CBSE Class 12 Physics Formulas

Cheatsheet Content

### Electrostatics - **Coulomb's Law:** $F = \frac{1}{4\pi\epsilon_0} \frac{q_1q_2}{r^2}$ - **Electric Field:** $E = \frac{F}{q_0} = \frac{1}{4\pi\epsilon_0} \frac{q}{r^2}$ - **Electric Potential:** $V = \frac{1}{4\pi\epsilon_0} \frac{q}{r}$ - **Electric Dipole Moment:** $\vec{p} = q(2\vec{a})$ - **Torque on Dipole:** $\vec{\tau} = \vec{p} \times \vec{E}$ - **Potential Energy of Dipole:** $U = -\vec{p} \cdot \vec{E}$ - **Capacitance:** $C = \frac{Q}{V}$ - **Capacitance of Parallel Plate:** $C = \frac{\epsilon_0 A}{d}$ - **Energy Stored in Capacitor:** $U = \frac{1}{2}CV^2 = \frac{1}{2}\frac{Q^2}{C} = \frac{1}{2}QV$ - **Capacitors in Series:** $\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + ...$ - **Capacitors in Parallel:** $C_{eq} = C_1 + C_2 + ...$ ### Current Electricity - **Ohm's Law:** $V = IR$ - **Resistance:** $R = \rho \frac{L}{A}$ - **Current Density:** $J = \frac{I}{A} = n e v_d$ - **Drift Velocity:** $v_d = \frac{eE\tau}{m}$ - **Mobility:** $\mu = \frac{v_d}{E} = \frac{e\tau}{m}$ - **Kirchhoff's Junction Rule:** $\sum I = 0$ - **Kirchhoff's Loop Rule:** $\sum \Delta V = 0$ - **Resistors in Series:** $R_{eq} = R_1 + R_2 + ...$ - **Resistors in Parallel:** $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + ...$ - **Electric Power:** $P = VI = I^2R = \frac{V^2}{R}$ - **Internal Resistance of Cell:** $r = \left(\frac{E}{V} - 1\right)R$ ### Magnetic Effects of Current - **Biot-Savart Law:** $d\vec{B} = \frac{\mu_0}{4\pi} \frac{I d\vec{l} \times \vec{r}}{r^3}$ - **Magnetic Field due to Straight Wire:** $B = \frac{\mu_0 I}{2\pi r}$ - **Magnetic Field at Center of Loop:** $B = \frac{\mu_0 I}{2R}$ - **Ampere's Circuital Law:** $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enc}$ - **Force on Moving Charge:** $\vec{F} = q(\vec{v} \times \vec{B})$ - **Lorentz Force:** $\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$ - **Force on Current Carrying Conductor:** $\vec{F} = I(\vec{L} \times \vec{B})$ - **Torque on Current Loop:** $\vec{\tau} = \vec{M} \times \vec{B}$, where $\vec{M} = NI\vec{A}$ - **Magnetic Field of Solenoid:** $B = \mu_0 n I$ - **Magnetic Field of Toroid:** $B = \frac{\mu_0 N I}{2\pi r}$ ### Magnetism and Matter - **Magnetic Dipole Moment:** $M = I A$ - **Magnetic Field Strength (H):** $H = \frac{B}{\mu_0} - M$ - **Intensity of Magnetization (I):** $I = \frac{M_{net}}{V}$ - **Magnetic Permeability:** $\mu = \mu_r \mu_0$ - **Magnetic Susceptibility:** $\chi_m = \frac{M}{H}$ - **Relation between $\mu_r$ and $\chi_m$:** $\mu_r = 1 + \chi_m$ ### Electromagnetic Induction - **Magnetic Flux:** $\Phi_B = \int \vec{B} \cdot d\vec{A} = BA \cos\theta$ - **Faraday's Law of Induction:** $\mathcal{E} = -\frac{d\Phi_B}{dt}$ - **Motional EMF:** $\mathcal{E} = BLv$ - **Self-Inductance:** $L = \frac{\Phi_B}{I}$ - **Self-Induced EMF:** $\mathcal{E} = -L \frac{dI}{dt}$ - **Energy Stored in Inductor:** $U = \frac{1}{2}LI^2$ - **Mutual Inductance:** $M = \frac{\Phi_{B2}}{I_1}$ or $M = \frac{\Phi_{B1}}{I_2}$ - **Mutual Induced EMF:** $\mathcal{E}_2 = -M \frac{dI_1}{dt}$ ### Alternating Current - **AC Voltage/Current:** $V = V_0 \sin(\omega t + \phi)$, $I = I_0 \sin(\omega t)$ - **RMS Value:** $V_{rms} = \frac{V_0}{\sqrt{2}}$, $I_{rms} = \frac{I_0}{\sqrt{2}}$ - **Inductive Reactance:** $X_L = \omega L = 2\pi f L$ - **Capacitive Reactance:** $X_C = \frac{1}{\omega C} = \frac{1}{2\pi f C}$ - **Impedance (Series RLC):** $Z = \sqrt{R^2 + (X_L - X_C)^2}$ - **Phase Angle:** $\tan\phi = \frac{X_L - X_C}{R}$ - **Power in AC Circuit:** $P_{avg} = V_{rms} I_{rms} \cos\phi$ (Power Factor $\cos\phi$) - **Resonant Frequency:** $f_r = \frac{1}{2\pi\sqrt{LC}}$ - **Transformer Relation:** $\frac{V_s}{V_p} = \frac{N_s}{N_p} = \frac{I_p}{I_s}$ (for ideal transformer) ### Electromagnetic Waves - **Speed of EM Wave:** $c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$ - **Relation between E and B:** $E_0 = c B_0$ - **Energy Density:** $u = u_E + u_B = \frac{1}{2}\epsilon_0 E^2 + \frac{1}{2\mu_0} B^2$ - **Poynting Vector:** $\vec{S} = \frac{1}{\mu_0} (\vec{E} \times \vec{B})$ ### Ray Optics and Optical Instruments - **Mirror Formula:** $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ - **Magnification (Mirror):** $m = -\frac{v}{u} = \frac{h'}{h}$ - **Refractive Index:** $n = \frac{c}{v}$ - **Snell's Law:** $n_1 \sin i = n_2 \sin r$ - **Total Internal Reflection:** $\sin C = \frac{n_2}{n_1}$ (for $n_1 > n_2$) - **Lens Maker's Formula:** $\frac{1}{f} = (n-1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$ - **Lens Formula:** $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$ - **Magnification (Lens):** $m = \frac{v}{u} = \frac{h'}{h}$ - **Power of Lens:** $P = \frac{1}{f}$ (in dioptres, f in meters) - **Power of Lenses in Contact:** $P_{eq} = P_1 + P_2 + ...$ - **Magnifying Power of Simple Microscope:** $M = 1 + \frac{D}{f}$ (image at near point), $M = \frac{D}{f}$ (image at infinity) - **Magnifying Power of Compound Microscope:** $M = M_o M_e = \left(\frac{L}{f_o}\right)\left(1 + \frac{D}{f_e}\right)$ - **Magnifying Power of Astronomical Telescope:** $M = -\frac{f_o}{f_e}$ ### Wave Optics - **Young's Double Slit Experiment:** - **Path Difference:** $\Delta x = d \sin\theta = \frac{yd}{D}$ - **Condition for Maxima (Bright Fringes):** $\Delta x = n\lambda$ - **Condition for Minima (Dark Fringes):** $\Delta x = (n + \frac{1}{2})\lambda$ - **Fringe Width:** $\beta = \frac{\lambda D}{d}$ - **Diffraction (Single Slit):** - **Condition for Minima:** $a \sin\theta = n\lambda$ - **Width of Central Maxima:** $2\theta = \frac{2\lambda}{a}$ - **Brewster's Law:** $\tan i_p = n$ - **Malus' Law:** $I = I_0 \cos^2\theta$ ### Dual Nature of Radiation and Matter - **Photon Energy:** $E = h\nu = \frac{hc}{\lambda}$ - **Momentum of Photon:** $p = \frac{h}{\lambda}$ - **Einstein's Photoelectric Equation:** $K_{max} = h\nu - \Phi_0 = h\nu - h\nu_0$ - **Stopping Potential:** $eV_s = K_{max}$ - **De Broglie Wavelength:** $\lambda = \frac{h}{p} = \frac{h}{mv}$ - **De Broglie Wavelength of Electron (accelerated by V):** $\lambda = \frac{h}{\sqrt{2meV}}$ ### Atoms - **Rutherford's Model:** - **Distance of Closest Approach:** $r_0 = \frac{1}{4\pi\epsilon_0} \frac{Z e^2}{K}$ - **Bohr's Model:** - **Quantization Condition:** $L = mvr = \frac{nh}{2\pi}$ - **Radius of nth orbit:** $r_n = \frac{n^2 h^2 \epsilon_0}{\pi m e^2 Z} = 0.529 \frac{n^2}{Z} \text{ Å}$ - **Energy of nth orbit:** $E_n = -\frac{m Z^2 e^4}{8\epsilon_0^2 h^2 n^2} = -13.6 \frac{Z^2}{n^2} \text{ eV}$ - **Wavelength of Emitted Photon:** $\frac{1}{\lambda} = RZ^2 \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$ (Rydberg constant $R = 1.097 \times 10^7 \text{ m}^{-1}$) ### Nuclei - **Nuclear Radius:** $R = R_0 A^{1/3}$ (where $R_0 \approx 1.2 \times 10^{-15} \text{ m}$) - **Mass Defect:** $\Delta m = [Z m_p + (A-Z) m_n] - M_{nucleus}$ - **Binding Energy:** $E_b = \Delta m c^2$ - **Binding Energy per Nucleon:** $E_{bn} = \frac{E_b}{A}$ - **Radioactive Decay Law:** $N = N_0 e^{-\lambda t}$ - **Half-Life:** $T_{1/2} = \frac{\ln 2}{\lambda} = \frac{0.693}{\lambda}$ - **Mean Life:** $\tau = \frac{1}{\lambda}$ - **Activity:** $A = \frac{dN}{dt} = \lambda N$ ### Semiconductor Electronics - **Conductors, Insulators, Semiconductors:** Based on energy band gap ($E_g$) - Conductors: $E_g \approx 0$ - Semiconductors: $E_g \approx 1 \text{ eV}$ - Insulators: $E_g > 3 \text{ eV}$ - **Diode Current (Ideal):** - Forward Bias: $I = I_0 (e^{eV/k_B T} - 1)$ - Reverse Bias: $I \approx -I_0$ - **Transistor (Current Gains):** - Common Emitter ($\beta$): $\beta_{ac} = \left(\frac{\Delta I_C}{\Delta I_B}\right)_{V_{CE}}$, $\beta_{dc} = \frac{I_C}{I_B}$ - Common Base ($\alpha$): $\alpha_{ac} = \left(\frac{\Delta I_C}{\Delta I_E}\right)_{V_{CB}}$, $\alpha_{dc} = \frac{I_C}{I_E}$ - Relation: $\beta = \frac{\alpha}{1-\alpha}$ - **Logic Gates:** - **AND Gate:** $Y = A \cdot B$ - **OR Gate:** $Y = A + B$ - **NOT Gate:** $Y = \bar{A}$ - **NAND Gate:** $Y = \overline{A \cdot B}$ - **NOR Gate:** $Y = \overline{A + B}$