Physics (Theory) CBSE Physics XII Board Paper SET C. General Instructions: (i) All questions are compulsory.

Transcription

1 Physics (Theory) [Tie allowed: 3 hours] [Maxiu arks:7] General Instructions: (i) All questions are copulsory. (ii) (iii) (iv) (v) There are 3 questions in total. Questions to 8 carry one ark each. Questions 9 to 8 carry two arks each. Question 9 to 7 carry three arks each. Question 8 to 3 carry five arks each. There is no overall choice. However, an internal choice has been provided in one question of two arks; one question of three arks and all three questions of five arks each. You have to attept only one of the choices in such questions. Use of calculators is not peritted. You ay use the following values of physical constants wherever necessary: C = 3 8 s H = Js e =.6 9 C = 4 7 T A 9 9 N C 4 Mass of electron e = 9. 3 kg Mass of neutron n kg Boltzann s constant k =.38 3 JK Avogadro s nuber N A = 6. 3 ol Radius of earth = 64 k

2 . A plot of agnetic flux ( ) versus current (I) is shown in the figure for two inductors A and Β. Which of the two has larger value of self inductance? Inductor A has the larger value of self-inductance.. Figure shows three point charges +q, q and + 3q. Two charges + q and q are enclosed within a surface S. What is the electric flux due to this configuration through the surface S? The net electric flux through the surface S is q, where is the perittivity of free space. 3. In which orientation, a dipole placed in a unifor electric field is in (i) stable, (ii) unstable equilibriu? A dipole placed in a unifor electric filed is in (i) Stable equilibriu when the electric field is directed along the direction of the dipole i.e., when E is parallel to p. (ii) Unstable equilibriu when the electric filed is directed at an angle of 8 degrees with the direction of the dipole, i.e., when E is anti-parallel to p. 4. Which part of electroagnetic spectru is used in radar systes? The icrowave range of electroagnetic spectru is used in radar systes.

3 5. Calculate the speed of light in a ediu whose critical angle is 3. Speed of light in the ediu Speed of light in air Refractive index of the ediu with respect to air 8 3 /s sin /s 8.5 /s 6. A glass lens of refractive index.45 disappears when iersed in a liquid. What is the value of refractive index of the liquid? The refractive index of the liquid is Write the expression for Bohr s radius in hydrogen ato. h The expression for Bohr s radius in hydrogen ato is a πe. 8. A wire of resistance 8R is bent in the for of a circle. What is the effective resistance between the ends of a diaeter AB? The effective resistance between the ends of diaeter AB is 4R 4R R R.

4 9. Explain the function of a repeater in a counication syste. A repeater is used for extending the range of a counication syste. It consists of a receiver and a transitter. The receiver of a repeater collects the signal fro the transitter of another repeater and after aplifying, it retransits the signal. Soeties, it also changes the carrier frequency of the pick-up signal before transitting it to the receiver.. (i) Write two characteristics of a aterial used for aking peranent agnets. (ii) Why is the core of an electroagnet ade of ferroagnetic aterials? OR Draw agnetic field line when a (i) diaagnetic, (ii) paraagnetic substance is placed in an external agnetic field. Which agnetic property distinguishes this behaviour of the field line due to the substances? (i) The aterial used for aking peranent agnets should have the following characteristics: (a) High retentivity: It ensures that the agnet reains strong even after reoval of the agnetising field. (b) High coercivity: It ensures that the agnetis of the aterial does not get easily lost. Apart fro these two criteria, the aterial should have high pereability. (ii) The core of an electroagnet should have high pereability and low retentivity. The high pereability of the core of an electroagnet ensures that the electroagnet is strong. On the other hand, low retentivity of the core ensures that the agnetis of the core aterial gets lost as soon as the current is switched off. Ferroagnetic aterials have both high pereability and low retentivity. Hence, ferroagnetic aterials are the ost suitable for aking the core of an electroagnet. OR (i) The agnetic field lines, when a diaagnetic aterial is placed in an external agnetic field, can be diagraatically represented as (ii) The agnetic field lines, when a paraagnetic aterial is placed in an external agnetic field, can be diagraatically represented as

5 Diaagnetic and paraagnetic aterials are distinguished by the agnetic property called agnetic susceptibility. For diaagnetic aterials, agnetic susceptibility is negative, whereas for paraagnetic aterials, agnetic susceptibility is slightly positive.. What is the range of frequencies used in satellite counication? What is coon between these waves and light waves? The waves used for satellite counication lie in the following two frequency ranges. (i) GHz for downlink (ii) GHz for uplink The waves used for satellite counication and light waves are both electroagnetic waves. Both of the travel in a straight line.. A coil Q is connected to low voltage bulb B and placed near another coil P as shown in the figure. Give reasons to explain the following observations: (a) The bulb B lights (b) Bulb gets dier if the coil Q is oved towards left. (a) The A.C. source creates a varying agnetic field in coil P. This varying agnetic field of P is linked to coil Q. Hence, an induced current is produced in Q, which lights bulb B. (b) As coil Q oves away fro P, the rate of variation of agnetic flux changes. Therefore, the induced e..f. inside coil Q decreases and bulb B gets dier. 3. Find the radius of curvature of the convex surface of a plano-convex lens, whose focal length is.3 and the refractive index of the aterial of the lens is.5.

6 The focal length of a cobined lens can be deterined by the forula ( ) f R R Here, R and f.3 ( ).3 R R.3( ).3(.5 ) c 4. An electron is accelerated through a potential difference of 64 volts. What is the de-broglie wavelength associated with it? To which part of the electroagnetic spectru does this value of wavelength correspond? de-broglie wavelength, Where, h ev 3 Massof electron 9. kg This value of wavelength corresponds to the X-ray region of the electroagnetic spectru. 5. (i) Out of blue and red light which is deviated ore by a pris? Give reason. (ii) Give the forula that can be used to deterine refractive index of aterials of a pris in iniu deviation condition.

7 (i) Between blue and red light, blue light is deviated ore by a pris. This is because the wavelength of blue light is saller than that of red light. Therefore, the speed of blue light is lower than that of red light in a ediu. (ii) The forula used for deterining the refractive index of aterials of a pris in iniu deviation condition, n sin ( A D ) / sin A Where, n Refractive index of pris aterial with respect to the surrounding ediu A Angle of the pris Angle of iniu deviation D 6. Plot a graph showing the variation of stopping potential with the frequency of incident radiation for two different photosensitive aterials having work functions W and W (W > W ). On what factors does the (i) slope and (ii) intercept of the lines depend? (i) The slope of the graph is content and equals to h e. Therefore, the slope does not depend on any factor. (ii) The intercept of the lines depends on the work function of the etals. 7. Draw the circuit diagra of an illuinated photodiode in reverse bias. How is photodiode used to easure light intensity? The circuit diagra of an illuinated photodiode in reverse bias can be represented as

8 The greater the intensity of light, the greater is the nuber of photons falling per second per unit area. Thus, the greater the intensity of light, the greater is the nuber of electron hole pairs produced at the junction. The photocurrent is, thus, directly proportional to the intensity of light. This can be used for easuring the intensity of incident light. 8. A heavy nucleus X of ass nuber 4 and binding energy per nucleon 7.6 MeV is split into two fragents Y and Z of ass nubers and 3. The binding energy of nucleons in Y and Z is 8.5 MeV per nucleon. Calculate the energy Q released per fission in MeV. Total energy of nucleus X = = 84 MeV Total energy of nucleus Y = 8.5 = 935 MeV Total energy of nucleus Z = = 5 MeV Therefore, energy released fro fission, Q = = 6 MeV 9. (a) Depict the equipotential surfaces for a syste of two identical positive point charges placed a distance d apart. (b) Deduce the expression for the potential energy of a syste of two point charges q and q brought fro infinity to the points r and r respectively in the presence of external electric field E. 3 (a)

9 (b) The work done in bringing charge q fro infinity to r is q V( r ). Work done on q against external field = q V( r ) qq Work done on q against the field due to q 4π o r Where, r is the distance between q and q. By the superposition principle for fields, Work done in bringing q to r is qv ( r ) qq 4π o r. Thus, Potential energy of syste = The total work done in assebling the configuration qv ( r) qv ( r ) qq 4π o r. In a eter bridge, the null point is found at a distance of l c fro A. If now a resistance of X is connected in parallel with S, the null point occurs at l c. Obtain a forula for X in ters of l, l and S. 3 Initially, when X is not connected R l Condition for balance ( i) S l The equivalent resistance (R eq ) of the cobination of X and S is

10 R X S R eq eq R R SX X S l l eq R( X S) SX l ( l ) ( ii) On dividing (i) by (ii), we obtain R SX l ( l) R( X S) X l ( l ) X l ( l) X S l ( l ) Xl ( l ) ( X S) l ( l ) Xl ( l ) Xl ( l ) Sl ( l ) X Sl( l) l ( l ) l ( l ) This is the expression for X in ters of S, l and l.. What is space wave propagation? Give two exaples of counication syste which use space wave ode. A TV tower is 8 tall. Calculate the axiu distance upto which the signal transitted fro the tower can be received. 3 Space wave propagation is the propagation of waves whose frequencies lie above 4 MHz. Exaples of counication systes which use space wave ode are (i) Television broadcast (ii) Microwave links (iii)satellite counication (Any two exaples can be taken) The axiu distance up to which signals can be received, d R E h T

11 k Hence, the axiu distance up to which the transitted signal can be received is 3 k.. (i) Define activity of a radioactive aterial and write its S.I. units. (ii) Plot a graph showing variation of activity of a given radioactive saple with tie. (iii) The sequence of stepwise decay of a radioactive nucleus is D D D If the atoic nuber and ass nuber of D are 7 and 76 respectively, what are their corresponding values of D? 3 (i) The activity of a radioactive aterial is defined as the decay rate of a saple containing one or ore radio nuclides. The SI unit of radioactivity is becquerel (B). (ii) (iii) D D D 76 7 Therefore, D D D Therefore, D D D So, the corresponding values of atoic nuber and ass nuber for D are 74 and 8.

12 3. What is an unpolarized light? Explain with the help of suitable ray diagra how an unpolarized light can be polarized by reflection fro a transparent ediu. Write the expression for Brewster angle in ters of the refractive index of denser ediu. 3 An unpolarised light is one in which the vibration of electric field vector is not restricted in one particular plane. When an unpolarised light falls on the surface, the reflected light is such that the vibration of its electric field vector is confined to one particular plane. The direction of this plane is parallel to the surface of reflection. A coponent of electric field vector is absent fro the refracted light. Therefore, the refracted light is partially polarised. The expression for Brewster angle in ters of the refractive index of denser ediu is tan i B Where, is the refractive index of the denser ediu with respect to the rarer ediu. 4. Write the principle of working of a potentioeter. Describe briefly, with the help of a circuit diagra, how a potentioeter is used to deterine the internal resistance of a given cell. 3 The working principle of a potentioeter is based on Kirchhoff s voltage law. According to this rule, the algebraic su of changes in voltage around any closed loop involving resistors and cells in the loop is zero. Let be the potential drop per unit length in the potentioeter wire.

13 When only a cell is connected, the balance point is N. Appling Kirchhoff s voltage law, = l [l = Length at which the balance point is achieved] When soe current is drawn using the resistance box, the balance point is achieved at N. V = l This gives, l V l = I (r + R) [R = Resistance of the resistance box] V = IR This gives, r R V R r l R l The internal resistance of the cell can be deterined by plugging-in the easured values of l and l. 5. Write the expression for the agnetic oent ( ) due to a planar square loop of side l carrying a steady current I in a vector for. 3 In the given figure this loop is placed in a horizontal plane near a long straight conductor carrying a steady current I at a distance l as shown. Give reason to explain that the loop will experience a net force but no torque. Write the expression for this force acting on the loop. The expression for the agnetic oent ( ) due to a planar square loop of side l carrying a steady current I in a vector for is given as I A Therefore, I() l nˆ Where, ˆn is the unit vector along the noral to the surface of the loop. The attractive force per unit length on the loop is

14 F l II π l a Fa II π The repulsive force per unit length on the loop is Fr II l π l II Fr π l F F F net a r II π Fnet II 4π Since the attractive force is greater than the repulsive force, a net force acts on the loop. The torque on the loop is given as B Bsin IAB sin = ( Area vector is parallel to the agnetic field) = IAB sin = The torque acting on the loop is zero. 6. A long straight wire of a circular cross-section of radius a carries a steady current I. The current is uniforly distributed across the cross-section. Apply Apere s circuital law to calculate the agnetic field at a point r in the region for (i) r < a and (ii) r > a. OR State the underlying principle of working of a oving coil galvanoeter. Write two reasons why a galvanoeter can not be used as such to easure current in a given circuit. Nae any two factors on which the current sensitivity of a galvanoeter depends. 3 (i) For r < a

15 B dl I πa I I πr r I a I enclosed enclosed encolsed B dl Bdl Bdl r I a cos r B dl I a r B(π r) I a B I π a r (ii) For r > a Fro Apere s circuital law,

16 B dl B dl B dl I enclosed Bdl enclosed Bdl cos B(π r) I I π r Bdl I I B dl I B OR I The underlying principle for the working of a oving coil galvanoeter is that when a current-carrying conductor is placed inside a agnetic field, it experiences a agnetic force. The two reasons why a galvanoeter cannot be used for easuring current are The high resistance of galvanoeter can disturb the original current flowing through the circuit The high current present in the circuit can destroy the coil windings present in the galvanoeter The factors on which the current sensitivity of a galvanoeter depends are Nuber of turns in the coil Torsional spring constant Area of the coil Strength of the agnetic field (Any two can be taken as the answer) 7. A parallel-plate capacitor is charged to a potential difference V by a dc source. The capacitor is then disconnected fro the source. If the distance between the plates is doubled, state with reason how the following change: 3 (i) electric field between the plates (ii) capacitance, and (iii) energy stored in the capacitor (i) Q = CV A Q d Q E AE Q A ( Ed)

17 Therefore, the electric field between the parallel plates depends only on the charge and the plate area. It does not depend on the distance between the plates. Since the charge as well as the area of the plates does not change, the electric field between the plates also does not change. (ii) Let the initial capacitance be C and the final capacitance be C'. Accordingly, A C d A C d C C C C Hence, the capacitance of the capacitor gets halved when the distance between the plates is doubled. (iii) Q Energy of a capacitor, U C Since Q reains the sae but the capacitance decreases, Q U C U U U U The energy stored in the capacitor gets doubled when the distance between the plates is doubled. 8. (a) Explain the foration of depletion layer and potential barrier in a p n junction. (b) In the figure given below the input wavefor is converted into the output wavefor by a device X. Nae the device and draw its circuit diagra. (c) Identify the logic gate represented by the circuit as shown and write its truth table.

18 OR (a) With the help of circuit diagra explain the working principle of a transistor aplifier as an oscillator. (b) Distinguish between a conductor, a seiconductor and an insulator on the basis of energy band diagras. 3 (a) In a p n junction, a p-type and an n-type aterial are joined together. The concentration of holes is higher in p-type aterial as copared to that in n-type aterial. Therefore, there is a concentration gradient between the p-type and n-type aterials. As a result of this concentration gradient, holes ove fro p- side to n-side (p n) by the process of diffusion. Siilarly, electrons ove fro n-side to p-side (n p). As the holes diffuse fro p-side, they leave ionised spaces (negatively charged) on p-side near the junction. These ionised spaces are iobile. Hence, a negative space-charge region is fored on the p- side near the junction. Siilarly, a positive space-charge region is fored on the n-side. These two spacecharge regions on either sides of the junction constitute what is called a depletion layer. Since the n-side loses electrons and p-side gains electrons, a potential difference is developed across the junction of the two regions. This potential difference tends to oppose further otions of electron fro the n-region into the p-region. The sae happens for holes too. The reverse polarity of this potential opposes further flow of carriers and is thus called the barrier potential. (b) The device is a full-wave rectifier. The circuit diagra of a full-wave rectifier is represented as (c) The logic gate represented by the circuit is an AND gate. The truth table of the AND gate is represented as A B Α.B

19 OR (a) The circuit diagra for a transistor aplifier as an oscillator is represented as In an oscillator, a sustained Α.C. output is obtained without any input oscillation. For this to happen, the output of a transistor aplifier is fed back into its input. This is achieved by coupling the winding T to winding T. When key S is closed, the collector current begins to increase, which supports the forward bias of the eitter base circuit. Collector current increases until it reaches saturation. When the saturation is reached, the agnetic flux linked to winding T becoes steady. Hence, the forward bias of the eitter base circuit is no longer supported. The transistor is now driven into cut-off. This cycle repeats itself and an oscillating output is obtained. (b) The energy-band diagra of a conductor is represented as The energy-band diagra of a seiconductor is represented as The energy-band diagra of an insulator is represented as

20 9. Describe briefly, with the help of a labelled diagra, the basic eleents of an A.C. generator. State its underlying principle. Show diagraatically how an alternating ef is generated by a loop of wire rotating in a agnetic field. Write the expression for the instantaneous value of the ef induced in the rotating loop. OR A series LCR circuit is connected to a source having voltage v = v sin t. Derive the expression for the instantaneous current I and its phase relationship to the applied voltage. Obtain the condition for resonance to occur. Define power factor. State the conditions under which it is (i) axiu and (ii) iniu. 5 Basic eleents of an A.C. generator An A.C. generator consists of a rotor shaft on which a coil is ounted. A agnetic field is created around an arature coil with the help of peranent agnets. The terinals of the coil are connected to two slip rings. Carbon brushes are attached to slip rings so as to ake connection with an external circuit. Underlying principle of an A.C. generator The underlying principle responsible for the working of an Α.C. generator is electroagnetic induction. According to this principle, if a conductor is placed in a varying agnetic field, then current is induced in the conductor.

21 Generation of an alternating e..f. by a loop of wire rotating in a agnetic field Expression of the instantaneous value of the induced e..f. in a rotating loop = NBA sin t Where N = nuber of turns in arature coil B = Magnetic field vector A =Area vector of the coil = Angular speed OR v = v sin t Let the current in the circuit be led the applied voltage by an angle. i i sin( t ) di q The Kirchhoff s voltage law gives L Ri v. dt C It is given that v = v sin t (applied voltage) d q dq q sin... L R v t dt dt C On solving the equation, we obtain

22 q q sin( t ) dq dt dq q cos( t ) q sin( t ) dt On substituting these values in equation (), we obtain q R cos( t ) ( X X )sin( t ) v sin t X C X C L C Z R ( X X ) C L C L R ( X X ) q Z t Z Z t v t Let cos R X and C XL Z sin This gives tan XC XL R On substituting this in equation (), we obtain C L cos( ) sin( ) sin... q Z cos( t ) v sin t On coparing the two sides, we obtain v q Z i Z i q and ( ) π or π i dq q dt cos( t ) i cos( t ) Or i i sin( t ) Where, i And v v Z R ( X X ) C L tan X X R C L

23 The condition for resonance to occur i v R ( X X ) C L For resonance to occur, the value of i has to be the axiu. The value of i will be the axiu when X C C πf f X L L LC LC LC π LC Power factor = cos Where, cos R R Z R ( X X ) C L (i) Conditions for axiu power factor (i.e., cos = ) X C = X L Or R = (ii) Conditions for iniu power factor When the circuit is purely inductive When the circuit is purely capacitive

24 3. State Huygens s principle. Show, with the help of a suitable diagra, how this principle is used to obtain the diffraction pattern by a single slit. Draw a plot of intensity distribution and explain clearly why the secondary axia becoes weaker with increasing order (n) of the secondary axia. OR Draw a ray diagra to show the working of a copound icroscope. Deduce an expression for the total agnification when the final iage is fored at the near point. In a copound icroscope, an object is placed at a distance of.5 c fro the objective of focal length.5 c. If the eye piece has a focal length of 5 c and the final iage is fored at the near point, estiate the agnifying power of the icroscope. 5 Huygen s principle states that Each point on a wave front behaves as a source of secondary wavelets The secondary wavelets travel with the speed of light in that ediu The position of new wave front at a later tie can be found out by drawing a coon tangent to all these secondary wavelets Intensity distribution of single slit distribution For the first secondary axia (n = ), only one-third of the slit contributes to its intensity. Secondly, for n =, only one-fifth of the slit contributes to the intensity. Therefore, with increasing n, the intensity decreases. OR Ray diagra for a copound icroscope

25 Total angular agnification, Angle subtended by the iage Angle subtended by the object Since and are sall, tan and tan tan tan AB tan D And AB tan D tan A B D A B tan D AB AB On ultiplying the nuerator and the denoinator with A B, we obtain A B A B A B AB Now, agnification produced by objective, Magnification produced by eyepiece, Therefore, Total agnification, () = e v u f e v e e e AB AB A'B' AB (Iage distance for iage produced by objective lens ) (Object distance for the objective lens) D f Focal length of eyepiece v u e D f e L (Separation between the lenses)

26 u u f f L D f f e.5 c.5c f v u.5 v.5 v.5.5 e v 875 v f v 7.5 c 5 c D u f e