| Formula | Description |
|---|---|
| \( v = u + at \) | Velocity with acceleration |
| \( s = ut + \frac{1}{2} at^2 \) | Displacement with acceleration |
| \( F = ma \) | Newton's second law |
| \( P = Fv \) | Power in terms of force and velocity |
| Formula | Description |
|---|---|
| \( W = Fd \cos\theta \) | Work done |
| \( P = \frac{W}{t} \) | Power |
| \( K.E. = \frac{1}{2} mv^2 \) | Kinetic energy |
| \( P.E. = mgh \) | Potential energy |
| Formula | Description |
|---|---|
| \( F = G \frac{m_1 m_2}{r^2} \) | Newton's law of gravitation |
| \( g = \frac{GM}{R^2} \) | Acceleration due to gravity |
| \( v_{escape} = \sqrt{\frac{2GM}{R}} \) | Escape velocity |
| Formula | Description |
|---|---|
| \( V = IR \) | Ohm's law |
| \( R = \frac{\rho l}{A} \) | Resistance |
| \( P = VI = I^2 R = \frac{V^2}{R} \) | Power in circuit |
| \( C = \frac{Q}{V} \) | Capacitance |
| Formula | Description |
|---|---|
| \( Q = mc\Delta T \) | Heat energy |
| \( W = P\Delta V \) | Work done in thermodynamics |
| \( \eta = \frac{W}{Q_1} = 1 - \frac{T_2}{T_1} \) | Efficiency of Carnot engine |
| Formula | Description |
|---|---|
| \( PV = nRT \) | Ideal gas equation |
| \( K.E. = \frac{3}{2} kT \) | Kinetic energy per molecule |
| Formula | Description |
|---|---|
| \( T = 2\pi \sqrt{\frac{L}{g}} \) | Time period of pendulum |
| \( T = 2\pi \sqrt{\frac{m}{k}} \) | Time period of spring-mass system |
| \( x = A \sin(\omega t + \phi) \) | SHM displacement |
| Formula | Description |
|---|---|
| \( F = k \frac{q_1 q_2}{r^2} \) | Coulomb's law |
| \( E = \frac{F}{q} = k \frac{Q}{r^2} \) | Electric field |
| \( \Phi = EA \) | Electric flux |
| \( p = q \times 2a \) | Dipole moment |
| Formula | Description |
|---|---|
| \( V = \frac{kQ}{r} \) | Electric potential |
| \( C = \frac{Q}{V} \) | Capacitance |
| \( \frac{1}{C_{series}} = \frac{1}{C_1} + \frac{1}{C_2} \) | Series capacitance |
| \( C_{parallel} = C_1 + C_2 \) | Parallel capacitance |
| \( U = \frac{1}{2} CV^2 \) | Energy stored in capacitor |
| Formula | Description |
|---|---|
| \( F = qvB \sin\theta \) | Force on moving charge |
| \( F = ILB \sin\theta \) | Force on current-carrying wire |
| \( B_{circular\ loop} = \frac{\mu_0 I}{2R} \) | Magnetic field of circular loop |
| Formula | Description |
|---|---|
| \( e = -\frac{d\Phi}{dt} \) | Faraday's law |
| \( e = Blv \sin\theta \) | Motional EMF |
| \( e = -L \frac{di}{dt} \) | Self-induced EMF |
| \( e = -M \frac{di}{dt} \) | Mutual-induced EMF |
| Formula | Description |
|---|---|
| \( i = I_0 \sin\omega t \) | AC current |
| \( I_{rms} = \frac{I_0}{\sqrt{2}} \) | RMS current |
| \( Z = \sqrt{R^2 + (X_L - X_C)^2} \) | Impedance |
| \( P = V_{rms} I_{rms} \cos\phi \) | Power in AC circuit |
| Formula | Description |
|---|---|
| \( c = 3 \times 10^8 \, \text{m/s} \) | Speed of light |
| \( c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \) | Speed of EM waves |
| Formula | Description |
|---|---|
| \( \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \) | Lens/mirror equation |
| \( m = \frac{h'}{h} = -\frac{v}{u} \) | Magnification |
| \( P = \frac{100}{f \, (\text{cm})} \) | Power of lens |
| Formula | Description |
|---|---|
| \( \beta = \frac{\lambda D}{d} \) | Fringe width in diffraction |
| \( \Delta x = n\lambda \) | Constructive interference |
| \( \Delta x = (2n - 1) \frac{\lambda}{2} \) | Destructive interference |
| Formula | Description |
|---|---|
| \( E = h\nu \) | Photon energy |
| \( K.E. = h\nu - W \) | Kinetic energy in photoelectric effect |
| \( \lambda = \frac{h}{p} = \frac{h}{mv} \) | de Broglie wavelength |
| Formula | Description |
|---|---|
| \( E_n = -\frac{13.6}{n^2} \, \text{eV} \) | Energy of nth orbit |
| \( r_n = n^2 a_0 \) | Radius of nth orbit |
| \( h\nu = E_{high} - E_{low} \) | Photon energy in transition |
| Formula | Description |
|---|---|
| \( E = mc^2 \) | Mass-energy equivalence |
| \( BE = \Delta m \times 931.5 \, \text{MeV} \) | Binding energy |
| \( T_{1/2} = \frac{0.693}{\lambda} \) | Half-life |
| Formula | Description |
|---|---|
| \( R = \frac{\rho l}{A} \) | Resistance |
| \( Y = A \cdot B \) | AND Gate output |
| \( Y = A + B \) | OR Gate output |
| \( Y = \overline{A} \) | NOT Gate output |
| Formula | Description |
|---|---|
| \( \Delta t = \frac{\Delta t_0}{\sqrt{1 - \frac{v^2}{c^2}}} \) | Time dilation |
| \( L = L_0 \sqrt{1 - \frac{v^2}{c^2}} \) | Length contraction |
| \( E = mc^2 \) | Mass-energy equivalence |
| Formula | Description |
|---|---|
| \( \lambda = \frac{c}{f} \) | Wavelength |
| \( L_{antenna} = \frac{\lambda}{4} \) | Antenna length |