KENDRIYA VIDYALAYA SANGATHAN, NEW DELHI
KENDRIYA VIDYALAYA SANGATHAN, NEW DELHINUMERICAL WORKSHEETS FOR CLASS XIISUBJECT: - PHYSICSZONAL INSTITUTE OF EDUCATION AND TRAINING, MUMBAIKVS COMPLEX, NCH COLONY, KANJUR MARG (W), MUMBAI1
FOREWORDThis small pocket book on numerical problems has been designedto help students of Class XII to improve their performance insolving numerical problems, and improving their individual scores.Numericals are an important part of Physics and many studentsscore less than their potential because of neglecting this area. Thisbook, prepared by Mr. M Gopala Reddy, PGT Physics of ZIETMumbai, can be used as a regular workbook in class or can be usedas a resource book and kept in the library.My earnest request to the Principals and teachers is to ensure thatthis resource material reaches the individual student. Please dosend us your feedback so that the errors and shortcomings, if any,can be overcome.Wishing all my dear students of Kendriya Vidyalayas the very bestof luck for their crucial board exams.USHA ASWATH IYERDIRECTORKVS ZIET MUMBAI2
INDEXSUBJECT: -UNIT No.PHYSICSCLASS:-XIINAME OF THE UNITPAGE NO.1ELECTROSTATICS52CURRENT ELECTRICITY173MAGNETIC EFFECTS OF CURRENT ANDMAGNETISM334ELECTROMAGNETIC INDUCTION AND A.C485ELECTROMAGNETIC WAVES616OPTICS647DUAL NATURE OF MATTER AND RADIATION788ATOMIC NUCLEI919ELECTRONIC DEVICES10410COMMUNICATION SYSTEM1133
KENDRIYA VIDYALAYA SANGATHAN, NEW DELHIKENDRIYA VIDYALAYA SANGATHAN, REGIONAL OFFICE----------------WORK SHEET FOR SOLVING NUMERICAL PROBLEMS IN PHYSICSNAME OF THE UNIT:---CLASS:-XIINAME OF THE CHAPTER/S:NAME OF THE KENDRIYA VIDYALAYA:- -------------------------------NAME OF THE STUDENT:- ---------------------------------------- ROLL NO.-----------DATE OF ISSUE OF WORK SHEET:----------------DATE OF -------------SIGNATURE OF THE ------SIGNATURE OF THE STUDENT:------------NAME OF THE SUBJECT TEACHER:--------------------SIGNATURE OF THE SUBJECT TEACHERCOUNTER SIGNATURE OF THE PRINCIPAL/VICE PRINCIPAL4
UNITβIβELECTROSTATICSIMPORTANT FORMULAE1. Electrostatic force between two chargesπ πππ ππ π². ππ π . ππ ππππ ππ πππFor air, ππ πππ πFair . π π π π πππππ ππππ πππππβ π₯π’π¦π2. Electric field intensity due to a point charge, π¬π π πππ3. Electric field intensity due to infinite linear charge density (Ξ»)π¬ πππ ππ.πππ4. Electric field intensity near an infinite thin sheet of surface charge densityππ¬ ππππFor thick sheet πππ.5. Electric potential, π½ π₯π’π¦ππ ππππElectric potential due to a point charge, π½ π.πππ ππ π6. Relation between electric field and potential π¬ π π½π π π½π(numerically)β π. ππ7. Dipole moment, βπ·β .8. Torque on a dipole in uniform electric field, πβ πβ π¬9. Potential energy of dipole, πβ . βπ¬ ππ¬ ππ¨π¬ π½10. Work done in rotating the dipole in uniform electric field from orientation Q1to Q2 isπΎ πΌπ πΌπ ππ¬(ππ¨π¬ π½π ππ¨π¬ π½π)11. Electric field due to a short dipole(i)at axial point, π¬ππππ (ii)at equatorial point,π.ππππ ππ ππππ¬π ππ ππ.πππ12. Electric potential due to a short dipoleπAt axial point, π½ππππ (ii)At equatorial point, π½ π.13. Dielectric constant, π² πππ.π(i)ππ ππ ππ πͺπππ πͺπππ14. Capacitance of parallel plate capacitor(i)πͺ π¨πππ²π , in medium of dielectric constant K5
(ii)πͺ π¨ππππ²; if space between plate partially filled with dielectric ofπ π(π )thickness t.15. Combination of capacitors :(i)In series,ππͺ ππͺπ ππͺπ ππͺπ, ππ ππ ππ , π½ π½π π½π π½π(ii)In parallel, C πͺπ πͺπ πͺπ , π ππ ππ ππ, π½π π½π π½π π½16. Energy stored by capacitorππΈππππͺ πͺπ½π π πΈπ½π17. Electrostatic energy densityπππ ππ π¬π , in airππππ ππ¬π , in mediumππ18. Total electric flux, π± βπ¬. ββββπ π πππ ππππππ ππππππππ ππ πππ πππππππππ6
NUMERICALSLEVEL I1. What is the charge acquired by a body when 1 million electrons are transferred toit?2. An attractive force of 5N is acting between two charges of 2.0 ΞΌC & -2.0 ΞΌCplaced at some distance. If the charges are mutually touched and placed again atthe same distance, what will be the new force between them?3. A charge of 3.0 x 10-6 C is 0.25 m away from a charge of -6.0 x 10-6C.a. What is the force on the 3.0 x 10-6 C charge?b. What is the force on the -6.0 x 10-6 C charge?4. An electric dipole consist of a positive and a negative charge of 4Β΅C each placedat a distance of 5mm. Calculate dipole moment.5. Three capacitors of capacitances 2Β΅F, 3Β΅F and 4Β΅F are connected in parallel.What is the equivalent capacitance of the combination? Determine charge oneach capacitor, if the combination is connected to 100V supply?7
6. An electric dipole with dipole moment 4x10-9C-m is aligned at 300 with directionof electric field of magnitude 5x104N/C. Calculate the magnitude of the torqueacting on the dipole.7. A point charge of 2Β΅C is at the centre of cubic Gaussian surface 9.0 cm in edge.What is the net electric flux through the surface?8. What is the amount of work done in moving a 200nC charge between two points5 cm apart on an equipotential surface?9. How much work must be done to charge a 24 ΞΌF capacitor, when the potentialdifference between the plates is 500 V?10. What is the equivalent capacity of the network given below?8
LEVEL II1. What is the work done in moving a charge of 100ΞΌC through a distance of 1cmalong the equatorial line of dipole?2. The given graph shows that variation of charge q versus potential difference V fortwo capacitors C 1 and C2. The two capacitors have same plate separation but theplate area of C2 is double than that of C1. Which of the lines in the graphcorrespond to C1 and C2 and why?3.4.5.6.Two point charges 5Β΅C and β 4 Β΅C are separated by a distance of 1 m in air. Atwhat point on the line joining the charges is the electric potential zero?Two charges 5Β΅C and 20Β΅C are placed 15 cm apart. At what point on the linejoining the two charges is the electric field zero?Two charges 16Β΅C and 9Β΅C are placed 8 cm apart. At what point on the linejoining the two charges is the electric field zero?A 600 pF capacitor is charged by a 200 V supply. It is then disconnected andfrom the supply and is connected to another uncharged 600 pF capacitor. Howmuch electrostatic energy is lost in the process.9
7. Keeping the voltage of the charging source constant, what will be thepercentage change in the energy stored in a parallel plate capacitor if theseparation between its plates were to be decreased by 10%.8. Four charges are placed at the vertices of a square of side d as shown in thefigure.(i) Find the work done to put together this arrangement. (ii) A charge q 0isbrought to the center E of the square, the four charges being held fixed at itscorners. How much extra work is needed to do this?9. If S1 and S 2 are two hollow spheres enclosing charges Q and 2Q respectively asshown in the figure(i) What is the ratio of the electric flux through S1 and S2?10
(ii) How will the flux through the sphere S 1 change, if a medium of dielectricconstant 5 is filled in the space inside S 1.10. A charge of 24ΞΌC is given to a hollow sphere of radius 0.2m. Find the potential(i) at the surface of the sphere, and(ii) at a distance of 0.1 m from the centre of the sphere.(iii)at the centreLEVEL III1. A slab of material of dielectric constant has the same area as the plates of aparallel plate capacitor but has a thickness 3d / 4, where d is the separation ofthe plates. How is the capacitance changed when the slab is inserted betweenthe plates?2. A parallel plate capacitor with air between the plates has a capacitance of 8Β΅F.What will be the capacitance if the distance between the plates is doubled andthe space between them is filled with a substance of dielectric constant K 6?3. Two dipoles, made from charges q and Q, respectively, have equal dipolemoments. Give the (i) ratio between the βseparationsβ of these two pairs ofcharges (ii) angle between the dipole axis of these two dipoles.11
4. The capacitors C1, and C2, having plates of area A each, are connected inseries, as shown. Compare the capacitance of this combination with thecapacitor C3, again having plates of area A each, but βmade upβ as shown in thefigure.5. A point charge 10ΞΌC is at a distance 5cm directly above the centre of a squareof side 10cm as shown in fig. What is the magnitude of flux through the square?6. Calculate equivalent capacitance of the given network and determine the chargeand voltage across each capacitor.12
7. Two identical charges ,Q each are kept at a distance r from each other. A thirdcharge q is placed on the line joining the two charges such that all the threecharges are in equilibrium. What is magnitude, sign and position of the charge q?8. ABCD is a square of side 5m. Charges of 50C, -50C and 50C are placed atA,C and D respectively . Find the magnitude of resultant electric field at B.9. A cube with each side a is kept in electric field given by E Cx as shown in thefigure where C is a positive dimensional constant. Find(i) The electric flux through the cube, and(ii) The net charge inside the cube.13
10.Two parallel plate capacitor X and Y have same area of plates andsame separation between them. X has air between the plates whereas Y has adielectric of constant k 4(i) Calculate capacitance of each capacitor if equivalent capacitance is4 ΞΌF.(ii) Calculate potential difference between the plates of X and Y.(iii) What is the ratio of electrostatic energy stored in X and Y.14
UNIT: I ELECTROSTATICSANSWERSLEVEL I1. Q Ne 1.6 x10-13C2. F 03. FAB FBA 2.736N4. P 2x10-8 C-m5. 9 Β΅F, 0.02 Β΅C, 0.03 Β΅C, 0.04 Β΅C6. 10-4Nm7. 2,26x105Nm2/C8. W 09. W 3J10. C 15Β΅FLEVEL II1. 02. A3.4.5.6.7.8.59π from 5Β΅C charge5 cm from 5 Β΅C charge24cm from -9 Β΅C charge6x10-6 J11.11%π24π 0(4 2)9. 1: 3, , 0π5 010. (i) 1.08x106V (ii) 1.08x106V (iii)1.08x106VLEVEL III1.4ππΆπ 3 02. 24 Β΅F3. q a Q Aor a/A Q/q ΞΈ 04. C3 C eq5. 1.88x105Nm2/C6.2003ππΉ,100 V, 50V, 50V, 200V,10 -8C, 10-8C, 10-8C,2x10-8 C15
7. Q/4, Positive, r/28. 2.7x1010N/C9. a3C N-m2/C, a3Cπ0 Coulombs.10. Cx 5ΞΌF Cy 20Ξf16
UNIT- II- CURRENT ELECTRICITYImportant Formulae1 Electric current πΆβππππππππor I π π‘πππ‘2. In case of an electron revolving in a circle of radius r with speed v, period ofrevolution is T 2πππ£Frequency of revolution, v 3. Ohmβs law, R π£πΌ1π π£, Current, I ev 2ππππ£2ππor V IR4. Current in terms of drift velocity (ππ ) is I enAπ£ππΌ5. Resistance of a uniform conductor, R π7. Conductance 8. Conductivity π π΄π 6. Resistivity or specific resistance,π΄πΌππΌ ππ 2ππ΄πππ οΏ½π¦9. Current density or Ο πΆπ’πππππ‘π΄πππor j 1π πΌπ΄ππ π΄ enπ£π10. Relation between current density and electric field,j Ο E or E π j11. Mobility Β΅ πππΈ12. Temperature coefficient of resistance, Ξ± πΉπ πΉππΉπ(ππ ππ )13. The equivalent resistance π π of a number of resistances connected in series is givenbyπ π π 1 π 2 π 3 .14. The equivalent resistance π π of a number of resistances connected in parallel isgiven by1π π 1π 1 1π 2 1π 3 .17
15. EMF of a cell, E ππ16. For a cell of internal resistance r, the emf is E V Ir I (R r)17. Terminal p.d of a cell,V IR πΈπ π π18. Terminal p.d. when a current is being drawn from the cell, V E β Ir19. Terminal p.d. when the cell is being charged, V E Ir20. Internal resistance of a cell, r R [21. For n cell in series, I πΈ ππ]ππΈπ ππ22. For n cells in parallel, I ππΈππ π23. Heat produced by electric current, H πΌ 2 Rt joule 24. Electric power, P ππ‘ VI πΌ 2 R πΌ2 Rt4.18calπ2π 25. Electric energy, W Pt VIt πΌ 2 Rt26. Potential gradient of the potentiometer wire, k 27. For comparing e.m.f.s of two cells,πΈ2πΈ1 X πππΌπΌ2πΌ128. For measuring internal resistance of a cell, r 29. For a balanced Wheatstone bridge,ππ ,ππΌ1 πΌ2πΌ2xRIf X is the unknown resistanceππ π ππ ππ30. In a slide wire bridge, if balance point is obtained at l cm from the zero end, then π πor πππ(100 π)18
WORKSHEET (NUMERICALS) : LEVEL - I1. What happens to the power dissipation if the value of electric current passingthrough a conductor of constant resistance is doubled?Ans .2. A cell of emf 2 V and internal rΓ©sistance 0.1 is connected to a 3.9 externalresistance. What will be the current in circuit?Ans .3. Calculate the resistivity of a material of a wire 1 m long, 0.4 mm in diameter andhaving a resistance of 2 ohm.Ans .4. In a potentiometer arrangement; a cell of emf 1.25 V gives a balance point at 35.0cm length of the wire. If the cell is replaced by another cell and the balance pointshifts to 63.0 cm, what is the emf of the second cell?Ans . .5. A current is maintained in a conductor of cross-section 10-4 m2. If the number densityof free electrons be 9 x 1028 m-3and the drift velocity of free electrons be 6.94 x10 β 9m/s, calculate the current in the conductor.Ans .19
6. A silver wire has a resistance of 2.1 at 27.5 0C, and a resistance of 2.7 at 1000C. Determine the temperature coefficient of resistivity of silver.Ans .7. Three resistors 1 , 2 and 3 are combined in series. (a) What is the totalresistance of the combination? (b) If the combination is connected to a battery of emf12 V and negligible internal resistance, determine the total current drawn from thebattery.Ans .8. (a) Three resistors 2 , 4 and 5 are combined in parallel. What is the totalresistance of the combination? (b) If the combination is connected to a battery of emf20 V and negligible internal resistance and the total current drawn from the battery.Ans .9. A Voltage of 30V is applied across a carbon resistor with first second and third ringsof blue, black and yellow colours respectively. Calculate the value of current in mA,through the resistor.Ans .10. In a meter bridge the balance point is found to be 39.5 cm from one end A, when theresistor Y is of 12.5 . Determine the resistance of X.20
Ans .LEVEL - II1. A cell of emf 2 V and internal rΓ©sistance 0.1 is connected to a 3.9 externalresistance. What will be the p.d. across the terminals of the cell?Ans .2. Out of the two bulbs marked 25W and 100W, which one has higher resistance.Ans .3. A cell of 6 V and internal resistance 2 is connected to a variable resistor. For whatvalue of current does maximum power dissipation occur in the circuit?Ans .4. What is the largest voltage you can safely put across a resistor marked 98 - 0.5W?Ans .5. Two heater wires of the same dimensions are first connected in series and them inparallel to a source of supply . What will be ratio of heat produced in two cases?Ans .6. Using data given in graph determine (i) emf (ii) internal resistance of the cell.(iii) For what current, does maximum power dissipation occur in the circuit?21
Ans ------------------7. You are given βnβ resistors each of resistance βrβ. These are first connected to get ofminimum possible resistance. In the second case these are again connecteddifferently to get maximum possible resistance. Compute the ratio between themaximum and minimum values resistance so obtained.8. Two primary cells of emf E1 and E 2 (E 1 E2) are connected to the potentiometerwire as shown in the figure. If the balancing lengths for the cells are 250 cm and400 cm. Find the ratio of E1 and E 2.Ans .9. Two identical cells of emf 1.5V each are joined in parallel providing supply to anexternal circuit consisting of two resistors of 13 each joined in parallel . A very highresistance voltmeter reads the terminal voltage of the cells to be 1.4V. Find theinternal resistance of each cell.Ans .10. Three cells of emf 2V, 1.8V and 1.5V are connected in series. Their internalresistances are 0.05 , 0.7 and 1 respectively. If this battery is connected to anexternal resistance of 4 , calculate :22
(i) the total current flowing in the circuit. (ii) the p.d. across the terminals of the cell ofemf 1.5V.Ans --------------------------WORKSHEET (NUMERICALS): LEVEL - III1. What is the current flowing in the arm BD of this circuit.Ans .2. A cylindrical metallic wire is stretched to increase its length by 5%. Calculate thepercentage change in its resistance.Ans .3. Two cells of EMF 1V, 2V and internal resistances 2β¦ and 1β¦ respectively areconnected in (i) series, (ii) parallel. What should be the external resistance in thecircuit so that the current through the resistance be the same in the two cases? Inwhich case more heat is generated in the cells?Ans .4. Calculate the temperature at which the resistance of a conductor becomes 20%more than its resistance at 270C. The value of the temperature coefficient ofresistance of the conductor is 2 x 10-4 / K.Ans .5. Two metallic wires of the same material have the same length but cross sectionalarea is in the ratio of 1:2. They are connected (i) in series and (ii) in parallel.Compare the drift velocities of electrons in the two wires in both the cases.23
Ans .6. Two wires X, Y have the same resistivity but their cross-sectional areas in the ratio2:3 and lengths in the ratio 1:2. They are first connected in series and then in parallelto a dc source. Find out the ratio of the drift speeds of the electrons in the two wiresfor the two cases.Ans .7. A room has AC run for 5 hours a day at a voltage of 220V. The wiring of the roomconsists of Cu of 1 mm radius and a length of 10m. Power consumption per day is10 commercial units. What fraction of it goes in the joule heating in the wires? Whatwould happen if the wiring is made of Al of the same dimensions? [Ο Cu 1.7 x 10-8Ξ©m, ΟAl 2.7 x 10-8 Ξ©m]Ans .8. Two cells of emf 1.5 V and 2V and internal resistance 1 and 2 are connected inparallel to pass a current in the same direction through an external resistance of 5 .(a) Draw Circuit Diagram. (b) Using Kirchhoffβs laws, calculate the current througheach branch of the circuit and p.d. across the 5 resistor.Ans .9. E2 1.02V, PQ 1m. When switch S open, null position is obtained at a distance of 51cm from P. Calculate (i) potential gradient (ii) emf of the cell E1 (iii) when switch S isclosed, will null point move towards P or Q. Give reason for your answer.24
Ans .10. AB 100 cm, RAB 10 . Find the balancing length AC.Ans .11. Find the value of the unknown resistance X in the circuit, if no current flows throughthe section AO. Also calculate the current drawn from the battery of emf 6V.Ans .12. E1 2V, E2 4V, r1 1 , r2 2 , R 5 Calculate (i) current (ii) p.d. between B and A (iii) p.d. between A and C.25
Ans .13. 12 cells, each of emf 1.5V and internal resistance 0.5β¦, are arranged in m rowseach containing n cells connected in series, as shown. Calculate the values of n andm for which this combination would send maximum current through an externalresistance of 1.5β¦Ans .
SUBJECT: -- PHYSICS CLASS:-XII UNIT No. NAME OF THE UNIT PAGE NO. 1 ELECTROSTATICS 5 2 CURRENT ELECTRICITY 17 3 MAGNETIC EFFECTS OF CURRENT AND MAGNETISM 33 4 ELECTROMAGNETIC INDUCTION AND A.C 48 . 12 4. The capacitors C1, and C2, having plates of area A each, are connected in series, as sh
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tank; 2. Oil composition and API gravity; 3. Tank operating characteristics (e.g., sales flow rates, size of tank); and 4. Ambient temperatures. There are two approaches to estimating the quantity of vapor emissions from crude oil tanks. Both use the gas-oil ratio (GOR) at a given pressure and temperature and are expressed in standard cubic feet per barrel of oil (scf per bbl). This process is .
