE): H⁺(1M) | H₂(1 atm) | Pt(s) E° = 0 V More +ve SRP → Strong oxidising agent More −ve SRP → Strong reducing agent Low SRP metals → Highly reactive 3. EMF of a Cell Formula: E° cell = E° cathode − E° anode E cell = RP cathode + OP anode Spontaneity: E° cell > 0 → Spontaneous E° cell < 0 → Non-spontaneous 4. Nernst Equation E cell = E° cell − (0.0591 / n) log Q Example: Zn | Zn²⁺ || Cu²⁺ | Cu E cell = E° cell − (0.0591 / 2) log ([Zn²⁺]/[Cu²⁺]) 5. Relation between EMF, ΔG & Kc ΔG° = −nF E° cell E° cell = (0.0591 / n) log K c Condition Infer...

    Modern Physics – Complete & Elaborated Revision (JEE Main) Modern Physics explains physical phenomena where classical physics fails. In JEE Main, this chapter is highly scoring because questions are formula-driven but concept-sensitive . A small misunderstanding leads to a wrong option. 1. Dual Nature of Radiation and Matter Experiments like the photoelectric effect proved that light behaves not only as a wave, but also as a stream of particles called photons . Similarly, matter particles also show wave nature. (A) Photoelectric Effect When light of sufficiently high frequency falls on a metal surface, electrons are emitted instantaneously. This phenomenon cannot be explained using wave theory alone. Einstein’s Photoelectric Equation: $h\nu = \phi + K_{\max}$ Here, $h\nu$ is photon energy, $\phi$ is work function of metal, and $K_{\max}$ is maximum kinetic energy of emitted electrons. Important derived relations: $K_{\max} = h\nu - \p...

  Ionic Equilibrium – Complete Formula & Concept Sheet (JEE Main + Advanced) Ionic equilibrium deals with reversible ionisation in aqueous solutions . This chapter merges equilibrium, logarithms, and electrostatics of ions . 1. Electrolytes Strong electrolytes: Complete ionisation (HCl, NaOH) Weak electrolytes: Partial ionisation (CH₃COOH, NH₄OH) Trap: Strong electrolyte ≠ concentrated, weak electrolyte ≠ dilute 2. Ionisation of Water H₂O ⇌ H⁺ + OH⁻ K w = [H⁺][OH⁻] = 1.0 × 10 −14 (at 25°C) Pure water: [H⁺] = [OH⁻] = 10 −7 M Neutral ≠ pH 7 at all temperatures 3. pH, pOH and Scale pH = −log[H⁺] pOH = −log[OH⁻] pH + pOH = 14 (at 25°C) Classic Trap: Log values must be approximated correctly (10⁻⁵.⁶ ≠ 4×10⁻⁶) 4. Weak Acids (Ka) For a weak acid HA: HA ⇌ H⁺ + A⁻ K a = [H⁺][A⁻] / [HA] If initial concentration = C and degree of ionisation = α: K a = Cα² / (1 − α) ≈ Cα² (if α ≪ 1) [H⁺] = √(K a · C) 5. Weak Bases...

  Chemical Equilibrium – Complete Formula & Concept Sheet (JEE Main + Advanced) Chemical equilibrium deals with reversible reactions where forward and backward reaction rates become equal. Equilibrium is dynamic , not static. 1. Law of Mass Action For a general reaction: aA + bB ⇌ cC + dD The equilibrium constant: K c = [C] c [D] d / [A] a [B] b Only concentration of gases and solutes appear Pure solids and liquids are omitted 2. Equilibrium Constant K c and K p For gaseous reactions: K p = K c (RT) Δn where Δn = (moles of gaseous products − moles of gaseous reactants) Trap: Δn counts only gases, not solids or liquids. 3. Reaction Quotient (Q) Same expression as K c , but using initial concentrations . Q < K → Reaction proceeds forward Q > K → Reaction proceeds backward Q = K → System at equilibrium 4. Characteristics of Chemical Equilibrium Equilibrium can be achieved from either side Equilibrium consta...

  Atomic Structure – Complete Conceptual & Numerical Revision Atomic Structure explains why atoms behave the way they do. JEE doesn’t test history — it tests quantization, wave–particle duality, hydrogen spectrum logic, and hidden unit traps . 1. Fundamental Picture of Atom Atom consists of nucleus (protons + neutrons) surrounded by electrons. Classical physics fails → quantum concepts required. Key Idea: Electron does NOT move in a classical orbit — it exists as a probability wave 2. Photoelectric Effect (Concept + Formula) When light of frequency ≥ threshold frequency strikes a metal, electrons are ejected. $E = h\nu$ $h\nu = h\nu_0 + KE_{max}$ $KE_{max} = \frac{1}{2}mv^2 = h(\nu - \nu_0)$ JEE Trap: Intensity affects number of electrons, NOT their kinetic energy 3. Dual Nature of Matter (de Broglie) Every moving particle behaves like a wave. $\lambda = \dfrac{h}{p} = \dfrac{h}{mv}$ $\lambda = \dfrac{h}{\sqrt{2mKE}}$ Trap: El...

  Mole Concept – Complete Quantitative Chemistry Revision The Mole Concept is the backbone of Physical Chemistry. Almost every numerical problem in chemistry starts or ends here. JEE tests this chapter through unit conversion, limiting reagent logic, stoichiometry, and concentration traps . 1. Fundamental Definitions Mole: Amount of substance containing $6.022 \times 10^{23}$ entities Avogadro Number: $N_A = 6.022 \times 10^{23} \, mol^{-1}$ Molar Mass: Mass of 1 mole of a substance (in g/mol) Golden Relation: $\text{Moles} = \dfrac{\text{Given quantity}}{\text{Molar mass}}$ 2. Mole – Particle – Mass Relations $\text{Number of particles} = n \times N_A$ $n = \dfrac{w}{M}$ JEE Trap: Atoms vs molecules vs ions — always check entity asked 3. Mole Concept in Gases Molar Volume (STP): $1 \text{ mole gas} = 22.4 \, L \; (STP)$ $n = \dfrac{V}{22.4} \quad (STP)$ Using Ideal Gas Equation: $PV = nRT$ Trap: STP vs RTP confusion ...

  Hydrocarbons – Complete NCERT Revision (Reactions + Mechanisms) Hydrocarbons are organic compounds containing only carbon and hydrogen. This chapter is heavily tested in JEE Main via reactions and in Advanced via mechanisms & exceptions. 1. Alkanes (Paraffins) General formula: $C_nH_{2n+2}$ Hybridisation: $sp^3$ (tetrahedral, $109.5^\circ$) Preparation of Alkanes Wurtz Reaction: $2R–X + 2Na \rightarrow R–R + 2NaX$ Limitation: Mixture with different alkyl halides

    Circular Motion – Complete Formula & Concept Revision Circular motion refers to motion of a particle along a circular path. Although speed may remain constant, velocity always changes due to continuous change in direction. 1. Angular Quantities Angular displacement: $\theta$ (radians) Angular velocity: $\omega = \dfrac{d\theta}{dt}$ Angular acceleration: $\alpha = \dfrac{d\omega}{dt}$ Relation with linear quantities: $v = r\omega$ $a_t = r\alpha$ $a_c = r\omega^2 = \dfrac{v^2}{r}$ 2. Time Period & Frequency Time period: $T = \dfrac{2\pi}{\omega}$ Frequency: $f = \dfrac{1}{T}$ $\omega = 2\pi f$ 3. Centripetal Acceleration $a_c = \dfrac{v^2}{r} = r\omega^2$ Always directed toward centre Changes direction of velocity, not magnitude Trap: Zero centripetal acceleration means no circular motion. 4. Non-Uniform Circular Motion Acceleration has two components: Centripetal: $a_c = \dfrac{v^2}{r}$ Tangential: $a_t = \dfr...

    Work, Energy and Power – Complete JEE Revision This chapter connects force and motion through energy. JEE loves testing signs, reference frames, variable forces, and conservation traps . 1. Work (a) Work by Constant Force $W = \vec{F}\cdot\vec{s} = Fs\cos\theta$ Work depends on the component of force along displacement . $\theta=0^\circ$ → Maximum work $\theta=90^\circ$ → Zero work (centripetal force) $\theta=180^\circ$ → Negative work (b) Variable Force $W = \int \vec{F}\cdot d\vec{r}$ Work equals area under F–x graph . 2. Special Forces & Work Gravity: Conservative → path independent Friction: Non-conservative → path dependent Normal force: Usually zero work Centripetal force: Always zero work 3. Kinetic Energy (KE) $K = \frac{1}{2}mv^2$ Work–Energy Theorem Net work done = Change in kinetic energy $W_{\text{net}} = \Delta K$ Applies even when forces are complicated. 4. Potential Energy (PE) (a) Gr...