CBSE Class 12 PCM Physics Board Paper 2026 — Set 5

Two small identical metallic balls having charges q and – 2q are kept far at a separation r. They are brought in contact and then separated at distance r/2 . Compared to the initial force F, they will now :

The figure represents the variation of the electric potential V at a point in a region of space as a function of its position along the x-axis. A charged particle will experience the maximum force at :

Four long straight thin wires are held vertically at the corners A, B, C and D of a square of side ‘a’, kept on a table and carry equal current ‘I’. The wire at A carries current in upward direction whereas the current in the remaining wires flows in downward direction. The net magnetic field at the centre of the square will have the magnitude:

The magnetic flux through a loop placed in a magnetic field can be changed by changing:

Which of the following statements is not true for electric energy in ac form compared to that in dc form?

The magnetic field in a plane electromagnetic wave travelling in glass (n = 1.5) is given by Bᵧ = (2 × 10⁻⁷ T) sin (αx + 1.5 × 10¹¹ t) where x is in metres and t is in seconds. The value of α is:

Light of which of the following colours will have the maximum energy in a photon associated with it ?

Nuclides with the same number of neutrons are called:

The energy of an electron in an orbit in hydrogen atom is –3.4 eV. Its angular momentum in the orbit will be:

A good diode checked by a multimeter should indicate:

The rms and the average value of an ac voltage V = V₀ sin ωt volt over a cycle respectively will be:

Assertion (A): Induced emf produced in a coil will be more when the magnetic flux linked with the coil is more. Reason (R): Induced emf produced is directly proportional to the magnetic flux.

Assertion (A): In Young’s double-slit experiment, the fringe width for dark and bright fringes is the same. Reason (R): Fringe width is given by β = λD/d, where symbols have their usual meanings.

Assertion (A): Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion. Reason (R): For heavy nuclei, binding energy per nucleon increases with increasing Z while for light nuclei, it decreases with increasing Z.

Assertion (A): Photoelectric effect is a spontaneous phenomenon. Reason (R): According to the wave picture of radiation, an electron would take hours/days to absorb sufficient energy to overcome the work function and come out from a metal surface.

An electric iron rated 2.2 kW, 220 V is operated at 110 V supply. Find:
(i) its resistance, and
(ii) heat produced by it in 10 minutes.

A current of 4.0 A flows through a wire of length 1 m and cross-sectional area 1.0 mm², when potential difference of 2 V is applied across its ends.
Calculate the resistivity of the material of the wire.

A plane circular coil is rotated about its vertical diameter with a constant angular speed ω in a uniform horizontal magnetic field. Initially the plane of the coil is parallel to the magnetic field. Draw plots showing the variation of the following physical quantities as the function of ωt, where t represents time elapsed:
(a) Magnetic flux ϕ linked with the coil, and
(b) emf induced in the coil.

A tank is filled with a liquid to a height of 12.5 m. The apparent depth of a needle lying at the bottom of the tank is measured to be 9.0 m. Calculate the speed of light in the liquid.

Two thin lenses of focal length f₁ and f₂ are placed in contact with each other coaxially. Prove that the focal length f of the combination is given by f = (f₁f₂)/(f₁ + f₂)

Suppose a pure Si crystal has 5 × 10²⁸ atoms per m³. It is doped with 5 × 10²² atoms per m³ of Arsenic. Calculate the majority and minority carrier concentration in the doped silicon. (Given: nᵢ = 1.5 × 10¹⁶ m⁻³)

Two parallel plate capacitors X and Y are connected in series to a 6 V battery. They have the same plate area and same plate separation but capacitor X has air between its plates, whereas capacitor Y contains a material of dielectric constant 4.
(a) Calculate the capacitances of X and Y, if the equivalent capacitance of the combination is 4 μF.
(b) Calculate the potential difference across the plates of X and Y.

Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field 𝐁⃗ at a point (1 m, 1 m, 0).

A long solenoid of length L and radius r₁ having N₁ turns is surrounded symmetrically by a coil of radius (r₂ > r₁) having N₂ turns (N₂ << N₁) around its mid-point. Derive an expression for the mutual inductance of solenoid and coil. Is M₁₂ = M₂₁ valid in this case?

What is displacement current (i_d)? Considering the case of charging of a capacitor, show that i_d = ε₀ (dΦ_E/dt). What is the value of i_d for a conductor across which a constant voltage is applied?

(i) Write any two features of nuclear forces.
(ii) If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.

(i) Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.
(ii) If Bohr's quantization postulate (angular momentum = nh/2π) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.

Photoemission of electrons occurs from a metal (ϕ₀ = 1.96 eV) when light of frequency 6.4 × 10¹⁴ Hz is incident on it. Calculate:
(a) Energy of a photon in the incident light,
(b) The maximum kinetic energy of the emitted electrons, and
(c) The stopping potential.

Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

(i) Derive the condition for which a Wheatstone Bridge is balanced.
(ii) Determine the current in 3 Ω branch of a Wheatstone Bridge in the circuit shown in the figure.

(i) Consider a cylindrical conductor of length l and area of cross-section A. Current I is maintained in the conductor and electrons drift with velocity v_d(|𝐯⃗_d| = e|𝐄⃗ |/m τ), (where symbols have their usual meanings). Show that the conductivity σ of the material of the conductor is given by
σ = ne²/mτ.
(ii) The resistance of a metal wire at 20°C is 1.05 Ω and at 100°C is 1.38 Ω. Determine the temperature coefficient of resistivity of this metal.

(i) A rectangular loop of sides a and b carrying current I is placed in a magnetic field 𝐁⃗ such that its area vector 𝐀⃗ makes an angle θ with 𝐁⃗. With the help of a suitable diagram, show that the torque τ(vector) acting on the loop is given by τ(vector) = 𝐦⃗× 𝐁⃗, where m(vector) (= I 𝐀⃗) is the magnetic dipole moment of the loop.
(ii) A circular coil of 100 turns and radius (10/√π) cm carrying current of 5.0 A is suspended vertically in a uniform horizontal magnetic field of 2.0 T. The field makes an angle 30° with the normal to the coil. Calculate:
(a) the magnetic dipole moment of the coil, and
(b) the magnitude of the counter torque that must be applied to prevent the coil from turning.

(i) Derive an expression for the force 𝐅⃗ acting on a conductor of length L and area of cross-section A carrying current I and placed in a magnetic field 𝐁⃗ .
(ii) A part of a wire carrying 2.0 A current and bent at 90° at two points is placed in a region of uniform magnetic field 𝐁⃗ = −(0.50 T) k̂, as shown in the figure. Calculate the magnitude of the net force acting on the wire.

(i) A parallel beam of monochromatic light falls normally on a single slit of width ‘a’ and a diffraction pattern is observed on a screen placed at distance D from the slits. Explain :

(I) the formation of maxima and minima in the diffraction pattern, and

(II) why the maxima go on becoming weaker and weaker with its increasing number (n).

(ii) Write any two points of difference between interference pattern due to double-slit and diffraction pattern due to single-slit.

(i) With the help of a ray diagram, describe the construction and working of a compound microscope.

(ii) (I) The real image of an object placed between f and 2f from a convex lens can be seen on a screen placed at the image location. If the screen is removed, is the image still there ? Explain.

(II) Plane and convex mirrors produce virtual images of objects. Can they produce real images under some circumstances ? Explain.