Question Browser

A wire of resistance R is stretched so that its length becomes twice its original length. What will be the new resistance of the wire? Justify your answer.

State Kirchhoff's laws of electrical circuits. Using Kirchhoff's laws, find the current through each branch of the following circuit.

The SI unit of electrical resistivity is:

Define drift velocity. Derive the expression for electric current in a conductor in terms of drift velocity.

Choose the correct option from the following:

In a Wheatstone bridge, the resistances in the four arms are P = 10Ω, Q = 10Ω, R = 10Ω and S = 10Ω. A galvanometer of resistance 100Ω is connected between B and D. Calculate the current through the galvanometer when a battery of EMF 2V and negligible internal resistance is connected across AC.

State Gauss's Law in electrostatics. Using Gauss's Law, derive the expression for the electric field due to an infinitely long straight uniformly charged wire.

Define electric potential. Derive an expression for the electric potential at a point due to a point charge. Also obtain the expression for the potential energy of a system of two point charges.

The electric field inside a conductor in electrostatic equilibrium is:

A parallel plate capacitor has plates of area A separated by distance d. It is connected to a battery of voltage V.

Choose the correct option:

Three point charges q₁ = +2μC, q₂ = -4μC, and q₃ = +3μC are placed at the vertices of an equilateral triangle of side 0.2 m. Calculate the electrostatic potential energy of the system.

State Biot-Savart Law. Using it, derive the expression for the magnetic field at the centre of a circular current-carrying loop of radius R carrying current I.

A straight wire carrying current I is placed in a uniform magnetic field B. Derive the expression for the force per unit length between two parallel current-carrying conductors. Under what condition do they attract each other?

A charged particle moves in a magnetic field. The work done by the magnetic force on the particle is:

Describe the principle, construction, and working of a moving coil galvanometer. How is it converted into (a) an ammeter and (b) a voltmeter?

State Faraday's laws of electromagnetic induction and Lenz's law. How does Lenz's law relate to the principle of conservation of energy?

A rectangular coil of 200 turns, each of area 0.05 m², is placed in a uniform magnetic field of 0.1 T. The coil is rotated at 50 rev/s about an axis perpendicular to the field. Calculate the peak EMF and the instantaneous EMF when the coil has rotated 30° from the position of zero EMF.

A copper ring is held horizontally and a bar magnet is dropped through it with its length along the axis of the ring. The acceleration of the falling magnet is:

Define the term 'critical angle'. Derive the relation between critical angle and refractive index. Describe with a diagram the phenomenon of total internal reflection and give two applications.

An object is placed at a distance of 30 cm from a concave mirror of focal length 20 cm. Find the image distance and state the nature of the image formed.

Draw a labelled ray diagram of a compound microscope. Derive an expression for its total magnification when the final image is formed at the near point (D = 25 cm).

Define molar conductivity. How does the molar conductivity of (a) a strong electrolyte and (b) a weak electrolyte vary with dilution? Explain the difference.

Calculate the EMF of the cell: Zn | Zn²⁺ (0.001 M) || Cu²⁺ (0.1 M) | Cu. Given E°cell = +1.10 V, T = 298 K.

In the electrolysis of dilute H₂SO₄, which gas is liberated at the cathode?

Define activation energy. Using the Arrhenius equation, explain how temperature affects the rate of reaction. A reaction has an activation energy of 80 kJ/mol. By what factor does the rate constant increase when temperature is raised from 300 K to 310 K?

Evaluate: ∫₀^π x sin x / (1 + cos²x) dx

Evaluate: ∫ x² / (x² + 4)(x² + 9) dx using partial fractions.

A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability that the card drawn is (a) a king or a queen, (b) a red card or a king.

Bag I contains 3 red and 4 black balls. Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it was drawn from Bag II. (Use Bayes' theorem.)

If A = [[2, 3], [1, -4]] and B = [[1, -2], [3, 5]], verify that (AB)ᵀ = BᵀAᵀ.

State Newton's second law of motion. A body of mass 5 kg is acted upon by two forces: F₁ = 8N due east and F₂ = 6N due north. Find the magnitude and direction of the resultant acceleration.

A bullet of mass m moving with velocity v strikes a stationary wooden block of mass M and embeds itself in it. The velocity of the combined system after collision is:

State the first law of thermodynamics. In a thermodynamic process, 500 J of heat is added to a system and the system does 200 J of work. What is the change in internal energy of the system?

Derive an expression for the escape velocity from the surface of the Earth. Calculate the escape velocity for Earth (R = 6.4 × 10⁶ m, g = 9.8 m/s²).

State Heisenberg's uncertainty principle. An electron has a velocity of (3 ± 0.01) × 10⁵ m/s. Calculate the uncertainty in position of the electron (mass of electron = 9.1 × 10⁻³¹ kg, h = 6.626 × 10⁻³⁴ J·s).

Explain why BF₃ is a Lewis acid but NF₃ is not. What happens when BF₃ reacts with NH₃?