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Important Derivations

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Comprehensive List of Derivations for

CBSE Class 12 Physics


Prepared by: Your Name
February 13, 2025

Important:
This document contains a curated list of all important derivations for the CBSE
Class 12 Physics exam. Each derivation is organized chapter-wise for easy reference.

1. Electric Charges and Fields


1. Coulomb’s Law: Force between two point charges.

2. Electric Field due to a Point Charge: Expression for electric field intensity.

3. Electric Field due to an Electric Dipole:

• Along the axial line.


• Along the equatorial line.

4. Torque on an Electric Dipole in a Uniform Electric Field.

5. Gauss’s Law Applications:

• Electric field due to a uniformly charged infinite plane sheet.


• Electric field due to a uniformly charged thin spherical shell (inside and outside).
• Electric field due to a long straight charged wire.

2. Electrostatic Potential and Capacitance


1. Electric Potential due to a Point Charge.

2. Potential Energy of a System of Two Point Charges.

3. Electric Potential due to an Electric Dipole.

4. Capacitance of a Parallel Plate Capacitor:

• Without dielectric medium.


• With dielectric medium.

1
CBSE Class 12 Physics Derivations 2

5. Energy Stored in a Capacitor: U = 12 CV 2 .

6. Effect of Dielectric on Capacitance.

3. Current Electricity
1. Drift Velocity and Ohm’s Law.

2. Combination of Resistors:

• Equivalent resistance in series.


• Equivalent resistance in parallel.

3. Wheatstone Bridge: Condition for balance.

4. Meter Bridge: Principle and working.

5. Potentiometer:

• Comparison of emfs of two cells.


• Internal resistance of a cell.

4. Moving Charges and Magnetism


1. Biot-Savart Law: Magnetic field due to a current-carrying conductor.

2. Ampere’s Circuital Law:

• Magnetic field inside a solenoid.


• Magnetic field inside a toroid.

3. Magnetic Field due to a Current-Carrying Circular Loop:

• At the center.
• On the axis.

4. Force Between Two Parallel Current-Carrying Conductors.

5. Torque on a Current Loop in a Uniform Magnetic Field.

6. Force on a Moving Charge in a Magnetic Field: F = qvB sin θ.

5. Magnetism and Matter


Important:
No derivations in this chapter.
CBSE Class 12 Physics Derivations 3

6. Electromagnetic Induction
1. Faraday’s Laws of Electromagnetic Induction.

2. Lenz’s Law: Direction of induced current.

3. Self-Inductance: Derivation for a solenoid.

4. Mutual Inductance: Between two coils.

5. Energy Stored in an Inductor: U = 12 LI 2 .

7. Alternating Current
1. Impedance of a Series LCR Circuit.

2. Resonance in LCR Circuit: Condition and resonant frequency.

3. Power in an AC Circuit.

4. Transformer: Relationship between primary and secondary voltages.

8. Electromagnetic Waves
Important:
No derivations in this chapter.

9. Ray Optics and Optical Instruments


1. Mirror Formula: For concave and convex mirrors.

2. Refraction at Spherical Surfaces.

3. Lens Maker’s Formula.

4. Combination of Thin Lenses in Contact.

5. Refraction Through a Prism: Angle of deviation and minimum deviation condition.

6. Magnification of Optical Instruments:

• Simple microscope.
• Compound microscope.
• Astronomical telescope.
CBSE Class 12 Physics Derivations 4

10. Wave Optics


1. Huygens’s Principle:

• Proof of laws of reflection.


• Proof of laws of refraction.

2. Young’s Double Slit Experiment:

• Conditions for constructive and destructive interference.


• Fringe width.

3. Diffraction Grating: Condition for maxima.

11. Dual Nature of Radiation and Matter


1. Einstein’s Photoelectric Equation: hν = ϕ + KEmax .

2. de Broglie Wavelength: λ = hp .

12. Atoms
1. Bohr’s Model of the Hydrogen Atom:

• Radius of the nth orbit.


• Energy of the electron in the nth orbit.
• Frequency of emitted radiation during transitions.

2. Rydberg Formula: Spectral series of hydrogen atom.

13. Nuclei
Important:
No derivations in this chapter.

14. Semiconductor Electronics


1. Conductivity of Semiconductors.

2. Diode Current Equation: Forward and reverse bias.

3. Transistor Characteristics:

• Input and output characteristics in common emitter configuration.


• Voltage gain and current gain of a transistor amplifier.

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