OMTEX AD 2

12th HSC Physics Formula Sheet (Maharashtra Board)

12th HSC Physics Formula Sheet (Maharashtra Board)

12th HSC Physics Formula Sheet (Maharashtra Board)

Comprehensive formula list for Semester 1 and Semester 2 prepared for quick revision.

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Semester 1

Rotational Dynamics

(i) Torque: \(\tau = \vec{r} \times \vec{F} = rF \sin\theta\)
(ii) Moment of inertia (I): \(I = \sum mr^2\)
(iii) Angular momentum: \(L = I\omega\)
(iv) Rotational Kinetic Energy: \(KE = \frac{1}{2} I \omega^2\)
(v) Torque and Angular acceleration: \(\tau = I\alpha\)
(vi) Rolling motion (without slipping): \(v = r\omega, \quad a = r\alpha\)
(vii) Parallel Axis Theorem: \(I_o = I_{cm} + Md^2\)
(viii) Perpendicular Axis Theorem: \(I_z = I_x + I_y\)

Mechanical Properties of Fluids

(i) Pressure: \(P = F / A\)
(ii) Buoyant Force: \(F_b = \rho gV\)
(iii) Equation of continuity: \(A_1 v_1 = A_2 v_2\)
(iv) Bernoulli's Equation: \(P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}\)
(v) Viscous Force (Stokes Law): \(F = 6\pi \eta rv\)

Kinetic Theory & Radiation

(i) Pressure: \(P = \frac{1}{3}\rho c^2\)
(ii) Avg. K.E.: \(E_k = \frac{3}{2}kT\)
(iii) RMS speed: \(v_{rms} = \sqrt{\frac{3kT}{m}} = \sqrt{\frac{3RT}{M}}\)
(iv) Stefan's Law: \(E = \sigma T^4\)
(v) Newton's Law of Cooling: \(\frac{dT}{dt} \propto (T - T_{sur})\)

Thermodynamics

(i) First Law: \(dQ = dU + dW\)
(ii) Isothermal Work: \(W = nRT \ln(V_f/V_i)\)
(iii) Adiabatic Work: \(W = \frac{P_i V_i - P_f V_f}{\gamma - 1}\)
(iv) Adiabatic Eqn: \(PV^\gamma = \text{constant}\)
(v) Carnot Efficiency: \(\eta = 1 - \frac{T_c}{T_h}\)

Oscillations

(i) Acceleration: \(a = -\omega^2 x\)
(ii) Displacement: \(x = A \sin(\omega t + \phi)\)
(iii) Velocity: \(v = \omega \sqrt{A^2 - x^2}\)
(iv) Period: \(T = 2\pi / \omega\)
(v) Simple Pendulum: \(T = 2\pi \sqrt{\frac{l}{g}}\)
(vi) Spring-Mass: \(T = 2\pi \sqrt{\frac{m}{k}}\)

Semester 2

Superposition of Waves

(i) Resultant Displacement: \(y = y_1 + y_2\)
(ii) Constructive Interference: \(\Delta x = n\lambda\)
(iii) Destructive Interference: \(\Delta x = (2n + 1)\frac{\lambda}{2}\)
(iv) Beats: \(f_{beat} = |f_1 - f_2|\)
(v) Stationary wave: \(y = 2A \sin(kx) \cos(\omega t)\)

Wave Optics

(i) Snell's Law: \(\frac{\sin i}{\sin r} = \frac{v_1}{v_2} = \frac{n_2}{n_1} = {}_1n_2\)
(ii) YDSE Position: \(y = \frac{n \lambda D}{d}\)
(iii) Fringe width: \(X = \frac{\lambda D}{d}\)
(iv) Diffraction: \(a \sin \theta = n\lambda\)

Electrostatics

(i) Coulomb's Law: \(F = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r^2}\)
(ii) Electric Field: \(E = \frac{F}{q} = \frac{1}{4\pi\epsilon_0}\frac{q}{r^2}\)
(iii) Electric Potential: \(V = \frac{1}{4\pi\epsilon_0}\frac{q}{r}\)
(iv) Capacitance: \(C = \frac{Q}{V}, \quad C = \frac{A\epsilon_0}{d}\)
(v) Energy: \(U = \frac{1}{2}CV^2\)

Current Electricity

(i) Ohm's Law: \(V = IR\)
(ii) Resistance: \(R = \rho \frac{l}{A}\)
(iii) Series Combination: \(R_{eq} = R_1 + R_2 + ...\)
(iv) Parallel Combination: \(\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + ...\)
(v) Power: \(P = VI = I^2 R = \frac{V^2}{R}\)
(vi) EMF: \(V = \epsilon - Ir\)

Magnetism

(i) Biot-Savart Law: \(dB = \frac{\mu_0}{4\pi}\frac{I dl \sin \theta}{r^2}\)
(ii) Center of loop: \(B = \frac{\mu_0 I}{2R}\)
(iii) Ampere's Law: \(\oint B \cdot dl = \mu_0 I\)
(iv) Force on charge: \(F = q(\vec{v} \times \vec{B})\)
(v) Force on wire: \(F = I(\vec{l} \times \vec{B})\)

Electromagnetic Induction

(i) Faraday's Law: \(e = -\frac{d\phi}{dt}\)
(ii) Lenz's Law: Opposes change
(iii) Self Induction: \(e = -L \frac{dI}{dt}\)
(iv) Energy in inductor: \(U = \frac{1}{2}LI^2\)

AC Circuits

(i) AC Voltage: \(V = V_0 \sin(\omega t)\)
(ii) RMS Voltage: \(V_{rms} = V_0 / \sqrt{2}\)
(iii) Impedance: \(Z = \sqrt{R^2 + (X_L - X_C)^2}\)
(iv) Reactance: \(X_L = \omega L, \quad X_C = \frac{1}{\omega C}\)
(v) Resonance Frequency: \(f = \frac{1}{2\pi\sqrt{LC}}\)

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