12th HSC Physics Formula Sheet (Maharashtra Board)
Comprehensive formula list for Semester 1 and Semester 2 prepared for quick revision.
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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