List of top Questions asked in CBSE CLASS XII- 2025

According to the band theory of solids, a semiconductor has a valence band and a conduction band separated by a gap, known as energy band gap. Pure semiconductors are called intrinsic semiconductors. At room temperature, some electrons from the valence band can acquire enough energy to cross the band gap and enter the conduction band. The number of conduction electrons is equal to the number of holes in an intrinsic semiconductor. The number of charge carriers can be changed by doping of a suitable impurity in a pure semiconductor. Such semiconductors are known as extrinsic semiconductors. These are of two types (n-type and p-type).

A p-n junction is the basic building block of semiconductor devices. Two important processes occur during formation of a p-n junction: diffusion and drift. A 'depletion layer' is formed in a p-n junction. This is responsible for a junction potential barrier. A semiconductor diode is basically a p-n junction with metallic contacts provided at the ends for the application of an external voltage. A diode can be forward-biased or reverse-biased. The barrier height and the depletion layer width in a p-n junction changes depending on the nature of the biasing.

A compound microscope is an optical instrument used for observing highly magnified images of tiny objects. It consists of two convex lenses. The lens near the object is called the objective and the lens near the eye is called the eyepiece. The magnifying power of a compound microscope is given by \(m = m_o m_e\), where \(m_o\) is the magnification produced by objective lens and \(m_e\) is the magnification produced by eyepiece lens. The expression for \(m_e\) depends on whether the final image is formed at the near point or at infinity (normal adjustment).

State Huygens principle. Using it, draw a diagram and discuss the case of refraction of plane wave of light from a rarer medium to a denser medium at their plane interface. Hence derive Snell's law.

A ray of light is incident on one face of a triangular glass prism of refractive index n and is refracted out from the opposite face. Deduce the expression for refractive index of glass prism in terms of the angle of minimum deviation and angle of the prism. Write the condition on n for refraction to take place on the opposite face.

(i) Prove that the voltage is ahead of the current in phase by \(\dfrac{\pi}{2}\) rad in an ac circuit containing an ideal inductor.

(ii) The currents through two inductors of self-inductance 12 mH and 24 mH are increasing with time at the same rate. Draw graphs showing the variation of the: (I) magnitude of emf induced with the rate of change of current in each inductor. (II) energy stored in each inductor with the current flowing through it.

(i) Write Coulomb's law of electrostatics in vector form. Apply it to determine the electric field at a point due to a system of point charges.

(ii) ABC is an equilateral triangle of side \(l\). Two point charges \(+2\,\mu\text{C}\) each, are located at points B and C. Find the sign and magnitude of the point charge \(q\) to be kept at the midpoint M of the side BC, so that the net electric field at point A becomes zero.

(i) A series combination of L, C and R is connected to an ac source \(V = V_m \sin \omega t\). Obtain:

(I) the impedance of the circuit using phasor diagram,

(II) the expression for the instantaneous current I, and

(III) the phase relationship of current to the applied voltage.

(ii) Define power factor of an ac circuit. State the conditions under which it is: (I) maximum, (II) minimum.

(i) A parallel plate capacitor A of capacitance C is charged by a battery to a potential 'V'. The battery is disconnected and an uncharged identical capacitor B is connected across it. Calculate for the capacitor A the new value of the: (I) charge (II) potential difference (III) energy stored. Justify your answers.

(ii) Draw the pattern of electric field lines due to: (I) a positively charged conducting sphere, and (II) an electric dipole.

Define the term 'drift velocity' of electrons in a current carrying conductor and derive, in its term, the expression for current flowing through the conductor.

Define binding energy (BE) of a nucleus. An unstable nucleus has mass number A = 240 and \(\dfrac{BE}{A} = 7.6\) MeV. It splits in two fragments, each of A = 120 with \(\dfrac{BE}{A} = 8.5\) MeV. Calculate the energy released.

A rectangular loop \((4\,\text{cm} \times 5\,\text{cm})\) of wire carrying current of 0.25 A is placed in a magnetic field \(\vec{B} = [(0.20\,\text{T})\hat{j} + (0.50\,\text{T})\hat{k}]\) such that outward unit vector normal to the plane of the loop is \((0.80\,\hat{i} - 0.60\,\hat{j})\).

Calculate:

(a) the magnetic moment \(\vec{m}\) of the loop, and

(b) the torque \(\vec{\tau}\) acting on the loop.

Light of wavelength 640 nm incident on the slits in a Young's double-slit experiment produces an interference pattern on the screen with fringe width 7.2 mm. Calculate the wavelength of light which will produce a pattern of fringe width 8.1 mm.

An electron (mass \(9 \times 10^{-31}\) kg and charge \(1.6 \times 10^{-19}\) C) is moving in a circle with a speed of \(3.2 \times 10^7\) m/s in a magnetic field of \(4.5 \times 10^{-4}\) T perpendicular to it. Calculate: (i) the radius of the circular path, (ii) its frequency of rotation, and (iii) its energy.

Depict the variation of electric and magnetic fields in an electromagnetic wave as it propagates along the z-axis. In a plane electromagnetic wave in free space, the electric field oscillates sinusoidally at a frequency of \(1.5 \times 10^{10}\) Hz with amplitude \(36\,\text{Vm}^{-1}\). Find:

(a) the wavelength of the wave, and

(b) the amplitude of the associated magnetic field.

With the help of a circuit diagram, describe the method to obtain the p-n junction diode characteristic when it is forward biased. Draw the shape of the characteristic.

A \(20\,\mu\text{F}\) capacitor is connected to a 220 V, \(\dfrac{125}{\pi}\) Hz ac source.

(i) Find the capacitive reactance and the peak value of current in the circuit.

(ii) If the frequency of the ac source is doubled, by what factor will the capacitive reactance and the current be changed?

Write the three postulates of Bohr model of hydrogen atom. Show that, in this model, the frequency of revolution of an electron in its \(n^{th}\) orbit is proportional to \(\left(\dfrac{1}{n^3}\right)\).

Define electric flux. Is it a scalar or a vector quantity?

A point charge \(q\) is kept at a distance of \(\dfrac{d}{2}\) directly above the centre of a square of side \(d\). Use Gauss' law to obtain the expression for the electric flux through this square.

Now if this point charge is moved to a point at a distance 'd' directly above the centre of the square and the side of the square is doubled, explain how the electric flux through the square will be affected.

The figure shows a network of resistors connected across a battery. Find the current supplied by the battery of emf 5 V and internal resistance \(\dfrac{2}{3}\,\Omega\).