List of practice Questions

The currents passing through two inductors of self-inductances 10 mH and 20 mH increase with time at the same rate. Draw graphs showing the variation of:
(I) The magnitude of emf induced with the rate of change of current in each inductor:
(II) The energy stored in each inductor with the current flowing through it:

The ends of six wires, each of resistance R (= 10 \(\Omega\)) are joined as shown in the figure. The points A and B of the arrangement are connected in a circuit. Find the value of the effective resistance offered by it to the circuit.

A rectangular glass slab ABCD (refractive index 1.5) is surrounded by a transparent liquid (refractive index 1.25) as shown in the figure. A ray of light is incident on face AB at an angle \(i\) such that it is refracted out grazing the face AD. Find the value of angle \(i\).

An electron of mass \(m\) and charge \(-e\) is revolving anticlockwise around the nucleus of an atom. (a) Obtain the expression for the magnetic dipole moment \(\mu\) of the atom.

(b) If \( \vec{L} \) is the angular momentum of the electron, show that:
\[ \vec{\mu} = -\frac{e}{2m} \vec{L} \]

Two infinitely long straight wires ‘1’ and ‘2’ are placed \(d\) distance apart, parallel to each other, as shown in the figure. They are uniformly charged having charge densities \(\lambda\) and \(-\frac{\lambda}{2}\) respectively. Locate the position of the point from wire ‘1’ at which the net electric field is zero and identify the region in which it lies.

Two small solid metal balls A and B of radii \(R\) and \(2R\) having charge densities 2 and 3 respectively are kept far apart. Find the charge densities on A and B after they are connected by a conducting wire.

In Young's double slit experiment, the separation between the two slits is 1.0 mm and the screen is 1.0 m away from the slits. A beam of light consisting of two wavelengths, 500 nm and 600 nm, is used to obtain interference fringes. Calculate:
(a) The distance between the first maxima for the two wavelengths.
(b) The least distance from the central maximum, where the bright fringes due to both the wavelengths coincide.

A parallel plate capacitor has plate area \( A \) and plate separation \( d \). Half of the space between the plates is filled with a material of dielectric constant \( K \) in two ways as shown in the figure. Find the values of the capacitance of the capacitors in the two cases.

The resistance of a wire at 25°C is 10.0 \( \Omega \). When heated to 125°C, its resistance becomes 10.5 \( \Omega \). Find (i) the temperature coefficient of resistance of the wire, and (ii) the resistance of the wire at 425°C.

Draw the energy-band diagram for conductors, semiconductors, and insulators at T = 0 K. How is an electron-hole pair formed in a semiconductor at room temperature?

A point object is placed in air at a distance \( \frac{R}{3} \) in front of a convex surface of radius of curvature \( R \), separating air from a medium of refractive index \( n \) (where \( n<4 \)). Find the nature and position of the image formed.

A voltmeter of resistance 1000 \( \Omega \) can measure up to 25 V. How will you convert it so that it can read up to 250 V?

Carbon and silicon both are members of the IV group of the periodic table and have the same lattice structure. Carbon is an insulator whereas silicon is a semiconductor. Explain.

Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
% Assertion Assertion (A): During the formation of a nucleus, the mass defect produced is the source of the binding energy of the nucleus.
Reason (R): For all nuclei, the value of binding energy per nucleon increases with mass number.

The kinetic energy of an alpha particle is four times the kinetic energy of a proton. The ratio \( \left( \frac{\lambda_\alpha}{\lambda_p} \right) \) of de Broglie wavelengths associated with them will be:

Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C), and (D) as given below.
Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
Assertion (A): The Balmer series in the hydrogen atom spectrum is formed when the electron jumps from a higher energy state to the ground state.
Reason (R): In Bohr's model of the hydrogen atom, the electron can jump between successive orbits only.

Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C), and (D) as given below.
Assertion (A): The impurities in p-type Si are not pentavalent atoms.
Reason (R): The hole density in the valence band in a p-type semiconductor is almost equal to the acceptor density.

A compound microscope has an objective and an eyepiece of focal lengths \( f_0 \) and \( f_e \), respectively. To obtain a large magnification of a small object, the microscope should have:

Four resistors, each of resistance R and a key K are connected as shown in the figure. The equivalent resistance between points A and B when key K is open will be:

A current of \( \frac{10}{\pi} \) A is maintained in a circular loop of radius 14 cm. The value of dipole moment associated with the loop is:

A metal sheet is inserted between the plates of a parallel plate capacitor of capacitance C. If the sheet partly occupies the space between the plates, the capacitance:

Let P be the foot of the perpendicular from the point \( (1, 2, 2) \) on the line \[ \frac{x-1}{1} = \frac{y + 1}{-1} = \frac{z - 2}{2} \] Let the line \( \mathbf{r} = (-\hat{i} + \hat{j} - 2\hat{k}) + \lambda (\hat{i} - \hat{j} + \hat{k})\), \( \lambda \in \mathbb{R} \), intersect the line \(L\) at \(Q\). Then \( 2(PQ)^2 \) is equal to:

How many grams of sodium chloride (NaCl) are produced when 2.0 moles of sodium (Na) react with excess chlorine gas (Cl\(_2\)? The balanced chemical equation for the reaction is: \[ 2 \, \text{Na} (s) + \text{Cl}_2 (g) \rightarrow 2 \, \text{NaCl} (s) \]