Class 12th physics formulae

 

1. Electrostatics

Important Formulas:

1. Coulomb's Law:

   $$F = \frac{k q_1 q_2}{r^2}$$

   where $k = \frac{1}{4\pi\epsilon_0}$.

2. Electric Field:

   $$E = \frac{F}{q} = \frac{kq}{r^2}$$

3. Electric Potential:

   $$V = \frac{kq}{r}$$

4. Capacitance of a Parallel Plate Capacitor:

   $$C = \frac{\epsilon_0 A}{d}$$

5. Energy Stored in a Capacitor:

   $$U = \frac{1}{2} C V^2$$

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2. Current Electricity

Important Formulas:

1. Ohm's Law:

   $$V = IR$$

2. Resistance in Series:

   $$R_{\text{eq}} = R_1 + R_2 + \dots$$

3. Resistance in Parallel:

   $$\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots$$

4. Power:

   $$P = VI = I^2R = \frac{V^2}{R}$$

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3. Magnetic Effects of Current and Magnetism

Important Formulas:

1. Biot-Savart Law:

   $$dB = \frac{\mu_0}{4\pi} \frac{I \, dl \, \sin\theta}{r^2}$$

2. Magnetic Field due to a Long Straight Conductor:

   $$B = \frac{\mu_0 I}{2\pi r}$$

3. Force on a Moving Charge in Magnetic Field:

   $$F = q (\vec{v} \times \vec{B})$$

4. Torque on a Magnetic Dipole:

   $$\tau = \vec{M} \times \vec{B}$$

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4. Electromagnetic Induction

Important Formulas:

1. Faraday's Law of Induction:

   $$\mathcal{E} = -\frac{d\Phi_B}{dt}$$

2. Induced EMF in a Coil:

   $$\mathcal{E} = -N \frac{d\Phi_B}{dt}$$

3. Self-Inductance:

   $$L = \frac{\mu_0 N^2 A}{l}$$

4. Energy Stored in an Inductor:

   $$U = \frac{1}{2} L I^2$$

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5. Alternating Current

Important Formulas:

1. Impedance in an LCR Circuit:

   $$Z = \sqrt{R^2 + (X_L - X_C)^2}$$

2. Inductive Reactance:

   $$X_L = \omega L = 2\pi f L$$

3. Capacitive Reactance:

   $$X_C = \frac{1}{\omega C} = \frac{1}{2\pi f C}$$

4. Average Power:

   $$P = V_{\text{rms}} I_{\text{rms}} \cos\phi$$

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6. Optics

Important Formulas:

1. Lens Maker's Formula:

   $$\frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$$

2. Mirror Equation:

   $$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$$

3. Magnification:

   $$m = \frac{h'}{h} = \frac{-v}{u}$$

4. Snell's Law:

   $$n_1 \sin\theta_1 = n_2 \sin\theta_2$$

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7. Modern Physics

Important Formulas:

1. Photoelectric Equation:

   $$K.E_{\text{max}} = h\nu - \phi$$

2. De Broglie Wavelength:

   $$\lambda = \frac{h}{p} = \frac{h}{mv}$$

3. Einstein’s Mass-Energy Relation:

   $$E = mc^2$$

4. Energy of an Electron in the nth Orbit (Bohr Model):

   $$E_n = -\frac{13.6}{n^2} \, \text{eV}$$