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K.V. No. 1 (Paper-I) Max. Marks : 70 Sub : Physics Class : XII Time : 3 Hrs General Instructions:1. All questions are compulsory 2. There are 29 question in total Q. No. 1 to 8 are very short question and carry one mark each. 3. Q. No. 9 to 16 carry two marks each, Q. No. 17 to 25 carry three marks each, question, 26 is value based question carry four marks and 27 to 29 carry five marks each. 4. There is no overall choice. However, an internal choice has been provided in one question of two marks, one question of three marks and all three questions of five marks each. You have to attempt only one of the given choices in such questions. 5. Use of calculators is not permitted. However, you may use log tables if necessary. 6. You may use the following values of physical constants wherever necessary. c 3 10 8 m / s; h 6.6 10 34 Js; e 1.6 10 19 C; 0 4x10 7 TmA 1 1 4 0 9 10 9 Nm 2 / C 2 m e 9.1x10 31 kg 1. A 500 c charge is at the centre of square of side 10cm. Find the work done in moving a charge of 10C between two diagonally opposite points on the square. 2. A wire of resistivity is stretched to four times its length. What will be its new resistivity? 3. A silver wire has a resistance of 2.1 at 27.50C, and a resistance of 2.7 at 1000C. Determine the temperature co-efficient of resistivity of silver. 4. An electron is moving with a velocity of 107m/s, enters uniform magnetic field of 1T. The direction of the velocity of election is parallel to the magnetic field. What would be its trajectory in this field? 5. What is the name given to the curve, the tangent to which at any point gives the direction of magnetic field at that point? Can two such curves intersect each other? Justify you answer. 6. An electric motor running on a 50V DC supply draws 12A current. Find the resistance of its windings. 7. What is meant by modulation? 8. A carrier wave of peak voltage 12V is used to transmit a message signal. What should be the peak voltage of modulating signal in order to have a modulation index of 75%? 9. Write the expression for electrostatic potential energy of a dipole, of dipole moment Pe in uniform electric filed and E . Draw a graph showing the value of this at different angles between Pe and E and indicate the positions of unstable and stable equilibrium. 10. Two identical cells each of emf E and internal resistance ‘r’ are connected in parallel to an external resistance R. Find an expression for the total current flowing in the circuit as shown in figure. 11. An ac generator has coil of 50 turns and area 2.5m2 rotating at an angular speed of 60 rad S-1 in a uniform magnetic field of B=0.3T between two pole pieces. The resistance of the windings is 500. (i) What is the maximum current drawn from the generator? (ii) What is the flux through the coil when the current is Zero? What is the flux when the current is maximum? 12. How is resolving power of a microscope affected when (i) (ii) The wavelength of illuminating radiations is decreased? The diameter of the objective lens is decreased? Justify your answer. 13. The following table gives the values of work function for a few photosensitive metals: S. No. 1 Na Metal Work function (ev) 1.92 2 K 2.15 3 Mo 4.17 If each of these metals is exposed to radiations of wavelength 300nm, which of them will not emit photo electrons and why? Or By how much would the stopping potential for a given photosensitive surface go up if the frequency of the incident radiations were to be increased from 4x1015 H 2 to 8x1015 H 2 ? Given h 6.4x10 34 Js e 1.6x10 19 C and c 3x108 m / s. 14. Draw of graph to show the variation of stopping potential with frequency of radiation incident on a metal plate. How can the value of Planck’s constant be determined from this graph? 15. Indentify the logic gate ‘1’ and ‘2’ in the logic circuit given. Also obtain the truth table for the final output for all possible combination of the input A and B. 16. Give any two difference between a half wave rectifier and a full wave rectifier. 17. When two known resistances R and S are connected in the left and right gaps of a meter bridge, the balance point is found at a distance l1 from the zero end of metre bridge wire. An unknown resistance X is now connected in parallel to the resistance S and the balance point is now found at a distance l 2 from the zero end of the metre bridge wire as shown in figure. Obtain a formula for X in terms of l1 x l2 and S. R 18. A galvanometer coil has a resistance of 30 and meter shows full scale deflection for a current of 2.0mA. Calculate the value of resistance required to convert it into an ammeter of range O to 1A. Also, calculate the resistance of ammeter. 19. A thick copper wire carrying a current of 10A is bent into semicircular arc of radius 7.0cm as shown in fig (a). State the direction and calculate the magnitude of field at the centre of the arc. How would your answer change if the same wire is bent into semicircular arc of the same radius but in opposite way as shown in fig (b) Or A closely wound solenoid of 2000 turns and area of cross-section 1.6x10 4 m 2 carrying current of 4.0A is suspended through its centre allowing it to turn in a horizontal plane. (a) What is the magnetic moment associated with the solenoid? (b) What is the force and torque on the solenoid if a uniform horizontal magnetic field of 7.5x10 2 T is set up at an angle of 30 0 with the axis of the solenoid? 20. Write the order of frequency range and one use of each of the following electromagnetic radiations. (i) Microwaves (ii) Ultraviolet rays (iii) Gamma rays 21. Which two main consideration are kept in mind while designing the objective of an astronomical telescope? Obtain an expression for the angular magnifying power and the length of the tube of an astronomical telescope in its ‘normal adjustment’ position. 22. Define the term Binding energy of a nucleus. Complete B.E per nucleon for 56 26 Fe . Given mass of portion = 1.0078254amu mass of neutron = 1.00866549amu mass of 56 26 Fe nucleus = 55.9349394amu and 1amu = 931.5 Mev. 13.6 eV . Calculate the n2 energy required to take an electron from ground state to the second excited state. 23. The energy of an electron in orbit is given by En 24. Draw a labelled circuit diagram to show the used of Zener diode as a voltage regulator. 25. (a) What does the term LOS communication mean? Name the types of waves that are used for this communication (b) Draw the block diagram of a communication system. 26. A student X sitting in the last row in the class have difficulty in reading the matter written on the black board. The teacher requests the student sitting in the front row to volunteer for exchange of seat to help X. Student Y sitting in the front row volunteers herself to exchange the seat with X. Now X was able to read the matter on black board clearly and Y also did not face any difficulty. The teacher also advised X to get his eyes checked up. Answer the following questions based on the above information. (i) Which eye defect of vision X is suffering from? (ii) Which values is the teacher displaying through her actions and advice? (iii) (iv) 27. Which values is Y displaying through volunteering? In what possible ways can X respond and reciprocate the help rendered by Y? Define the term electric dipole moment and magnetic dipole moment. Derive an expression for electric field intensity at a point on equitorial line of a electric dipole. Or With the help of a labelled diagram explain the working of Van de Graff generator. 28. A spherical surface of radius of curvature R, separates a rarer and a denser medium as shown in the figure. Complete the path of the incident ray of light, showing the formation of a real image. Hence derive the relation connecting the object distance, image distance, radius of curvature and refractive indices 1 and 2 of the two media. Or The figure, drawn here shows a modified Young’s double slit experimental set up. If SS2 – SS1 = /4. (i) State the conditions for constructive & destructive interference. (ii) Obtain an expression for the fringe width. (iii) Locate the position of the central fringe. 29. (a) An alternating voltage V= Vm Sin wt applied to a series LCR ckt drives a current given by I = Im Sin (wt +). Deduce an expression for the average power dissipated (c) For a circuit used for transporting electric power a low power factor implies large power loss in transmission line explain? Or (a) Current in a circuit falls from 5A to 0A in 0.1s if the average e.mf of 200V is induced what is the self inductance of the circuit? (b) An ac of 0.2A RMS and frequency 100/2 Hz flows in a LRC ckt with L=0.15H, R=20, C= 500F. Calculate the ac voltage (i) across each component (ii) across R&L together (iii) across L&C together (iv) The total voltage across L, C and R. What power is dissipated in each component? SOLUTIONS (Paper-I) Max. Marks : 70 Sub : Physics Class : XII 1. Zero, as the two points are at same potential. 2. Resistivity depends upon the nature of material and does not depend upon the dimension of the material. So, resistivity will be unchanged. (1) R 2 R 1 (1 T ), we get R 2 R1 2.7 2.1 R 1 T 2.1x (100 27.5) (1) 3. Using 4. Force on the electron in magnetic field will be F = q VB Sin O0 = O So there is no force on electron hence it will move along a straight line. 5. The name of the curve is “magnetic lines of force”. Two magnetic lines of force never intersect with each other because if they do so then two tangents drawn at the same point of intersection will give two directions of magnetic field at same point, which is impossible. (1) 6. Given V 50V and I 12A 0.6 .0039 0 C 1 2.1(72.5) Re sis tan ce of motor R V 50 4.18 I 12 (1) (1) 7. The phenomenon of superposing low frequency modulating signal on high frequency carrier wave in accordance to the same characteristics of modulating signal is called modulation. 8. Using Em we get E c 12 V, E m ? 75% Ec E m E c 9. (1) 75 x12 9V 100 The electrostatic potential energy Up of a dipole of dipole moment Pe in uniform electric field E is up = Pe. E = pe E cosIt varies since soidally with s follows (1) 10. Total e.m.f =E Total Resistance = R + r/2 Current I 11. (i) Eo = NABW I0 (ii) 12. 2E 2R r E o NABW 50x0.3x 2.5x60 4.5A R R 500 The flux is maximum when current is zero. The flux the current is maximum. is zero when The expression for R.P. of a microscope i.e. R.P. 2 Sin Where is R.I. of the medium between the object and the lower surface of the objective lens and ‘’ is the angle subtended by a radius of the objective on one of the points of the object obviously. (i) 13. Obviously R.P. is increased (ii) R.P. is decreased because is decreased. hc For photoelectric effect to occur h o or o hc 12375 evA 0 4.125 eV We calculate roughly 0 3000 A Obviously Mo will not emit photoelectrons when 30nm light is shined on it. Or U sin g h h 0 eVs and h1 h 0 eVs1 h ( 1 ) v 1s v s e Putting values Vs1 Vs 6.4x10 34 Js (8x1015 4x1015 )S 1 16V 19 1.6x10 C 14. The variation of stopping potential with the frequency of radiation incident on a metal plate is a straight line AB as shown in figure. Take two points C and D on the graph. Note down the corresponding frequency of radiations ( 1 and 2) and stopping potential (V1 and V2) Then, eV h o 1 1 and eV h o 2 2 15. e( V V ) h ( ) 2 1 2 1 e( V V ) Thus planck’s constant can be determined. 2 1 , or h 2 1 Logic gate ‘1’ is OR gate and logic gate ‘2’ is NOT gate. Truth table A 0 0 1 1 16. 17. B 0 1 0 1 Y 1 0 0 0 (i) In half wave rectifier, the output voltage is unidirectional intermittent and varying voltage. (ii) In half wave rectifier, the frequency of output signal in same as that of input signal. In full wave rectifier, the frequency of output voltage signal is double than that of input signal. When R and S are connected to the left and right gaps of metrebridge and bridge is balanced at length l1 from zero end l R 1 Then (i) S (100 l ) 1 When unknown resistance X is connected in parallel to S, then effective resistance in right gap is S1 SX SX (ii ) Now balance point is obtained at length l2 and So. l1 R 1 S (l00 l1 ) Putting the value of S11 we have R (S X) l2 SX (100 l 2 ) (iii ) Dividing (iii) by (i) we get SX l2 100 l1 x X (100 l 2 ) l1 Or S l (100 l 2 ) 1 2 X l 2 (100 l 2 ) S 100 l 2 100 l1 l1l 2 100 (l 2 l1 ) X l 2 (100 l 2 ) l1 (100 l 2 ) (100 l 2 )l1 xS 100 l 2 l1 Here, current through the galvanometer IG = 2mA = 2x10-3 A Resistance of galvanometer G = 30. Maximum value of correct = 1A I xG 0.002 x 30 R G 0.06 As, I I G 1 0.002 X 18. R 6x10 10 19. Here I = 10A Length to the semicircle L 2r r x 7x10 2 m 2 The magnetic field at the centre of the semicircle will be given as IL o Idl sin 90 B 2 2 dervied from dB 4r 4 r2 7 o I o I oI 4x10 x10 4.5x10 5 T. 2 4 r 4 r 4r 4x 7x10 Now if the same wire is bent into semicircular arc of the same radius but in opposite way as shown in fig (b) the direction of magnetic field at the centre will be inverted while magnitude will remain constant. Or (a) (b) 20. 21. As magnetic moment M = NIA = 2000 x 4 x 1.6x10-4Am2 = 1.28 Am2 Net force F = 0 But torque T = MB sin = 1.28x7.5x10-2 sin 300 = 4.8 x 10-2 N-m (1½) (1½) (i) Microwaves having frequency range 3x1011 Hz to 1x109 Hz. It is used in radar system. (ii) UV rays having frequency range 5x1017 H 2 5x1017 to 8x1014 Hz. It is used in checking of forged documents. (iii) Gamma rays having frequency range of 5x1022 Hz to 3x1019 Hz. it is used studying the nucleus. The objective of telescope must have (i) high R.P. (ii) large light gathering power. Thus it must have a large diameter. In normal adjustment as shown the magnifying power is given by M = . The final image is formed at infinity. AB AB EA OB AB EA OB fo M AB EA fe OB The length of the tube is fo + fe 22. As mass defect M = Zmp + (A-Z)mn-M and energy corresponding to M is E = MC2 E = M x 931.5MeV. Here M = 26xmp + (56-26)mn – 55.935 = (26x1.0079+30x1.0087) – 55.9350 = (26.2054+30.2610) – 55.9350 = 56.4664-55.9350 = 0.5314 amu. Now energy corresponding to this mass defect E = 0.5314 x 93.15 MeV = 494.9991 = 495 MeV. 23. The energy of nth orbit of the H-atom is given by 13.6 eV n2 13.6 13.6 E 2 E1 ( 2) 2 12 3.4 13.6 10.2eV. En Now energy required to take an electron from ground state to second excited state. 24. Here the zener diode is joined in reverse bias to functioning d.c. input voltage through a resistance R of suitable value depending upon the zener voltage and power rating of zenerdiode used. The constant output voltage is taken across a load resistance RL connected in parallel with zener diode. When the input d.c. voltage increases beyond a certain limit, the voltage across zener diode becomes constant equal to zener break down voltage, but the current through the zener diode circuit rises sharply as the dynamic resistance of zener diode becomes almost zero after zener break down voltage. Due to which there is an increase in voltage drop across R since R L is connected in parallel so the voltage across RL remains same as that of zener break down voltage. 25. (a) LOS means line of sight communication. The two type of waves used for LOS communication are (i) space waves (ii) waves from transmitting stations near the ground to flying air craft. Transmitted signal Received signal Message Signal Information source Transmitter Channel Receiver User of information Noise 26. (i) (ii) (iii) (iv) Myopia/short sightedness Concern for students, helpfulness, Duty/role as a guide counseling. Empathy, Helpfulness, Cooperation. Friendship, Sharing and caring, thanks and grate fullness. 27. Definition P = qx2l M = mx2l E 1 P 4eV0 ( r 2 a 2 ) 32 Or Construction Diagram will labeled Working - 28. i r sin i 2 sin r 1 Re lation 2 1 2 1 v u R 2 3 Or Initial path difference between S1 and S2 = SS2 – SS1 = x ; x S P S P path difference between disturbance from S1 and 1 2 1 4 2 S2 at point P. = yd D total path difference between the two disturbances at P yd x T x1 x 2 4 D For constructive interference yd X T n where n 0,1,2 ...... 4 D yd 1 n n (i) D 4 For destructive int erference yd X T 2n 1 2 4 D ynd 3 2n D 2 2 D d The position y o of Central fringe is obtained by putting n 0 in n (i) fringe width y n 1 y n d ud [- ve sign shows that the central fringe is obtained at a point below the central point O.] yo 29. (a) Let at any instant the current and voltage in an LCR series AC ckt is given by I= I0 sin wt V = V0 sin (wt+) The instantaneous power is given by P = VI = Vo sin (wt +)/ Io sin wt Vo I o 2 sin wt. sin ( wt 2 Vl P VI o o Cos Cos(2 wt 2 2 sin A sin B cos(A B) cos(A B) P (i) Work done for a very small time interval dt is given by dW = Pdt dW = IVdt Total W.D. over Ta complete cycle is given by T W VIdt T 0 T W But Pav T T (b) VIdt 0 T Vl I 0 0 0 Pav [Cos cos(2 wt )]dt T 2 T V I T o o cos dt Cos( 2 wt )dt 2T 0 0 VI o o cos [ t ]T0 0 2T VI o o cos T 2T V I o o cos 2 2 Vrms Irms Cos Power factor cos = R/Z R – Resistance Z- Impedance Low power factor (cos ) implies lower ohmic resistance and higher power loss as Pav 1/R in transmission. Or (a) (b) (i) dI e 200 or L 40 H. dt dI dt 5 0.1 We make use of phasor diagram e l 100 VL I RMS X L 0.2x 2x 0.15 3V 2 VR I RMS R 0.2x 20 4V VC I RMS X c I RMS X L L 2L 1 1 1 1 0.2x 4V X C 100 C C 2 fc 6 2x x500 x10 2 (ii) VLR VR2 VL2 4 2 32 5V (iii) VLC V:L VC 4 3 IV (iv) VLCR VR2 ( VL VC ) 2 4 2 12 17 4.1V (v) PL o; Pc O PR I 2RMS R 0.2 x20 0.8W 2 K.V. No. 1 (Paper-II) Max. Marks : 70 Sub : Physics Class : XII Time : 3 Hrs General Instructions:1. All questions are compulsory 2. There are 29 question in total Q. No. 1 to 8 are very short question and carry one mark each. 3. Q. No. 9 to 16 carry two marks each, Q. No. 17 to 25 carry three marks each, question, 26 is value based question carrying four marks and 27 to 29 carry five marks each. 4. There is no overall choice. However, an internal choice has been provided in one question of two marks, one question of three marks and all three questions of five marks each. You have to attempt only one of the given choices in such questions. 5. Use of calculators is not permitted. However, you may use log tables it necessary. 6. You may use the following values of physical constants wherever necessary. 1 8 34 19 7 1 9 2 2 c 3 10 m / s; h 6.6 10 Js; e 1.6 10 C; 4x10 Tm A 9 10 Nm / C ; 0 4C 0 31 m e 9.1x10 kg 1. Why are alloys used for making standard resistance coils? 2. How does focal length of a lens change when red light is replaced by blue light? 3. Name the series of hydrogen spectrum lying in the infrared region. 4. Would sky waves be suitable for transmission of TV singnals of 60 MHz freqneucy? 5. What is the colour code for a resistor of resistance 3.5K with 15% tolerance. 6. Which physical quantity has the unit Wb m-2? Is it a scalar or a vector quantity? 7. A solenoid is connected to a battery so that a steady current flows through it. If an iron core is inserted into the solenoid, will the current increase or decrease? Explain. 8. Why is ground wave transmission of signals restricted to a frequency of 1500 kHz? 9. A uniform field E exists between two charged plates as shown in figure. What would be work done in moving a charge q along the closed rectangular path ABCDA? 10. What is an ideal diode? Draw the output waveform across the load resistor R, if the input waveform is an shown in the figure. 11. Find the ratio of intensities of two points P and Q on a screen in Young’s double slit experiment when waves from sources S1 and S2 have phase difference of (i) 00 and (ii) respectively. 2 12. Two conductors are made of the same material and have the same length. Conductor A is solid wire of diameter 1mm. Conductor B is a hollow tube of outer diameter 2mm and inner diameter 1mm. Find the ratio of resistance RA to RB. 13. The current sensitivity of a moving coil galvanometer increases by 20% when its resistance is increased by a factor 2. Calculate by what factor the voltage sensitivity changes. 14. A coil of 0.01 H inductance and I resistance is connected to 200 V, 50 Hz ac supply. Find the impedance of the circuit and time lag between maximum alternating voltage and current. 15. With the help of an example, explain, how the neutron to proton ratio changes during alpha decay of a nucleus. 16. Tow long parallel wires are hanging freely. If they are connected to a battery (i) in series, (ii) in parallel, what would be the effect on their positions? 17. Obtain equivalent capacitance of the following network. For a 300 V supply, determine the charge and voltage across each capacitor. 18. Which of the following waves can be polarized? (i) X-rays (ii) Sound waves. Give reasons. Two polaroids are used to study polarization. One of them (the polarizer) is kept fixed and the other (the analyser) is initially kept with its axis parallel to the poalriser. The analyser is then rotated through angels of 45 0, 900 and 1800 in turn. How would the intensity of light coming out of anlayser be affected for these angles of rotation, as compared to the initial intensity and why? 19. Illustrate the basic elements required for transmitting and receiving an audio signal with the help of a block diagram. 20. Two cells of voltage 10 V and 2 V and internal resistance 10 and 5 respectively, are connected in parallel with the positive end of 10 V battery connected to negative pole of 2 V battery as shown in figure. Find the effective voltage and effective resistance of the combination. 21. A source contains two phosphorus radionuclides 33 15 and P(T1 2 25.3 days ) . Initially 10% of the decays come from must wait until 90% do so? 32 15 P (T1 14.3 days ) 33 15 P . How long one 2 22. The two plates of a parallel plate capacitor are 4 mm apart. A slab of dielectric constant 3 and thickness 3 mm is introduced between the plates with its faces parallel to them. the distance between the plates is so adjusted that the rd 2 capacitance of the capacitor becomes of its original value. What is the 3 new distance between the plates? Or Define the term electric potential due to a point charge. Find the electric potential at the centre of a square of side 2m , having charges 100 C,50 C,20 C and 60 C at the four corners of the square. 23. How would you establish an instantaneous displacement current of 2.0 A in the space between the two parallel plates of 1 F capacitor? 24. The figure shows a rectangular current carrying loop, placed 2 cm away from a long straight, current carrying conductor. What is the direction and magnitude of the net force acting on the loop? 25. Two lenses of powers + 15 D and -5 D are in contact with each other forming a combination lens. (a) What is the focal length of this combination. (b) An object of size 3 cm is placed at 30 cm from this combination of lenses. Calculate the position and size of the image formed. 26. In an experiment of photoelectric effect, Neet plotted graphs for different observation between photoelectric current and collector plate potential but her friend Megha has to help her in plotting the correct graph. Neeta thanked Megha for timely help. (a) What value was displaed by Megha and Neeta. (b) Draw the correct graph between I and V. 27. What is induced emft? Write Faraday’s law of electromagnetic induction. Express it mathematically. A conducting rod of length I, with one pivoted, is rotated with a uniform angular speed in a vertical plane, normal to a uniform magnetic field B. Deduce an expression for the emf induced in this rod. In India, domestic power supply is at 220V 50 Hz, while in USA it is 110 V, 50 Hz. Give one advantage and one disadvantage of 220 V supply over 110V supply. Or Explain the phenomenon of self induction. Define coefficient of self inductance. What are its units Calculate self inductance of a long solenoid. 28. (a) (c) With the help of a circuit diagram explain the working of transistor as oscillator. Draw a circuit diagram for a two inputs oR gate and explain its working with the help of input, output waveforms. Or Define the terms potential barrier and depletion region for a p-n junction. Explain with the help of a circuit diagram, the use of a p-n diode as a full wave rectifier. Draw the input and output wave form 29. Define magnifying power of an optical telescope. Draw ray diagram for an astronomical refracting telescope in normal adjustment showing the paths through the instrumental of three rays from a distant object. Derive an expression for its magnifying power. Write the significance of diameter of the objective lens on the optical performance of a telescope. Or State Huygens principle and prove laws of reflection and refraction on the basis of Huygens principle. SOLUTIONS (Paper-II) Max. Marks : 70 Sub : Physics Class : XII 1. Alloys are used for making standard resistance coils because they have low value of temperature coefficient (less temperature sensitivity) of resistance and high resistivity 2. According to lens maker’s formula, 1 1 1 1 f R1 R 2 As b r f b f r 3. 4. 5. 6. 7. 8. 9. 10. i.e. focal length of lens decreases. Paschen series, Brackett series and Pfund series. No, signals of frequency greater than 30 MHz will not be reflected by the ionosphere, but will pentetrate through the ionosphere. Given, resistance = 3.5k 5% = 35 x 102 5% Colour code of given resistor is orange, green, red and gold. Magnetic field induction has the unit Wb m-2. It is a vector quantity. The current will decrease. As the iron core is inserted in the solenoid, the magnetic field increase and the flux increase. Lenz’s Law implies that induced emf should resist this increase, which can be achieved by a decrease in current. In ground wave propagation, the loss of energy due to interaction with matter increase with the increase in frequency of wave. Therefore, the waves of frequency above 1500 kHz get heavily damaged in ground wave progagation. Hence the ground wave propagation is restricted to a frequency of 1500 kHz. Work done in moving a charge along the closed rectangular path would be zero, because field in the entire space is uniform and electrostatic forces are conservative forces. A p-n junction diode which offers zero resistance when forward biased and infinite resistance when reverse biased is called an ideal diode. The output waveform across R is as shown in the figure below. 11. In Young’s double slit experiment, the resultant intensity at any point on the screen is I I1 I 2 2 I1I 2 cos Where is the phase difference between the waves at that point. Here, we consider l1 = l2 = l0 Therefore, When = 00, the intensity at point P is I p I 0 I 0 2 I 0 I 0 cos 0 0 4I 0 the resultant intensity at point Q is 2 I Q I 0 I 0 2 I 0 I 0 cos 2I 0 2 Ip 2 IQ 1 When 12. Resistance of conductor A, l RA (0.5x10 3 ) 2 Resistance of conductor B, l RB 2 1x10 3 (0.5x10 3 ) 2 R A (1x10 3 ) 2 0.5x10 3 0.75 3 RB 0.25 1 0.5x10 3 2 2 13. Given I s I s 20 120 Is I s , R ' 2R 100 100 Then, initial voltage sensitivity, Vs New Voltage sensitivity, I' 3 120 1 Vs' s' I s x Vs R 100 2R 5 % decrease in voltage sensitivity 3 Vs Vs V V 5 x100 40% s x100 Vs Vs ' s ls R 14. Here, R = 1, = 50 Hz, The inductive reactance is L= 0.01 H X L L 2vL 2.x 3.14 x50x 0.01 3.14 The impedance of the circuit is Z R 2 X 2L 15. 12 3.142 10.86 3.3 The phase difference between current and voltage is X tan L 3.14 R 72 x tan 1 3.14 72 0 rad 180 72 x 1 Time lag , t s 180 x 2x50 250 Consider that -decays of nucleus A z A AZ24 Y 42 He 238 92 234 U 90 Th 42 He 238 92 1.58 92 234 90 1.60 After decay, neutron to proton ratio, n/p 90 Before decay, neutron to proton ratio, n/p Thus ratio increases. 16. (i) a (ii) 17. When a battery is connected in series to two long parallel wires, the currents in the two wires will be in opposite directions. Due to which force of repulsion will be acting between them and they move further apart. When a battery is connected in parallel to two long parallel wires, the currents in the two wires will be same direction. Due to which a force of attraction will be acting between them and they come closer to each other. Here , C 2 and C 3 are in series 1 1 1 2 1 Cs 200 200 200 100 Cs 100 pF Cs and C1 are in parallel C p Cs C1 100 20 pF Again C p and C 4 are in series , therefore the equivalent capaci tan ce of network is 1 1 1 1 1 3 C C p C 4 200 100 200 C Vp V4 300 200 pF 66.7x10 12 F 3 As C p and C 4 are in series 200 x10 12 x 300 3 2x10 8 C Ch arg e on C 4 is q 4 CV Potential difference across C4 is V4 q4 2x10 8 200V C 4 100x10 12 From (i), Vp 300 V4 300 200 100V Potential difference across C1 is V1 Vp 100V Charge on C1 is q1 C1V1 100x1012 x100 108 C Potential difference across C2 and C3 in series 100V Charge on C2 is q 2 C2 V2 200x1012 x50 108 C Charge on C3 is q 3 C3V3 200x10 12 x50 10 8 C 18. (i) Phenomenon of polarisaiton is shown by transverse waves only. X-rays are transverse in nature, and hence they can be polarized. According to Malus law I I 0 cos 2 Where I = intensity of light coming from analyser I0 = initial intensity. When 450 , then I I 0 cos 2 450 I0 2 When 900 , then I I 0 cos 2 900 0 When 1800 , then I I 0 cos 2 1800 l 0 19. A brief description of the various element is as given below:(i) A microphone converts sound waves into electrical waves i.e. audio signal. (ii) An oscillator generates carrier waves. (iii) There is a mixing of carrier waves and audio signal in modulator. (iv) The modulated waves are fed to transmitter, these waves are then radiated through transmitting antenna. (v) The receiving antenna receives the transmitting signal. (vi) The detector demodulates (separate out) the audio signal from the modulated waves. (vii) The loudspeaker converts the audio signal back into sound waves. 20. Applying Kirchhoff’s junction rule at junction B, we get I1= I + I2 (i) Applying Kirchhoff’s loop rule for closed loop ABCDEFA give 10 = IR + 10I1 Applying Kirchhoff’s loop rule for closed loop BCDEB gives 2 = 5I2 – IR = 5(I2-I)-IR (Using (i)) Or 4 = 1011-10I – 2IR (iii) Equation (i) – (iii) gives 6 = 3IR + 10I Or 10 2 1 R 3 Or 2 R R eff I Comparing with Veff R R eff I, we get Veff 2V and R eff 21. 10 3 Initially, the source has 90% of 32 15 P nuclides and 10% say after 1 days, the source has 10% of nuclides. Initial no. 32 15 P of nuclides = 9x; Initial no. 33 15 P of nuclides = x Final no. 32 15 P of nuclides = y; Final no. 33 15 P of nuclides = 9y n 1 1 As N 2 2 0 N t or N N ( 2) 0 t 32 15 33 15 P nuclides. Finally, P nuclides and 90% of 33 15 P T 1/ 2 2 t T 1/ 2 T 1/ 2 For 1533P isotope N 0 x; N 9 y; T 25.3 days 1 21. 2 9 y x ( 2) t 25.3 Here, distance between parallel plates d = 4mm = 0.004m, K =, thickness, t3mm = 0.003m Let the new distance between the plate bed d1. Dividing Eq. (ii ) by Eq. (i), we get 11t 1 t 14.3 25.3 9 ( 2) or 841 2 14.3x 25.3 9 11t log10 81 log10 2 14.3x 25.3 11tx 0.3010 or 1.9085 14.3x 25.3 1.9085 x14.3x 25.3 t 208 .5 days 11x 0.3010 A 0 A C 0 and C1 1 d d 1 t 1 K 2 Since C1 C 3 0 A 2 0 A 1 3 d d 1 t 1 K 1 2 1 3d d 1 t 1 K 1 1 1 3x 0.004 d1 0.0031 3 1 1 2 0.006 d1 0.003x 3 1 1 d1 0.002 0.006 1 1 d1 0.002 0.006 d1 0.006 0.002 0.008 m 8mm Or (Given ) Electric potential at a point is the amount of work done to bring a unit positive charge from infinity to that point against the electrostatic forces. AC BD 2 2 2 2 2m AO OC BO OD 1 m Potential at the Centre of the square Ois V qC 1 q qB qD 4 o AO BO OC OD 100 x10 6 50 x10 6 20 x10 6 60 x10 6 V 9x10 1 1 1 1 9x10 9 x10 x10 6 9x10 4 V 9 23. Here I D 2.0A, C 1F 10 6 F dE d dE 0 ( EA ) 0 A dt dt dt d V A dV dV 0 A 0 C dt d d dt dt 0 A V E and C d d dV I D 2.0 or 6 2x10 6 V s 1 dt C 10 I D 0 Thus a displacement current of 2.0 A can be set up by changing the potential difference across the parallel plates of capacitor at the rate of 2 x 106 Vs-1 24. Force between wires PQ and CD F1 0 I1I 2 I 2 r 2x10 7 x15x 25x 0.25 93.75x10 5 2 2x10 9.375 x10 4 N (Re pulsive ) Force between wires PQ and AB 2x10 7 x15x 25x 0.25 1.56 x10 4 N Attractive 0.12 Net force on the rec tan gular loop F2 F F1 F2 (9.375 1.56) x10 4 7.815x10 4 N (Re pulsive i.e., towards left ). 25. (a) Here, P1 = 15D, P2 = -5D Power of the combination, P = P1 + P2 = 15 D – 5 D = 10 D Focal length, f (b) or 1 1 x100 10 cm P 10 1 1 1 f v u 1 1 1 1 1 1 3 1 2 or v f u 10 30 v 30 30 v 15cm m v h1 u h0 h1 v 15 x 3 1.5cm u 30 26. (a) The values displayed by them is sharing and caring. (b) 27. Def – ½ Law ½ penvation -3 Advantage : At 220 V supply power loss due to heating effect is lesser. Disadvantage : At 220 V peak value of current is more. Thus, it is more dangerous. (1) Or Explanation -1 Define -1 1 units & calculation (3) 28. Calculate 29. Power – ½ rays dia -2 derivation – 2 significance – ½ Or Statement -1 Diagrams -1 proof 1½, 1½ (a) (b) Working OR Gate (3) (2)