CLASS XII ELECTROSTATICS


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1 PHYSICAL EDUCATION CLASS XII To do practice of specific game & develop skill. Answer the following questions: UNIT I a) Write type of tournament & explain. b) Draw know fixtures for number of teams 19,21,27. c) Define Intra mural & Extra mural. d) Define Bye & Seeding. UNIT II a) Define Camping, Rock climbing, Tracking, Mountaineering, River rafting & material required for them. b) Write safety measures for all mentioned Adventure Sports. CLASS XII ELECTROSTATICS ONE MARK QUESTIONS Q.1 What is the angle between the directions of electric field and electric dipole moment at any (i) axial and (ii) equatorial point due to an electric dipole? Q.2 What is the net force on a dipole in a uniform electric field? Q.3 Write S.I. unit of electrostatic flux, Is it a scalar or a vector quantity? Q.4 Write the S.I. unit of (i) electric field intensity and (ii) electric dipole moment. Q.5 A charge 'q' is placed at the centre of a cube. What is the electric flux passing through the cube? Q.6 An electric dipole of dipole moment 20x106 Cm is enclosed by a closed surface. What is the net flux coming out of the surface? Q.7 Why does the electric field inside a dielectric decrease when it is placed in an external electric field? Q.8 How does the coulomb force between two point charges depend upon the dielectric constant of the intervening medium.
2 Q.9 If the radius of the Gaussian surface enclosing a charge is halved, how does the electric flux through the Gaussian surface change? Q.10 What is the electrostatic potential due to an electric dipole at an equatorial point? TWO MARKS QUESTIONS Q.1 Define the term 'electric dipole moment'. Give its unit. Derive an expression for the maximum torque acting on an electric dipole, when held in a uniform electric field. Q.2 S1 and S2 are two hollow concentric spheres enclosing charges Q and 2Q respectively as shown in the figure. 1. What is the ratio of the electric flux through S1 and S2? 2. How will the electric flux through the sphere S1 change, if a medium of Dielectric constant 5 is introduced in the space inside S1 in place of air? Q.3 What is an electric line of force? Sketch lines of force due to two equal positive charges placed at a small distance apart in air. Q.4 Two similarly and equally charged identical metal spheres A and B repel to each other with a force 2x10 5 N. A third identical uncharged sphere C is touched with A and then placed at the midpoint between A and B. Calculate the net electric force on C. Q.5 State Gauss' theorem in electrostatics. Using this theorem, derive the expression for the electric field intensity at any point outside a uniformly charged thin spherical shell. 1 Q.6 Plot a graph showing the variation of coulomb force (F) versus 2, where r is the r distance between the two charges of each pair of charges: (1 C, 2 C) and (2 C, 3 C). Interpret the graphs obtained. Q.7 Two fixed point charges +4e and +e units are separated by a distance 'a'. Where should the third point charge be placed for it to be in equilibrium? Q.8 A system has two charges qa=2.5x10 7 C and qb= 2.5x10 7 C located at points A(0, 0, 15cm) and B (0, 0, + 15cm) respectively. Calculate the electric dipole moment of the system. What is its direction? Q.9 Define electric flux. Write its S.I. units. A spherical rubber ballon carries a charge that is uniformly distributed over its surface. As the ballon is blown up and increases in size, how does the total electric flux coming out of the surface change? Give reason.
3 Q.10 Define the dipole moment of an electric dipole. How does the electric potential due to a dipole vary on the dipole axis as a function of 'r' distance of the field point from the midpoint of the dipole at large distance? Q.11 A uniformly charged conducting sphere of 2.8 m diameter has a surface charge density of 100 C/m 2.(a) Find the charge on the sphere.(b) What is the total electric flux leaving the surface of the sphere? THREE MARKS QUESTIONS Q.1 An electric dipole of dipole moment P is placed in a uniform electrical field E. Write the expression for the torque experienced by the dipole. Identify two pairs of perpendicular vectors in the expression. Show diagrammatically the orientation of the dipole in the field for which the torque is (i) Maximum (ii) Half the maximum value (iii) Zero. Q.3 An electric dipole is held in a uniform electric field. Using suitable diagram, show that it does not undergo any translatory motion, and (ii) derive an expression for the torque acting on it and specify its direction. Q.4 State Gauss's theorem in electrostatics. Using it, deduce an expression for electric field intensity at a point near a thin infinite plane sheet of electric charge. ELECTRIC POTENTIAL AND CAPACITOR One mark questions Q.1 The graph shown here, shows the variation of the total energy (E) stored a capacitor against the value of the capacitance (C) itself. Which of the twothe charge on the capacitor or the potential used to charge it is kept constant for this graph? Q.2 Sketch a graph to show how the charge 'Q' acquired by a capacitor of capacitance 'C' varies with increase in potential difference between its plates. Q.3 A hollow metal sphere of radius 6cm is charged such that the potential on its surface is 12V. What is the potential at the centre of the sphere?
4 Q.4 The electric potential is constant in a region. What can you say about electric field there? Q.5 What is meant by capacitance? Give its S.I. unit. Q.6 Define the term' potential energy' of charge 'q' at a distance 'r' in an external electric field. Two marks questions Q.1 Two indentical plane metallic surfaces A and B are kept parallel to each other in air separated by a distance of 1.0 cm as shown in the figure. Surface A given a positive potential of 10V and outer surface of B is earthed. i) What is the magnitude and direction of the uniform electric field between points y and z? ii) What is the work done in moving a charge of 20 mc from point X and point Y? Q.2 Two point charges 3x 10 8 and 2 x 10 8 C are located 15 cm part in air. Find at what point on the line joining these charges the electric potential is zero. Take potential at infinity to be zero. Q.3 A 600 pf capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 600 Pf capacitor. How much electrostatic energy is lost in the process? Q.4 Find the equivalent capacitance of the combination of capacitors between the points A and B as shown in the figure. Also calculate the total charge that flows in the circuit when a 100 V battery is connected between the points A and B.
5 Q.5 The graph shows the variation of voltage, 'V' across the plates of two capacitors A and B versus increase of charge, 'Q' stored on them, which of the two capacitors has higher capacitance? Give reason for your answer. Q.6 Parallel plate capacitor with air between the plates has a capacitance of 8PF. The separation between the plates is now reduced by half and the space between them is filled with a medium of dielectric constant 5. Calculate the value of capacitance of the capacitor in the second case. Q.7 Define 'dielectric constant' of a medium. Briefly explain why the capacitance of a parallel plate capacitor increases, on introducing a dielectric medium between the plates. Q.8 Explain the underlying principle of working of a parallel plate capacitor. If two similar plates, each of area A having surface charge densities + and are separated by a distance d in air, write expressions for. 1. the electric field at points between the two plates. 2. the potential difference between the plates. 3. the capacitance of the capacitor so formed. Q.9 (i) Can two equipotential surfaces intersect each other? Give reasons. (ii) Two charges  q and +q are located at points A (0,0,a) and B (0,0,+a) respectively. How much work is done in moving a test charges from point P (7,0,0) to Q ( 3, 0,0)? Three marks questions Q.1 (a) Determine the electrostatic potential energy of a system consisting of two charges 7 C and  2 C (and no external field) placed at (9 cm,0,0) and (9 cm, 0, 0) respectively. (b) How much work is required to separate the two charges infinitely away from each other?
6 (c) Suppose that the same system of charges is now placed in an external field E= A. A=9x 10 5 cm 2. What would the electrostatic energy of the configuration be? 1, r2 Q.2 Deduce the expression for the electrostatic energy stored in a capacitor of capacitance 'C' and having charge 'Q'. How will the (i) energy stored and (ii) the electric field inside the capacitor be affected when it is completely filled with a dielectric material of dielectric constant 'K'? Q.3 A parallel Plate capacitor of plate separation 'd' is charged to a potential difference V. A dielectric slab of thickness 'd' and dielectric constant 'k' is introduced between the plates while the battery remains connected to the plates. 1. Find the ratio of energy stored in the capacitor after and before the dielectric is introduced. Give the physical explanation for this change in stored energy. 2. What happens to the charge on the capacitor? Q.4 The two plates of a parallel plate capacitor are 5mm apart. A slab of a dielectric of thickness 4 mm is introduced between the plates with its faces parallel to them. The distance between the plates is adjusted so the capacitance of the capacitor become equal to its original value. If the new distance between the plates equals 8 mm, what is the dielectric constant of the dielectric used? Q.5 Two parallel plate capacitor, X and Y have the same area of plates and same separation between them X has air between the plates while Y contains a dielectric medium of r = 4 (i) Calculate capacitance of each capacitor if equivalent capacitance of the combination is 4 F.
7 (ii) Calculate the potential difference between the plates of X and Y. (iii) What is the ratio of electrostatic energy stored in X and Y? FIVE MARKS QUESTIONS Q.1 A dielectric slab of thickness 't' is kept in between the plates, each of area 'A', of a parallel plate capacitor separated by a distance 'd'. Derive an expression for the capacitance of this capacitor for t << d. Q.2 (i). Explain briefly how a capacitor stores energy on charging. Obtain an expression for the energy thus stored. (ii)a battery of 10 V is connected to a capacitor of 0.1 F. The battery is now removed and the capacitor is then connected to a second uncharged capacitor of same capacitance. Calculate the total energy stored in the system. CURRENT ELECTROSTATICS QUESTIONS 1. How does the drift velocity of electrons in a metallic conductor vary with increase in temperature? 2. Two different wires X and Y of same diameter but different materials are joined in series cross a battery. If the number density of electrons in X is twice that of Y, find the ratio of drift velocity of electrons in the two wires. 3. A 4Ω non insulated wire is bent in the middle by and both the halves are twisted with each other. Find its new resistance? 4. The resistance in the left gap of a metre bridge is and the balance point is 45cm from the left end. Calculate the value of the unknown resistance. 5. Two wires of equal length one of copper and the other of manganin have the same resistance. Which wire is thicker? 6. The VI graph for a conductor makes angle Ѳ with V axis, what is the resistance of the conductor?
8 I θ V 7. It is found that electrons pass from point X towards another point Y in 0.1s. What are the current & its direction? 8. Two square metal plates A and B are of the same thickness and material. The side B is twice that of side A. If the resistance of A and B are denoted by RA and RB, find RA/ RB. 9.The VI graph of two resistors in their series combination is shown. Which one of these graphs shows the series combinations of the other two? Give reason for your answer. 10. Plot the graph showing the variation of conductive with the temperature in a metallic conductor. 11. Draw a graph to show the variation of resistance of the metallic wire as a function of its diameter keeping the other factor constant. 12. Two cells each of emf E and internal resistances r 1 and r 2 are connected in series to an external resistance R. Can a value of R be selected such that the potential difference of the first cell is A battery has an emf E and internal resistance r. A variable resistance R is connected across the terminals of the battery. Find the value of R such that (a)the current in the circuit is maximum (b)the potential difference across the terminal is maximum. 14. A piece of silver has a resistance of 1Ω. What will be the resistance of the constantan wire of one third length and one half diameter if the specific resistance of the constantan wire is 30 times that of the silver. 15.Calculate the current shown by the ammeter in the circuit shown (2) (2)
9 5Ω 5Ω A V 16. The plot shows the variation of current I through the cross section of a wire over a time interval of 10s. Find the amount of charge that flows through the wire over this time period. I(A) t(s) Find the resistance between the points (i)a and B and (ii) A and C in the following network (2) A B D C 18. Two wires of the same material having lengths in the ratio 1:2 and diameter 2:3 are connected in series with an accumulator. Compute the ratio of p.d. across the two wires. 19. An infinite ladder network of resistances is constructed with 1Ω and resistances shown A 1Ω C 1Ω 1Ω 1Ω (3) 6V B D A 6V battery between A and B has negligible resistance. Find the effective resistance between A and B. 20. The resistance of a tungsten filament at 150 C is 133Ω. What will be its resistance at C? The temperature coefficient of tungsten is C 1 at 0 0 C. 21.The circuit shown in the diagram contains two identical lamps P and Q. What will happen to the brightness of the lamps, if the resistance R h is increased? Give reason. 22.Using Kirchhoff s laws, calculate I 1, I 2 and I 3 (3) (3)
10 I 3 5Ω I 1 3Ω 12V I 2 6V 3Ω 8Ω 8Ω 4Ω I 1 I 2 I 3 9V 23. In the circuit, find the current th rough the 4Ω resistor. 24. How will you compare emf of two cells using a potentiometer? Explain with a neat circuit diagram. 25. Two cells of emfs E 1 and E 2 (E 1> E 2) are connected as shown A B C E 1 E 2 When a potentiometer is connected between A and B, the balancing length of the potentiometer wire is 300cm. On connecting the same potentiometer between A and C, the balancing length is 100cm. Calculate the ratio of E 1 and E Calculate the current drawn from the battery in the given network. 1Ω 5Ω 4Ω 4V 27. Find the value of X and current drawn from the battery of emf 6V. 28. Find the value of the unknown resistance X and the current drawn by the circuit from the battery if no current flows through the galvanometer. Assume the resistance per unit length of the wire is 0.01Ωcm 1. (3)
11 X G V 29. In the circuit shown, AB is a resistance wire of uniform cross section in which a potential gradient of 0.01V cm 1 exists. (a)if the galvanometer G shows zero deflection, what is the emf E 1 of the cell used? (b)if the internal resistance of the driver cell increases on some account, how will it change the balance point in the expt. E 1 A 180cm J B E 2 G E 1 E 2 G E 1 E A potentiometer wire of length 100cm has a resistance of is connected in series with a resistance and cell of emf 2V of negligible internal resistance. A source of emf of 10mV is balanced against a length of 40cm of potentiometer wire. What is the value of the external resistance? E = 2V A 100cm R 40cm J B (3) G E = 10mV
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