All flashcard decksCBSE Class 12 syllabus →
25 cardsCBSE Class 12

CBSE Class 12 Core Formulas and Derivations

25 flashcards to revise the key facts for the CBSE Class 12. Study material written for practice, not the official exam.

Start studyingPlay Match
PDF study sheet

Free account needed to save, copy or download. We bring you back here.

1 / 25
0 known
TermClick or press Space to flip
Gauss's Law of Electrostatics
GetMyMockTestQuestion side

Full list

Terms in this deck (25)

CBSE Class 12 mock tests →
1
Gauss's Law of Electrostatics
Total electric flux through any closed Gaussian surface equals the net enclosed charge divided by permittivity: Phi_E = closed_integral(E . dA) = q_enclosed / epsilon_0.
2
Capacitance of a Parallel Plate Capacitor with Dielectric
C = (K epsilon_0 A) / d; inserting a dielectric of dielectric constant K multiplies capacitance by K, increases stored energy (if connected to battery), or decreases voltage (if isolated).
3
Drift Velocity and Current Density Relation
v_d = (e E tau) / m, and Current I = n A e v_d; Current Density J = I / A = n e v_d = sigma E (microscopic Ohm's law).
4
Biot-Savart Law for Magnetic Field
dB = (mu_0 / 4pi) (I dl x r_hat) / r^2; magnetic field at center of a circular current loop of radius R is B = (mu_0 * I) / (2R).
5
Faraday's Law and Lenz's Law of Induction
EMF e = -dPhi_B / dt; the negative sign reflects Lenz's Law: the polarity of induced electromotive force opposes the change in magnetic flux producing it.
6
Resonance Frequency in Series LCR Circuit
omega_0 = 1 / sqrt(L C), or f_0 = 1 / (2 pi sqrt(L C)); at resonance, inductive and capacitive reactances cancel (X_L = X_C), impedance is minimum (Z = R), and current is maximum.
7
Lens Maker's Formula
1/f = (n_2/n_1 - 1) * (1/R_1 - 1/R_2), relating focal length of a thin spherical lens to its refractive index relative to surrounding medium and radii of curvature.
8
Young's Double Slit Fringe Width Formula
Fringe width beta = (lambda * D) / d, where lambda is wavelength, D is slit-to-screen distance, and d is separation between the two coherent slits.
9
Einstein's Photoelectric Equation
K_max = h nu - phi_0 = e V_0, where h*nu is incident photon energy, phi_0 is work function, and V_0 is stopping potential.
10
Bohr's Postulate of Quantized Angular Momentum
L = m v r = (n h) / (2 pi), where n is the principal quantum number (n = 1, 2, 3...).
11
Nuclear Binding Energy per Nucleon Curve Significance
Peaks around Iron-56 (approx 8.75 MeV/nucleon); lighter nuclei undergo nuclear fusion to gain binding energy, while heavy nuclei (Uranium) undergo nuclear fission.
12
Nernst Equation for Electrode Potential at 298 K
E = E_std - (0.0591 / n) * log10([Products] / [Reactants]); relates cell potential to reaction quotient under non-standard conditions.
13
Kohlrausch's Law of Independent Migration of Ions
Limiting molar conductivity of an electrolyte is the sum of limiting molar conductivities of its individual cations and anions: Lambda_m^0 = nu_+ lambda_+^0 + nu_- lambda_-^0.
14
Integrated Rate Equation for First-Order Reaction
k = (2.303 / t) * log10([A]_0 / [A]_t); half-life t_1/2 = 0.693 / k, which is strictly independent of initial reactant concentration.
15
Arrhenius Equation for Temperature Dependence of Rate Constant
k = A e^(-E_a / (R T)), or log10(k2 / k1) = (E_a / 2.303R) * (1/T1 - 1/T2).
16
SN1 vs SN2 Reaction Mechanisms in Haloalkanes
SN1: Two-step, tertiary > secondary > primary, forms carbocation intermediate, gives partial racemization; SN2: One-step, primary > secondary > tertiary, concerted backside attack, gives Walden inversion.
17
Aldol Condensation vs Cannizzaro Reaction
Aldol occurs in aldehydes/ketones possessing alpha-hydrogens in dilute base; Cannizzaro occurs in aldehydes lacking alpha-hydrogens (e.g., formaldehyde, benzaldehyde) via self redox in concentrated base.
18
Gabriel Phthalimide Synthesis Specificity
Synthesizes pure primary aliphatic amines exclusively; aryl amines (aniline) cannot be prepared by this method because aryl halides do not undergo nucleophilic substitution with potassium phthalimide.
19
Derivative of Inverse Trigonometric Functions
d/dx [arcsin(x)] = 1 / sqrt(1 - x^2); d/dx [arctan(x)] = 1 / (1 + x^2); d/dx [arccos(x)] = -1 / sqrt(1 - x^2).
20
Rolle's Theorem Conditions and Conclusion
If f(x) is continuous on [a, b], differentiable on (a, b), and f(a) = f(b), then there exists at least one c in (a, b) such that f'(c) = 0.
21
Lagrange's Mean Value Theorem
If f(x) is continuous on [a, b] and differentiable on (a, b), then there exists c in (a, b) such that f'(c) = [f(b) - f(a)] / (b - a).
22
Integration by Parts Formula
integral(u v dx) = u integral(v dx) - integral( u' * [integral(v dx)] dx ), prioritized by the ILATE rule (Inverse, Logarithmic, Algebraic, Trigonometric, Exponential).
23
Vector Cross Product Magnitude and Geometric Meaning
|a x b| = |a| |b| sin(theta); geometrically represents the area of the parallelogram formed with vectors a and b as adjacent sides.
24
Shortest Distance Between Two Skew Lines in 3D Space
d = |(a2 - a1) . (b1 x b2)| / |b1 x b2|, where lines are r = a1 + lambda b1 and r = a2 + mu b2.
25
Bayes' Theorem for Conditional Probability
P(E_i | A) = [P(E_i) P(A | E_i)] / sum_j [P(E_j) P(A | E_j)], updating prior probabilities given observed experimental evidence A.

More CBSE Class 12 practice

Other CBSE Class 12 flashcard decks

CBSE Class 12 mock tests

All CBSE Class 12 practice →