Important Physics Derivations asked in ISC Class 12

This article includes all the important derivations which are asked in ISC Class 12 in recent years which is helpful for you to prepare.

Click on the link provided to find the handwritten derivation.

1. Obtain an expression for intensity of electric field at a point in broadside position of an electric dipole.[2023,2020,2015]
2. Obtain an expression for intensity of electric field at a point in end-on position i.e. axial position of an electric dipole.[2018]
3. Obtain an expression for electric potential ‘V’ at a point in an end-on position i.e. axial position of an electric dipole. [2019]
4. Show that electric potential at a point P, at a distance ‘r’ from a fixed point charge Q, is given by

      

   [2017]
5. Deduce an expression for equivalent capacitance C when three capacitors C₁, C₂ and C₃ are connected in parallel.[2018]
6. Obtain an expression for equivalent capacitance C when three capacitors C₁, C₂ and C₃ are connected in series.[2024,2016,2012]
7. ‘n’ cells, each of emf ‘e’ and internal resistance ‘r’ are joined in series to form a row. ‘m’ rows are connected in parallel to form a battery of N=mn cells. This battery is connected to an external resistance ‘R’.
   • What is the emf of the battery and how much is its internal resistance?
   • Show that current ‘I’ flowing through the external resistance ‘R’ is given by-

        

     [2013]
8. Using Ampere circuital law, obtain an expression for magnetic flux density ‘B’ at a point ‘X’ at a perpendicular distance ’r’ from a long current carrying straight conductor.[2017,2023]
9. Obtain an expression for magnetic flux density ‘B’ at the centre of circular coil of radius ‘R’, having N turns and carrying current I.[2024,2015]
10. When two thin lenses are kept in contact, show that their equivalent focal length ‘F’ is given by:

       

    [2022,2020,2018,2014]
11. For refraction at convex spherical surface of denser medium η₂ surrounded by a rarer medium of refractive index η₁, derive a formula connecting object distance u, image distance v, and radius of curvature R for the object in rarer medium and a real image formed inside the denser medium. [2024 S,2023,2020]
12. Starting with an expression for refraction at a single spherical surface, obtain Lens Maker’s formula.[2017]
13. For any prism prove that,

       

    where the terms have their usual meaning.[2025,2023,2018,2012]
14. Draw a labelled ray diagram of an image formed by a refracting telescope with final image formed at infinity. Derive an expression for its magnifying power with the final image at infinity.[2018,2016]
15. Using Huygen’s wave theory, prove the law of reflection of light.[2023,2022,2019,2015]
16. Using Huygen’s wave theory, prove Snell’s Law for refraction of light.[2025,2024,2018,2016,2012]
17. In Young’s Double Slit experiment. Show that

       

    , where the terms have their usual meaning (either for bright or dark fringe).[2024,2019,2016,2013]
18. On the basis of Bohr’s Theory, derive an expression for the radius of the n^th orbit of an electron of hydrogen atom.[2015]
19. Using Bohr’s Theory of hydrogen atom, obtain an expression for the velocity of an electron in the n^th orbit of an atom.[2023]

Some Other Important Derivations

1. Derivation for Drift Velocity.
2. Relation between Current and Drift Velocity
3. Derivation of Ohm’s Law
4. Ohm’s Law in Microscopic Form
5. Torque on an Electric Dipole
6. Electric field due to an infinitely charged wire
7. Gauss Theorem and its derivation
8. Magnetic field due to a straight current carrying wire