ISC Class 12 Physics Formulas
Every ISC Class 12 Physics formula that the Prashnika physics formula calculator knows, by topic: 145 formulas with their letters and units, the same ones used to check the answers on this site. Use it as a revision sheet, then open the Physics formula calculator to work a numerical out.
Electrostatics: 28 formulas
| Formula | Equation | Letters and their units |
|---|---|---|
| Coulomb's law | $F = \dfrac{kq_1\,q_2}{Kr^{2}}$ | $F$ (N), $q_1$ (C), $q_2$ (C), $r$ (m), $k$ (N m² C⁻²), $K$ (no unit) |
| Field of a point charge (or outside a charged shell) | $E = \dfrac{kq}{Kr^{2}}$ | $E$ (N C⁻¹), $q$ (C), $r$ (m), $k$ (N m² C⁻²), $K$ (no unit) |
| Potential of a point charge | $V = \dfrac{kq}{Kr}$ | $V$ (V), $q$ (C), $r$ (m), $k$ (N m² C⁻²), $K$ (no unit) |
| Potential energy of two charges | $U = \dfrac{kq_1\,q_2}{Kr}$ | $U$ (J), $q_1$ (C), $q_2$ (C), $r$ (m), $k$ (N m² C⁻²), $K$ (no unit) |
| Work done moving a charge through a potential difference | $W = qV$ | $W$ (J), $q$ (C), $V$ (V) |
| Uniform field from potential difference | $E = \dfrac{V}{d}$ | $E$ (V m⁻¹), $V$ (V), $d$ (m) |
| Dipole moment (d is the separation 2a) | $p = qd$ | $p$ (C m), $q$ (C), $d$ (m) |
| Torque on a dipole | $\tau = pE\sin\,\theta$ | $\tau$ (N m), $p$ (C m), $E$ (N C⁻¹), $\theta$ (deg) |
| Potential energy of a dipole | $U = -pE\cos\,\theta$ | $U$ (J), $p$ (C m), $E$ (N C⁻¹), $\theta$ (deg) |
| Work turning a dipole from theta1 to theta2 | $W = pE\,\left(\cos\,\theta_1 - \cos\,\theta_2\right)$ | $W$ (J), $p$ (C m), $E$ (N C⁻¹), $\theta_1$ (deg), $\theta_2$ (deg) |
| Field of a short dipole on its axis | $E = \dfrac{2\,kp}{r^{3}}$ | $E$ (N C⁻¹), $p$ (C m), $r$ (m), $k$ (N m² C⁻²) |
| Field of a short dipole on its equator | $E = \dfrac{kp}{r^{3}}$ | $E$ (N C⁻¹), $p$ (C m), $r$ (m), $k$ (N m² C⁻²) |
| Field of a long line of charge | $E = \dfrac{2\,k\lambda}{r}$ | $E$ (N C⁻¹), $\lambda$ (C m⁻¹), $r$ (m), $k$ (N m² C⁻²) |
| Field of a thin infinite sheet of charge | $E = \dfrac{\sigma}{2\,\varepsilon_0}$ | $E$ (N C⁻¹), $\sigma$ (C m⁻²), $\varepsilon_0$ (C² N⁻¹ m⁻²) |
| Field near a charged conductor, or between two oppositely charged plates | $E = \dfrac{\sigma}{\varepsilon_0}$ | $E$ (N C⁻¹), $\sigma$ (C m⁻²), $\varepsilon_0$ (C² N⁻¹ m⁻²) |
| Surface charge density | $\sigma = \dfrac{q}{A}$ | $\sigma$ (C m⁻²), $q$ (C), $A$ (m²) |
| Gauss's law: flux through a closed surface | $\phi = \dfrac{q}{\varepsilon_0}$ | $\phi$ (N m² C⁻¹), $q$ (C), $\varepsilon_0$ (C² N⁻¹ m⁻²) |
| Charge on a capacitor | $Q = CV$ | $Q$ (uC), $C$ (uF), $V$ (V) |
| Parallel-plate capacitor (K for a dielectric filling it) | $C = \dfrac{K\varepsilon_0\,A}{d}$ | $C$ (F), $K$ (no unit), $\varepsilon_0$ (C² N⁻¹ m⁻²), $A$ (m²), $d$ (m) |
| Parallel-plate capacitor with a dielectric slab of thickness t | $C = \dfrac{\varepsilon_0\,A}{d - t + \dfrac{t}{K}}$ | $C$ (F), $\varepsilon_0$ (C² N⁻¹ m⁻²), $A$ (m²), $d$ (m), $t$ (m), $K$ (no unit) |
| Capacitance of an isolated sphere | $C = 4\,\pi\,\varepsilon_0\,Kr$ | $C$ (F), $\varepsilon_0$ (C² N⁻¹ m⁻²), $K$ (no unit), $r$ (m) |
| Two capacitors in series | $\dfrac{1}{C} = \dfrac{1}{C_1} + \dfrac{1}{C_2}$ | $C$ (uF), $C_1$ (uF), $C_2$ (uF) |
| Three capacitors in series | $\dfrac{1}{C} = \dfrac{1}{C_1} + \dfrac{1}{C_2} + \dfrac{1}{C_3}$ | $C$ (uF), $C_1$ (uF), $C_2$ (uF), $C_3$ (uF) |
| Capacitors in parallel | $C = C_1 + C_2 + C_3$ | $C$ (uF), $C_1$ (uF), $C_2$ (uF), $C_3$ (uF) |
| Energy stored in a capacitor | $U = \dfrac{CV^{2}}{2}$ $Q = CV$ | $U$ (J), $C$ (uF), $V$ (V), $Q$ (uC) |
| Energy density of an electric field | $u = \dfrac{K\varepsilon_0\,E^{2}}{2}$ | $u$ (J m⁻³), $K$ (no unit), $\varepsilon_0$ (C² N⁻¹ m⁻²), $E$ (V m⁻¹) |
| Two charged capacitors joined: common potential | $V = \dfrac{C_1\,V_1 + C_2\,V_2}{C_1 + C_2}$ | $V$ (V), $C_1$ (uF), $V_1$ (V), $C_2$ (uF), $V_2$ (V) |
| Two charged capacitors joined: energy lost | $\Delta U = \dfrac{C_1\,C_2\,\left(V_1 - V_2\right)^{2}}{2\,\left(C_1 + C_2\right)}$ | $\Delta U$ (J), $C_1$ (uF), $C_2$ (uF), $V_1$ (V), $V_2$ (V) |
Current Electricity: 24 formulas
| Formula | Equation | Letters and their units |
|---|---|---|
| Ohm's law | $V = IR$ | $V$ (V), $I$ (A), $R$ (ohm) |
| Resistance from resistivity | $R = \dfrac{\rho\,l}{A}$ | $R$ (ohm), $\rho$ (ohm m), $l$ (m), $A$ (m²) |
| Change of resistance with temperature | $R_2 = R_1\,\left(1 + \alpha\,\left(T_2 - T_1\right)\right)$ | $R_2$ (ohm), $R_1$ (ohm), $\alpha$ (K⁻¹), $T_2$ (K), $T_1$ (K) |
| Current and drift velocity | $I = neAv_d$ | $I$ (A), $n$ (m⁻³), $e$ (C), $A$ (m²), $v_d$ (m s⁻¹) |
| Current density | $J = \dfrac{I}{A}$ | $J$ (A m⁻²), $I$ (A), $A$ (m²) |
| Mobility | $\mu = \dfrac{v_d}{E}$ | $\mu$ (m² V⁻¹ s⁻¹), $v_d$ (m s⁻¹), $E$ (V m⁻¹) |
| Resistivity from relaxation time | $\rho = \dfrac{m_e}{ne^{2}\,\tau}$ | $\rho$ (ohm m), $m_e$ (kg), $n$ (m⁻³), $e$ (C), $\tau$ (s) |
| A cell of emf E and internal resistance r with external R (V is the terminal p.d.) | $E = I\,\left(R + r\right)$ $V = IR$ | $E$ (V), $I$ (A), $R$ (ohm), $r$ (ohm), $V$ (V) |
| n identical cells in series | $I = \dfrac{nE}{R + nr}$ | $I$ (A), $n$ (no unit), $E$ (V), $R$ (ohm), $r$ (ohm) |
| m identical cells in parallel | $I = \dfrac{E}{R + \dfrac{r}{m}}$ | $I$ (A), $E$ (V), $R$ (ohm), $r$ (ohm), $m$ (no unit) |
| m rows of n cells in series each | $I = \dfrac{nE}{R + \dfrac{nr}{m}}$ | $I$ (A), $n$ (no unit), $E$ (V), $R$ (ohm), $r$ (ohm), $m$ (no unit) |
| Two different cells in parallel: equivalent emf and internal resistance | $E = \dfrac{E_1\,r_2 + E_2\,r_1}{r_1 + r_2}$ $r = \dfrac{r_1\,r_2}{r_1 + r_2}$ | $E$ (V), $E_1$ (V), $E_2$ (V), $r_1$ (ohm), $r_2$ (ohm), $r$ (ohm) |
| Resistors in series | $R = R_1 + R_2 + R_3$ | $R$ (ohm), $R_1$ (ohm), $R_2$ (ohm), $R_3$ (ohm) |
| Two resistors in parallel | $\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_2}$ | $R$ (ohm), $R_1$ (ohm), $R_2$ (ohm) |
| Three resistors in parallel | $\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3}$ | $R$ (ohm), $R_1$ (ohm), $R_2$ (ohm), $R_3$ (ohm) |
| Electric power | $P = VI$ $V = IR$ | $P$ (W), $V$ (V), $I$ (A), $R$ (ohm) |
| Electrical energy | $W = Pt$ | $W$ (J), $P$ (W), $t$ (s) |
| Balanced Wheatstone bridge | $\dfrac{P}{Q} = \dfrac{R}{S}$ | $P$ (ohm), $Q$ (ohm), $R$ (ohm), $S$ (ohm) |
| Metre bridge balance (l from the end of R) | $\dfrac{R}{S} = \dfrac{l}{L - l}$ | $R$ (ohm), $S$ (ohm), $l$ (cm), $L$ (cm) |
| Potentiometer: comparing emfs | $\dfrac{E_1}{E_2} = \dfrac{l_1}{l_2}$ | $E_1$ (V), $E_2$ (V), $l_1$ (cm), $l_2$ (cm) |
| Potentiometer: internal resistance of a cell | $r = \dfrac{R\,\left(l_1 - l_2\right)}{l_2}$ | $r$ (ohm), $R$ (ohm), $l_1$ (cm), $l_2$ (cm) |
| Potential gradient of a potentiometer wire | $k = \dfrac{V}{L}$ | $k$ (V m⁻¹), $V$ (V), $L$ (m) |
| Shunt to turn a galvanometer into an ammeter | $S = \dfrac{I_gG}{I - I_g}$ | $S$ (ohm), $I_g$ (A), $G$ (ohm), $I$ (A) |
| Series resistance to turn a galvanometer into a voltmeter | $R = \dfrac{V}{I_g} - G$ | $R$ (ohm), $V$ (V), $I_g$ (A), $G$ (ohm) |
Magnetism: 15 formulas
| Formula | Equation | Letters and their units |
|---|---|---|
| Magnetic force on a moving charge | $F = qvB\sin\,\theta$ | $F$ (N), $q$ (C), $v$ (m s⁻¹), $B$ (T), $\theta$ (deg) |
| Radius of a charge's circle in a magnetic field | $r = \dfrac{mv}{qB}$ | $r$ (m), $m$ (kg), $v$ (m s⁻¹), $q$ (C), $B$ (T) |
| Cyclotron frequency | $f = \dfrac{qB}{2\,\pi\,m}$ | $f$ (Hz), $q$ (C), $B$ (T), $m$ (kg) |
| Force on a current-carrying wire | $F = BIl\sin\,\theta$ | $F$ (N), $B$ (T), $I$ (A), $l$ (m), $\theta$ (deg) |
| Force between two parallel wires (on length l) | $F = \dfrac{\mu_0\,I_1\,I_2\,l}{2\,\pi\,d}$ | $F$ (N), $\mu_0$ (T m A⁻¹), $I_1$ (A), $I_2$ (A), $l$ (m), $d$ (m) |
| Field of a long straight wire | $B = \dfrac{\mu_0\,I}{2\,\pi\,r}$ | $B$ (T), $\mu_0$ (T m A⁻¹), $I$ (A), $r$ (m) |
| Field at the centre of a circular coil | $B = \dfrac{\mu_0\,NI}{2\,r}$ | $B$ (T), $\mu_0$ (T m A⁻¹), $N$ (no unit), $I$ (A), $r$ (m) |
| Field on the axis of a circular coil, x from the centre | $B = \dfrac{\mu_0\,NIr^{2}}{2\,\left(r^{2} + x^{2}\right)^{3/2}}$ | $B$ (T), $\mu_0$ (T m A⁻¹), $N$ (no unit), $I$ (A), $r$ (m), $x$ (m) |
| Field inside a long solenoid (n turns per metre) | $B = \mu_0\,nI$ $n = \dfrac{N}{L}$ | $B$ (T), $\mu_0$ (T m A⁻¹), $n$ (m⁻¹), $I$ (A), $N$ (no unit), $L$ (m) |
| Field inside a toroid | $B = \dfrac{\mu_0\,NI}{2\,\pi\,r}$ | $B$ (T), $\mu_0$ (T m A⁻¹), $N$ (no unit), $I$ (A), $r$ (m) |
| Torque on a coil in a magnetic field (theta from the field to the coil's normal) | $\tau = NIAB\sin\,\theta$ | $\tau$ (N m), $N$ (no unit), $I$ (A), $A$ (m²), $B$ (T), $\theta$ (deg) |
| Magnetic moment of a coil | $M = NIA$ | $M$ (A m²), $N$ (no unit), $I$ (A), $A$ (m²) |
| Current sensitivity of a moving-coil galvanometer | $\dfrac{\phi}{I} = \dfrac{NBA}{k_t}$ | $\phi$ (rad), $I$ (A), $N$ (no unit), $B$ (T), $A$ (m²), $k_t$ (N m rad⁻¹) |
| Magnetisation, susceptibility and relative permeability | $\chi = \dfrac{M}{H}$ $\mu_r = 1 + \chi$ | $\chi$ (no unit), $M$ (A m⁻¹), $H$ (A m⁻¹), $\mu_r$ (no unit) |
| Earth's field: horizontal and vertical parts at dip delta | $B_H = B_E\cos\,\delta$ $B_V = B_E\sin\,\delta$ | $B_H$ (T), $B_V$ (T), $B_E$ (T), $\delta$ (deg) |
Emi And Ac: 21 formulas
| Formula | Equation | Letters and their units |
|---|---|---|
| Magnetic flux through a coil | $\phi = NBA\cos\,\theta$ | $\phi$ (Wb), $N$ (no unit), $B$ (T), $A$ (m²), $\theta$ (deg) |
| Faraday's law: average induced emf | $\varepsilon = \dfrac{N\Delta \phi}{\Delta t}$ | $\varepsilon$ (V), $N$ (no unit), $\Delta \phi$ (Wb), $\Delta t$ (s) |
| Emf across a rod moving through a field | $\varepsilon = Blv$ | $\varepsilon$ (V), $B$ (T), $l$ (m), $v$ (m s⁻¹) |
| Emf across a rod rotating about one end | $\varepsilon = \dfrac{B\omega\,l^{2}}{2}$ | $\varepsilon$ (V), $B$ (T), $\omega$ (rad s⁻¹), $l$ (m) |
| Peak emf of an AC generator | $e_0 = NBA\omega$ $\omega = 2\,\pi\,f$ | $e_0$ (V), $N$ (no unit), $B$ (T), $A$ (m²), $\omega$ (rad s⁻¹), $f$ (Hz) |
| Self-inductance of a long solenoid | $L = \dfrac{\mu_0\,N^{2}\,A}{l}$ | $L$ (H), $\mu_0$ (T m A⁻¹), $N$ (no unit), $A$ (m²), $l$ (m) |
| Self-induced emf | $\varepsilon = \dfrac{L\Delta I}{\Delta t}$ | $\varepsilon$ (V), $L$ (H), $\Delta I$ (A), $\Delta t$ (s) |
| Mutually induced emf | $\varepsilon = \dfrac{M\Delta I}{\Delta t}$ | $\varepsilon$ (V), $M$ (H), $\Delta I$ (A), $\Delta t$ (s) |
| Energy stored in an inductor | $U = \dfrac{LI^{2}}{2}$ | $U$ (J), $L$ (H), $I$ (A) |
| rms and peak values | $\text{rms} = \dfrac{\text{peak}}{\sqrt{2}}$ | $\text{rms}$ (any unit), $\text{peak}$ (any unit) |
| Inductive reactance | $X_L = 2\,\pi\,fL$ | $X_L$ (ohm), $f$ (Hz), $L$ (H) |
| Capacitive reactance | $X_C = \dfrac{1}{2\,\pi\,fC}$ | $X_C$ (ohm), $f$ (Hz), $C$ (F) |
| Impedance of a series LCR circuit (leave out the reactance it doesn't have) | $Z = \sqrt{R^{2} + \left(X_L - X_C\right)^{2}}$ $I = \dfrac{V}{Z}$ | $Z$ (ohm), $R$ (ohm), $X_L$ (ohm), $X_C$ (ohm), $I$ (A), $V$ (V) |
| Series LCR circuit from L, C and f | $Z = \sqrt{R^{2} + \left(X_L - X_C\right)^{2}}$ $X_L = 2\,\pi\,fL$ $X_C = \dfrac{1}{2\,\pi\,fC}$ $I = \dfrac{V}{Z}$ | $Z$ (ohm), $R$ (ohm), $X_L$ (ohm), $X_C$ (ohm), $f$ (Hz), $L$ (H), $C$ (F), $I$ (A), $V$ (V) |
| Phase angle of a series LCR circuit (current lags by phi) | $\phi = \tan^{-1}\left(\dfrac{X_L - X_C}{R}\right)$ | $\phi$ (deg), $X_L$ (ohm), $X_C$ (ohm), $R$ (ohm) |
| Resonant frequency | $f_0 = \dfrac{1}{2\,\pi\,\sqrt{LC}}$ | $f_0$ (Hz), $L$ (H), $C$ (F) |
| Quality factor of a series LCR circuit | $Q = \dfrac{\sqrt{\dfrac{L}{C}}}{R}$ | $Q$ (no unit), $L$ (H), $C$ (F), $R$ (ohm) |
| Power factor | $\cos\phi = \dfrac{R}{Z}$ | $\cos\phi$ (no unit), $R$ (ohm), $Z$ (ohm) |
| Average power in an AC circuit (rms values) | $P = VI\cos\phi$ | $P$ (W), $V$ (V), $I$ (A), $\cos\phi$ (no unit) |
| Ideal transformer | $\dfrac{V_s}{V_p} = \dfrac{N_s}{N_p}$ $I_sV_s = I_pV_p$ | $V_s$ (V), $V_p$ (V), $N_s$ (no unit), $N_p$ (no unit), $I_s$ (A), $I_p$ (A) |
| Efficiency of a transformer | $\eta = \dfrac{V_sI_s}{V_pI_p}$ | $\eta$ (no unit), $V_s$ (V), $I_s$ (A), $V_p$ (V), $I_p$ (A) |
Em Waves: 2 formulas
| Formula | Equation | Letters and their units |
|---|---|---|
| Speed, frequency and wavelength of an EM wave | $c = f\lambda$ | $c$ (m s⁻¹), $f$ (Hz), $\lambda$ (m) |
| Amplitudes of E and B in an EM wave | $E_0 = cB_0$ | $E_0$ (V m⁻¹), $c$ (m s⁻¹), $B_0$ (T) |
Optics: 32 formulas
| Formula | Equation | Letters and their units |
|---|---|---|
| Mirror formula and magnification | $\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$ $m = \dfrac{-v}{u}$ $h_i = mh_o$ | $v$ (cm), $u$ (cm), $f$ (cm), $m$ (no unit), $h_i$ (cm), $h_o$ (cm) |
| Lens formula and magnification | $\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$ $m = \dfrac{v}{u}$ $h_i = mh_o$ | $v$ (cm), $u$ (cm), $f$ (cm), $m$ (no unit), $h_i$ (cm), $h_o$ (cm) |
| Focal length of a mirror | $f = \dfrac{R}{2}$ | $f$ (cm), $R$ (cm) |
| Lens maker's formula (nm for a lens in another medium) | $\dfrac{1}{f} = \left(\dfrac{n}{n_m} - 1\right)\,\left(\dfrac{1}{R_1} - \dfrac{1}{R_2}\right)$ | $f$ (cm), $n$ (no unit), $n_m$ (no unit), $R_1$ (cm), $R_2$ (cm) |
| Power of a lens | $P = \dfrac{1}{f}$ | $P$ (dioptre), $f$ (m) |
| Thin lenses in contact | $\dfrac{1}{F} = \dfrac{1}{f_1} + \dfrac{1}{f_2}$ $P = \dfrac{1}{F}$ | $F$ (cm), $f_1$ (cm), $f_2$ (cm), $P$ (dioptre) |
| Two thin lenses a distance d apart | $\dfrac{1}{F} = \dfrac{1}{f_1} + \dfrac{1}{f_2} - \dfrac{d}{f_1\,f_2}$ | $F$ (cm), $f_1$ (cm), $f_2$ (cm), $d$ (cm) |
| Refraction at a spherical surface | $\dfrac{n_2}{v} - \dfrac{n_1}{u} = \dfrac{n_2 - n_1}{R}$ | $n_2$ (no unit), $v$ (cm), $n_1$ (no unit), $u$ (cm), $R$ (cm) |
| Snell's law (r in the second medium) | $r = \sin^{-1}\left(\dfrac{n_1\,\sin\,i}{n_2}\right)$ | $r$ (deg), $n_1$ (no unit), $i$ (deg), $n_2$ (no unit) |
| Refractive index from speeds | $n = \dfrac{c}{v}$ | $n$ (no unit), $c$ (m s⁻¹), $v$ (m s⁻¹) |
| Real and apparent depth | $n = \dfrac{\text{real depth}}{\text{apparent depth}}$ | $n$ (no unit), $\text{real depth}$ (cm), $\text{apparent depth}$ (cm) |
| Critical angle (n1 the denser medium) | $C = \sin^{-1}\left(\dfrac{n_2}{n_1}\right)$ | $C$ (deg), $n_2$ (no unit), $n_1$ (no unit) |
| Prism at minimum deviation | $D_m = 2\,\sin^{-1}\left(n\sin\left(\dfrac{A}{2}\right)\right) - A$ | $D_m$ (deg), $n$ (no unit), $A$ (deg) |
| Angles in a prism | $r_1 + r_2 = A$ $i + e = A + d$ | $r_1$ (deg), $r_2$ (deg), $A$ (deg), $i$ (deg), $e$ (deg), $d$ (deg) |
| Deviation by a thin prism | $d = \left(n - 1\right)\,A$ | $d$ (deg), $n$ (no unit), $A$ (deg) |
| Dispersive power | $w = \dfrac{n_v - n_r}{n_y - 1}$ | $w$ (no unit), $n_v$ (no unit), $n_r$ (no unit), $n_y$ (no unit) |
| Simple microscope, image at the near point D | $m = 1 + \dfrac{D}{f}$ | $m$ (no unit), $D$ (cm), $f$ (cm) |
| Simple microscope, image at infinity | $m = \dfrac{D}{f}$ | $m$ (no unit), $D$ (cm), $f$ (cm) |
| Compound microscope, image at the near point (sizes, no signs) | $m = \dfrac{v_o}{u_o}\,\left(1 + \dfrac{D}{f_e}\right)$ | $m$ (no unit), $v_o$ (cm), $u_o$ (cm), $D$ (cm), $f_e$ (cm) |
| Compound microscope, final image at infinity (sizes, no signs) | $m = \dfrac{v_o}{u_o}\,\dfrac{D}{f_e}$ | $m$ (no unit), $v_o$ (cm), $u_o$ (cm), $D$ (cm), $f_e$ (cm) |
| Astronomical telescope in normal adjustment | $m = \dfrac{f_o}{f_e}$ $L = f_o + f_e$ | $m$ (no unit), $f_o$ (cm), $f_e$ (cm), $L$ (cm) |
| Astronomical telescope, final image at the near point | $m = \dfrac{f_o}{f_e}\,\left(1 + \dfrac{f_e}{D}\right)$ | $m$ (no unit), $f_o$ (cm), $f_e$ (cm), $D$ (cm) |
| Young's double slit: fringe width | $\beta = \dfrac{\lambda\,D}{d}$ | $\beta$ (mm), $\lambda$ (nm), $D$ (m), $d$ (mm) |
| Young's double slit: the nth bright fringe from the centre | $y = \dfrac{n\lambda\,D}{d}$ | $y$ (mm), $n$ (no unit), $\lambda$ (nm), $D$ (m), $d$ (mm) |
| Phase difference from path difference | $\phi = \dfrac{2\,\pi\,\Delta x}{\lambda}$ | $\phi$ (rad), $\Delta x$ (nm), $\lambda$ (nm) |
| Resultant intensity of two waves | $I = I_1 + I_2 + 2\,\sqrt{I_1\,I_2}\,\cos\,\phi$ | $I$ (any unit), $I_1$ (any unit), $I_2$ (any unit), $\phi$ (deg) |
| Ratio of maximum to minimum intensity | $\dfrac{I_{max}}{I_{min}} = \left(\dfrac{\sqrt{I_1} + \sqrt{I_2}}{\sqrt{I_1} - \sqrt{I_2}}\right)^{2}$ | $\dfrac{I_{max}}{I_{min}}$ (no unit), $I_1$ (any unit), $I_2$ (any unit) |
| Single slit: angle of the nth minimum | $\theta = \sin^{-1}\left(\dfrac{n\lambda}{a}\right)$ | $\theta$ (deg), $n$ (no unit), $\lambda$ (nm), $a$ (mm) |
| Single slit: width of the central maximum | $w = \dfrac{2\,\lambda\,D}{a}$ | $w$ (mm), $\lambda$ (nm), $D$ (m), $a$ (mm) |
| Brewster's law | $i_p = \tan^{-1}\,n$ | $i_p$ (deg), $n$ (no unit) |
| Malus' law | $I = I_0\,\cos^{2}\,\theta$ | $I$ (any unit), $I_0$ (any unit), $\theta$ (deg) |
| Resolving power of a telescope (aperture a) | $\mathrm{R.P.} = \dfrac{a}{1.22\,\lambda}$ | $\mathrm{R.P.}$ (rad⁻¹), $a$ (m), $\lambda$ (nm) |
Modern Physics: 21 formulas
| Formula | Equation | Letters and their units |
|---|---|---|
| Energy of a photon | $E = hf$ $f = \dfrac{c}{\lambda}$ | $E$ (eV), $h$ (J s), $f$ (Hz), $c$ (m s⁻¹), $\lambda$ (nm) |
| Photons emitted per second | $n = \dfrac{P\lambda}{hc}$ | $n$ (s⁻¹), $P$ (W), $\lambda$ (nm), $h$ (J s), $c$ (m s⁻¹) |
| Einstein's photoelectric equation (K the maximum kinetic energy, V0 the stopping potential) | $K = hf - W_0$ $W_0 = hf_0$ $K = eV_0$ $f = \dfrac{c}{\lambda}$ $f_0 = \dfrac{c}{\lambda_0}$ | $K$ (eV), $h$ (J s), $f$ (Hz), $W_0$ (eV), $f_0$ (Hz), $e$ (C), $V_0$ (V), $c$ (m s⁻¹), $\lambda$ (nm), $\lambda_0$ (nm) |
| de Broglie wavelength (K the kinetic energy, V the accelerating p.d.) | $\lambda = \dfrac{h}{p}$ $p = mv$ $K = \dfrac{p^{2}}{2\,m}$ $K = qV$ | $\lambda$ (nm), $h$ (J s), $p$ (kg m s⁻¹), $m$ (kg), $v$ (m s⁻¹), $K$ (eV), $q$ (C), $V$ (V) |
| de Broglie wavelength of an electron through V volts | $\lambda = \dfrac{h}{\sqrt{2\,m_eeV}}$ | $\lambda$ (nm), $h$ (J s), $m_e$ (kg), $e$ (C), $V$ (V) |
| Radius of the nth Bohr orbit | $r = \dfrac{r_1\,n^{2}}{Z}$ | $r$ (angstrom), $r_1$ (angstrom), $n$ (no unit), $Z$ (no unit) |
| Energy of the nth Bohr level | $E = \dfrac{-E_1\,Z^{2}}{n^{2}}$ | $E$ (eV), $E_1$ (eV), $Z$ (no unit), $n$ (no unit) |
| Speed of the electron in the nth orbit | $v = \dfrac{v_1\,Z}{n}$ | $v$ (m s⁻¹), $v_1$ (m s⁻¹), $Z$ (no unit), $n$ (no unit) |
| Angular momentum in the nth orbit | $L = \dfrac{nh}{2\,\pi}$ | $L$ (J s), $n$ (no unit), $h$ (J s) |
| A jump from level n2 down to n1 (or up): energy, wavelength, frequency | $\Delta E = E_1\,Z^{2}\,\left(\dfrac{1}{n_1^{2}} - \dfrac{1}{n_2^{2}}\right)$ $\Delta E = \dfrac{hc}{\lambda}$ $\Delta E = hf$ | $\Delta E$ (eV), $E_1$ (eV), $Z$ (no unit), $n_1$ (no unit), $n_2$ (no unit), $h$ (J s), $c$ (m s⁻¹), $\lambda$ (nm), $f$ (Hz) |
| Rydberg formula | $\dfrac{1}{\lambda} = R_HZ^{2}\,\left(\dfrac{1}{n_1^{2}} - \dfrac{1}{n_2^{2}}\right)$ | $\lambda$ (nm), $R_H$ (m⁻¹), $Z$ (no unit), $n_1$ (no unit), $n_2$ (no unit) |
| Shortest X-ray wavelength from V volts | $\lambda = \dfrac{hc}{eV}$ | $\lambda$ (nm), $h$ (J s), $c$ (m s⁻¹), $e$ (C), $V$ (V) |
| Radioactive decay law | $N = N_0\,e^{-\lambda\,t}$ $\lambda = \dfrac{0.693}{T}$ | $N$ (any unit), $N_0$ (any unit), $\lambda$ (s⁻¹), $t$ (s), $T$ (s) |
| Amount left after t (T the half-life) | $N = \dfrac{N_0}{2^{\dfrac{t}{T}}}$ | $N$ (any unit), $N_0$ (any unit), $t$ (s), $T$ (s) |
| Decay constant, half-life and mean life | $\tau = \dfrac{1}{\lambda}$ $T = \dfrac{0.693}{\lambda}$ | $\tau$ (s), $\lambda$ (s⁻¹), $T$ (s) |
| Activity | $A = \lambda\,N$ $\lambda = \dfrac{0.693}{T}$ | $A$ (s⁻¹), $\lambda$ (s⁻¹), $N$ (no unit), $T$ (s) |
| Mass-energy equivalence | $E = mc^{2}$ | $E$ (J), $m$ (kg), $c$ (m s⁻¹) |
| Mass defect of a nucleus (M the atom's mass, A the mass number) | $\Delta m = Zm_H + \left(A - Z\right)\,m_n - M$ | $\Delta m$ (u), $Z$ (no unit), $m_H$ (u), $A$ (no unit), $m_n$ (u), $M$ (u) |
| Binding energy from mass defect, and per nucleon | $\mathrm{BE} = \Delta mc^2$ $\mathrm{BE}_n = \dfrac{\mathrm{BE}}{A}$ | $\mathrm{BE}$ (MeV), $\Delta m$ (u), $c^2$ (MeV u⁻¹), $\mathrm{BE}_n$ (MeV), $A$ (no unit) |
| Q value of a nuclear reaction (masses before and after, in u) | $Q = \left(m_{before} - m_{after}\right)\,c^2$ | $Q$ (MeV), $m_{before}$ (u), $m_{after}$ (u), $c^2$ (MeV u⁻¹) |
| Radius of a nucleus | $R = R_0\,A^{1/3}$ | $R$ (fm), $R_0$ (fm), $A$ (no unit) |
Semiconductors: 2 formulas
| Formula | Equation | Letters and their units |
|---|---|---|
| Transistor currents and gains | $I_e = I_b + I_c$ $\alpha = \dfrac{I_c}{I_e}$ $\beta = \dfrac{I_c}{I_b}$ | $I_e$ (mA), $I_b$ (mA), $I_c$ (mA), $\alpha$ (no unit), $\beta$ (no unit) |
| Voltage gain of a common-emitter amplifier | $A_v = \dfrac{\beta\,R_L}{R_i}$ | $A_v$ (no unit), $\beta$ (no unit), $R_L$ (ohm), $R_i$ (ohm) |
Constants the calculator fills in for you
| Letter | Constant | Value |
|---|---|---|
| R | gas constant | 8.314 J K⁻¹ mol⁻¹ |
| F | faraday | 96500 C mol⁻¹ |
| NA | Avogadro’s number | 6.022e23 mol⁻¹ |
| e | charge of an electron | 1.6e-19 C |
| h | Planck’s constant | 6.6e-34 J s |
| c | speed of light | 3e8 m s⁻¹ |
| eps0 | permittivity of free space | 8.85e-12 C² N⁻¹ m⁻² |
| mu0 | permeability of free space | 1.2566e-6 T m A⁻¹ |
| k | 1/(4πε₀) | 9e9 N m² C⁻² |
| me | mass of an electron | 9.1e-31 kg |
| mp | mass of a proton | 1.67e-27 kg |
| mn | mass of a neutron | 1.008665 u |
| mH | mass of a hydrogen atom | 1.007825 u |
| c2 | c² in energy units | 931.5 MeV u⁻¹ |
| g | acceleration due to gravity | 9.8 m s⁻² |
The values ISC papers use; if a question prints its own value, type that instead.
Common questions
How many ISC Class 12 Physics formulas are on this page?
145 formulas, grouped by topic. Each has its equation or equations and the letters it uses with their units.
Can I use these Physics formulas to solve numericals?
Yes: the Physics formula calculator on Prashnika takes any of them, converts the units you type and shows the working in SI units.
Do the formulas include derivations?
No. This page is the list to revise from; the derivations are asked in the paper as separate questions, which you can practise from the chapter pages.
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Last checked 2026-10-16.