CBSE Class 12 Physics Important Derivations - Complete List with Learning Tips

Derivations in CBSE Class 12 Physics can carry anywhere from 15 to 25 marks in the board exam. They appear as 3-mark and 5-mark questions, and knowing them well can be the difference between 70% and 90% in Physics. The challenge is that there are many derivations, and memorizing them without understanding leads to blank moments in the exam hall.

Here is a chapter-wise list of important derivations and practical tips on how to actually learn them.

Chapter 1: Electric Charges and Fields

• Derivation of electric field due to a dipole on the axial line
• Derivation of electric field due to a dipole on the equatorial line
• Derivation of torque on a dipole in a uniform electric field

Board exam frequency: Very high. At least one dipole derivation appears almost every year.

Chapter 2: Electrostatic Potential and Capacitance

• Derivation of potential due to a point charge
• Derivation of potential due to an electric dipole
• Derivation of capacitance of a parallel plate capacitor
• Derivation of capacitance of a parallel plate capacitor with a dielectric medium
• Energy stored in a capacitor derivation
• Capacitors in series and parallel combination

Board exam frequency: Parallel plate capacitor derivation is one of the most repeated derivations in CBSE Physics.

Chapter 3: Current Electricity

• Derivation of Ohm's law from drift velocity concept
• Derivation of resistivity in terms of drift velocity and relaxation time
• Kirchhoff's laws and their application (Wheatstone Bridge derivation)
• Meter bridge working principle derivation
• Potentiometer principle and its applications

Board exam frequency: Drift velocity derivation and Wheatstone bridge are frequently asked.

Chapter 4: Moving Charges and Magnetism

• Force on a current-carrying conductor in a magnetic field
• Derivation of magnetic field on the axis of a circular current loop (Biot-Savart law application)
• Ampere's circuital law and its application to find magnetic field due to a solenoid and toroid
• Force between two parallel current-carrying conductors (definition of Ampere)

Board exam frequency: Solenoid magnetic field derivation and force between parallel conductors appear very often.

Chapter 5: Magnetism and Matter

• Derivation of magnetic field intensity due to a bar magnet at axial and equatorial points (treated as magnetic dipole)

Board exam frequency: Moderate. Usually appears as a 3-mark question.

Chapter 6: Electromagnetic Induction

• Derivation of EMF induced in a rod moving in a magnetic field (motional EMF)
• Derivation of self-inductance of a solenoid
• Derivation of mutual inductance between two solenoids
• Energy stored in an inductor

Board exam frequency: Motional EMF and self-inductance derivations are very important.

Chapter 7: Alternating Current

• Derivation of average and RMS value of alternating current
• Derivation of impedance and phase angle in LCR series circuit
• Resonance condition in LCR circuit
• Power in AC circuit (power factor)

Board exam frequency: LCR circuit derivation is a favorite among examiners.

Chapter 9: Ray Optics and Optical Instruments

• Derivation of lens maker's formula
• Derivation of mirror formula (1/v + 1/u = 1/f)
• Derivation of refraction at a spherical surface (single surface formula)
• Total internal reflection conditions
• Derivation of magnification and power of a lens combination

Board exam frequency: Lens maker's formula and refraction at curved surface are very frequently asked.

Chapter 10: Wave Optics

• Derivation of conditions for constructive and destructive interference in Young's double slit experiment
• Derivation of fringe width formula
• Derivation of conditions for maxima and minima in single slit diffraction

Board exam frequency: YDSE fringe width derivation appears almost every year. This is a must-know.

Chapter 11: Dual Nature of Radiation and Matter

• Derivation of Einstein's photoelectric equation
• De Broglie wavelength derivation

Board exam frequency: Einstein's photoelectric equation is asked frequently as a 3-mark question.

Chapter 12: Atoms

• Derivation of Bohr's radius and energy of electron in nth orbit
• Derivation of spectral series of hydrogen atom

Board exam frequency: Bohr model derivations appear regularly.

Chapter 13: Nuclei

• Derivation of radioactive decay law (N = N0 e^(-lambda*t))
• Relation between half-life and decay constant

Board exam frequency: Moderate. Usually a 2-3 mark question.

Top 10 Most Important Derivations (If You Are Short on Time)

If you can only focus on a limited number, prioritize these:

1. Electric field due to a dipole (axial and equatorial)
2. Capacitance of parallel plate capacitor (with and without dielectric)
3. Drift velocity and Ohm's law derivation
4. Magnetic field due to a solenoid using Ampere's law
5. Force between two parallel current-carrying conductors
6. Motional EMF derivation
7. Self-inductance of a solenoid
8. Lens maker's formula
9. Young's double slit experiment - fringe width derivation
10. Bohr model - radius and energy in nth orbit

How to Learn Derivations Effectively

Rote memorization of derivations is risky. Here is a better approach:

Step 1: Understand the physics Before writing a single equation, understand what physical situation the derivation describes. What are we trying to prove? What assumptions are we making? Why does this matter?

Step 2: Learn the starting point Every derivation starts with a basic principle or formula. Know the starting point cold. For example, Biot-Savart law is the starting point for magnetic field derivations. Coulomb's law starts most electrostatics derivations.

Step 3: Follow the logic, not the equations Instead of memorizing each step, understand why each step follows from the previous one. This way, even if you forget a step during the exam, you can derive it logically.

Step 4: Draw the diagram first Every Physics derivation has an associated diagram. Draw it, label all variables, and the derivation often writes itself.

Step 5: Practice writing it out Write each derivation at least 5 times on paper. The motor memory of writing helps during the exam. Time yourself - you should be able to write any 5-mark derivation in under 8 minutes.

Step 6: Test yourself regularly Close your book and try to write the derivation from memory. Check against the original. Repeat for any steps you missed.

Presentation Tips for Derivation Questions

How you present a derivation in the exam matters:

• Start with the diagram. Draw it neatly, label all quantities
• State the formula or principle you are starting from
• Number each step or use clear "therefore" and "hence" transitions
• Box or underline the final result
• If the question asks you to "derive and hence show," make sure you explicitly state the "hence" part
• Write neatly. Sloppy handwriting in derivations confuses examiners
• Use proper notation. Do not mix up vector and scalar quantities

Practice Schedule

• Daily: Write 2-3 derivations from memory (rotate chapters)
• Weekly: Pick a random derivation and try to write it cold
• Monthly: Do a full revision of all important derivations
• Before exams: Focus on the top 10 list and ensure you can write each one perfectly

If you get stuck on a derivation or need a concept explained step by step, Padhaao can walk you through the logic behind each derivation. Understanding the physics behind the math makes derivations much easier to remember and reproduce in the exam hall.

Derivations are free marks in Physics. Unlike numericals where a calculation error can cost you everything, derivations reward methodical preparation. Learn them properly, and they will carry your Physics score.