Solution of Chapter 16. Sample Question Paper-1 (Physics - Exemplar Book)

Two positive charges q₂ and q₃ fixed along the y axis, exert a net electric force in the + x direction on a charge q₁ fixed along the x axis as shown. If a positive charge Q is added at (x, 0), the force on q₁

Two batteries of emf ε₁ and ε₂ (ε₂ > ε₁) and internal resistances r₁ and r₂ respectively are connected in parallel as shown.

A proton has spin and magnetic moment just like an electron. Why then its effect is neglected in magnetism of materials?

If a LC circuit is considered analogous to a harmonically oscillating spring-block system, which energy of the LC circuit would be analogous to potential energy and which one analogous to kinetic energy?

A variable frequency ac source is connected to a capacitor. How will the displacement current change with decrease in frequency?

In pair annihilation, an electron and a positron destroy each other to produce gamma radiation. How is the momentum conserved?

Can the potential barrier across a p-n junction be measured by simply connecting a voltmeter across the junction?

The conductivity of a semiconductor increases with increase in temperature because

charges q and –3q are placed fixed on x-axis separated by distance ‘d’. Where should a third charge 2q be placed such that it will not experience any force?

The battery remains connected to a parallel plate capacitor and a dielectric slab is inserted between the plates. What will be effect on its (i) potential difference, (ii) capacity, (iii) electric field, and (iv) energy stored?

Obtain an expression for the magnetic dipole moment of a revolving electron in a Bohr model.

A wire in the form of a tightly wound solenoid is connected to a DC source, and carries a current. If the coil is stretched so that there are gaps between successive elements of the spiral coil, will the current increase or decrease? Explain.

You are given a 2μF parallel plate capacitor. How would you establish an instantaneous displacement current of 1mA in the space between its plates?

There are two sources of light, each emitting with a power of 100 W. One emits X-rays of wavelength 1nm and the other visible light at 500 nm. Find the ratio of number of photons of X-rays to the photons of visible light of the given wavelength?

A particle is moving three times as fast as an electron. The ratio of the de Broglie wavelength of the particle to that of the electron is 1.813 × 10^–4. Calculate the particle’s mass and identify the particle.

Consider two different hydrogen atoms. The electron in each atom is in an excited state. Is it possible for the electrons to have different energies but the same orbital angular momentum according to the Bohr model?

What do the terms ‘depletion region’ and ‘barrier potential’ mean for a p-n junction?

If the whole earth is to be connected by LOS communication using space waves (no restriction of antenna size or tower height), what is the minimum number of antennas required? Calculate the tower height of these antennas in terms of earth’s radius?

Derive an expression (in vector form) for electric field of a dipole at a point on the equatorial plane of the dipole. How does the field vary at large distances?

What is relaxation time? Derive an expression for resistivity of a wire in terms of member density of free electrons and relaxation time.

First a set of n equal resistors of R each is connected in series to a battery of emf E and internal resistance R. A current I is observed to flow. Then the n resistors are connected in parallel to the same battery. It is observed that the current becomes 10 times. What is ‘n’?

An equi-convex lens (of refractive index 1.50) is placed in contact with a liquid layer on top of a plane mirror as shown. A small needle with its tip on the principal axis is moved along the axis until its inverted image is found at the position of the needle. The distance of the needle from the lens is measured to be 45.0 cm. The liquid is removed and the experiment is repeated. The new distance is measured to be 30.0 cm. What is the refractive index of the liquid?

Obtain an expression for focal length of a combination of thin lenses in contact.

Three immiscible liquids of densities d₁ > d₂ > d₃ and refractive indices μ₁ > μ₂ > μ₃ are put in a beaker. The height of each liquid column is . A dot is made at the bottom of the beaker. For near normal vision, find the apparent depth of the dot.

Define ‘half -life’ and ‘average-life’ of a radioactive substance. What is the relation between the two?

Using a suitable combination from a NOR, an OR and a NOT gate, draw circuits to obtain the truth tables given below:

(i)

(ii)

Define the terms ‘modulation index’ for an AM wave. What would be the modulation index for an AM wave for which the maximum amplitude is ‘a’ and the minimum amplitude is ‘b’?

(i) Derive an expression for the magnetic field at a point on the axis of a current carrying circular loop.

(ii) A coil of 100 turns (tightly bound) and radius 10 cm. carries a current of 1A. What is the magnitude of the magnetic field at the center of the coil?

OR

State Ampere’s circuital law. Consider a long straight wire of a circular cross section (radius a) carrying steady current I. The current I is uniformly distributed across this cross section. Using Ampere’s circuital law, find the magnetic field in the region r < a and r > a.

An ac voltage v = v_m sinωt is applied to a series LCR circuit. Obtain the expression for current in the circuit and the phase angle between current and voltage. What is the resonance frequency?

OR

An ac voltage v = v_m sinωt is applied to a pure inductor L. Obtain an expression for the current in the circuit. Prove that the average power supplied to an inductor over one complete cycle is zero.

(i) State and explain Huygens Principle. Using it, obtain Snell’s law of refraction.

(ii) When light travels from a rarer to a denser medium, the speed decreases. Does the reduction in speed imply a reduction in the energy carried by the light wave?

OR

With the help of a labeled ray diagram show the image formation by a compound microscope. Derive an expression for its magnifying power. How can the magnifying power be increased?