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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...

Class 12 Chemistry – Aldehydes, Ketones & Carboxylic Acids (MCQ Quiz) 50 Most Important Questions • CBSE ⏱ Total Time: 00:00 ⏳ Q Time: 00 s 🎯 Accuracy: 0% Next Explore More 🧭

Class 12 Chemistry – Alcohols, Phenols & Ethers (MCQ Quiz) 50 Most Important Questions • CBSE ⏱ Total Time: 00:00 ⏳ Q Time: 00 s 🎯 Accuracy: 0% Next Explore More 🧭

Class 12 Chemistry – Haloalkanes & Haloarenes (MCQ Quiz) 50 Most Important Questions • CBSE ⏱ Total Time: 00:00 ⏳ Q Time: 00 s 🎯 Accuracy: 0% Next Explore More 🧭

Class 12 Chemistry – d-Block & f-Block Elements (MCQ Quiz) 50 Most Important Questions • CBSE ⏱ Total Time: 00:00 ⏳ Q Time: 00 s 🎯 Accuracy: 0% Next Explore More 🧭

Class 12 Chemistry – Coordination Compounds (MCQ Quiz) 50 Most Important Questions • CBSE ⏱ Total Time: 00:00 ⏳ Q Time: 00 s 🎯 Accuracy: 0% Next Explore More 🧭

Class 12 CBSE  Chemistry – Chemical Kinetics (PYQ MCQ Quiz) 50 Most Important Previous Year Questions • CBSE ⏱ Total Time: 00:00 ⏳ Q Time: 00 s 🎯 Accuracy: 0% Next Explore More 🧭

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...

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 + ...