A quantity \( X \) is given by: \[ X = \frac{\epsilon_0 L \Delta V}{\Delta t} \] where:
- \( \epsilon_0 \) is the permittivity of free space,
- \( L \) is the length,
- \( \Delta V \) is the potential difference,
- \( \Delta t \) is the time interval.
The dimension of \( X \) is the same as that of:

Define 'Mass defect' and 'Binding energy' of a nucleus. Describe 'Fission process' on the basis of binding energy per nucleon.

Mention two information that you can get from these characteristics.

Show the shape of the characteristics of a diode.

Draw circuit arrangement for studying V-I characteristics of a p-n junction diode.

A parallel plate capacitor is charged by an ac source. Show that the sum of conduction current (\( I_c \)) and the displacement current (\( I_d \)) has the same value at all points of the circuit.

Consider two long co-axial solenoids \( S_1 \) and \( S_2 \), each of length \( l \) (\( l \gg r_2 \)) and radius \( r_1 \) and \( r_2 \) (\( r_2>r_1 \)). The number of turns per unit length are \( n_1 \) and \( n_2 \), respectively. Derive an expression for mutual inductance \( M_{12} \) of solenoid \( S_1 \) with respect to solenoid \( S_2 \). Show that \( M_{21} = M_{12} \).

Define the magnetic moment of a current-carrying coil. Write its SI unit.

When electrons drift in a conductor from lower to higher potential, does it mean that all the ’free electrons’ of the conductor are moving in the same direction?

Two batteries of emfs 3V and 6V and internal resistances 0.2 and 0.4 are connected in parallel. This combination is connected to a 4 resistor. Find:
(i) the equivalent emf of the combination
(ii) the equivalent internal resistance of the combination
(iii) the current drawn from the combination

A p-type Si semiconductor is made by doping an average of one dopant atom per \( 5 \times 10^7 \) silicon atoms. If the number density of silicon atoms in the specimen is \( 5 \times 10^{28} \, \text{atoms/m}^3 \), find the number of holes created per cubic centimetre in the specimen due to doping. Also, give one example of such dopants.

The energy of an electron in an orbit of Bohr hydrogen atom is \( -3.4 \, \text{eV} \). Find its angular momentum.

In a Young's double-slit experiment, two light waves, each of intensity \( I_0 \), interfere at a point, having a path difference \( \frac{\lambda}{2} \) on the screen. Find the intensity at this point.

In a diffraction experiment, the slit is illuminated by light of wavelength 600 nm. The first minimum of the pattern falls at \( \theta = 30^\circ \). Calculate the width of the slit.

Show that \( \mathbf{E} = \rho \mathbf{J} \) leads to Ohm's law. Write a condition in which Ohm's law is not valid for a material.

Assertion (A): It is difficult to move a magnet into a coil of large number of turns when the circuit of the coil is closed.
Reason (R): The direction of induced current in a coil with its circuit closed, due to motion of a magnet, is such that it opposes the cause.