Gurgaon TOPIC: ELECTROSTATIC Assignment 1 (2018)


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1 LJPS Class XII Gurgaon TOPIC: ELECTROSTATIC Assignment (08). A uniform electric field E exists between two charged plates as shown in figure. What would be the work done in moving a charge q along the closed rectangular path ABCDA?. What would be the work done if a point charge +q, is taken from a point A to the point B on the circumference of a circle drawn with another point charge +q at the centre? 3. If a point charge +q taken first from A to C and then from C to B of a circle drawn with another point charge +q as centre, then along which path more work will be done? 4. Sketch the electric lines of force for two positive charges Q and Q ( Q > Q ) separated by a distance d.
2 5. Figure given below shows three points A,B and C in a uniform electrostatic field. At which of the points will the electric potential be maximum?. 6 A parallel plate capacitor is to be designed with a voltage rating kv using a material of dielectric constant 7 3 and dielectric strength about0 Vm. For safety we would like the field never to exceed say, 0% of the dipole strength. What minimum area of the plates is required to have a capacitance of 50pF? [Ans. 9cm ] 7. A charge q is placed at the center of the line joining two equal charges Q. Show that the system of three charges will be in equilibrium if q = Q/4 8. 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?
3 9. X and Y are two parallel plate capacitors having the same area of plates and same separation between the plates. X has air between the plates and Y contains a dielectric medium of = 5 (i) Calculate the potential difference between the plates of X and Y (ii) What is the ratio of electrostatic energy stored in X and Y. An.s V =0V V =5V, 5 :. r 0. The flux of the electrostatic field, through the closed spherical surface S is found to be four times that through the closed spherical surface S. Find the magnitude of the charge Q. Given : q C, q C and q C 3 Ans. 6.5 C. Two similarly and equally charged identical metal spheres A and B repel each other with a force of 0 5 N. A third identical uncharged sphere C is touched with A and then placed at the mid point between A and B. Calculate the net electric force on C. Ans. x 05 Newton
4 . S and S are two hollow concentric sphere enclosing Q and Q respectively as shown in figure. (i) What is the ratio of electric flux through S and S? (ii) How will the electric flux through the sphere S change, if a medium of dielectric constant 5 is introduced in the space inside S in place of air? [Ans: (i) /3 (ii) reduces to /5 of original value] 3. Four point charges of C and 5 C q C C q A q B, and 5 C are located at the corners of a Square ABCD of side 0 cm. Find the force on a charge of q D C placed at the centre O of the square. [Ans: Zero N] 4. A spherical Gaussian surface encloses a charge of C (i) Calculate the electric flux passing through the Gaussian surface. (ii) If the radius of the Gaussian surface is doubled, how much flux would pass through the surface?
5 [Ans: (i) 0 4 Nm C (ii) No change in flux] 5. Four capacitors are connected as shown in the figure given below: Calculate the equivalent capacitance between the points X and Y (Ans : 5 F ] C eq 6. There is a point charge Q at a distance R/ from the centre of a circle of radius R. Another point charge q is to be moved from A to B, where A and B are two points on the circle diametrically opposite to each other. How much work is done by the electrostatic force exerted by Q on q. Ans. 4/3 kqq/r 7. A capacitor of capacitance C is charged fully by connecting it to a battery of e.m.f.. It is then disconnected from the battery. If the separation between the plates of the capacitor is now doubled, what will happen to
6 (a) charge stored by the capacitor? (b) potential difference across it? field strength between the plates. (d) energy stored by the capacitor. Ans. V =V, E= E, U /U = : 8. Figure given below shows tracks of three charged particles in a uniform electrostatic field. Give the sign of the three charges. Which particle has the highest charge to mass ratio? Explain Ans. q/m s y 9. Adjoining figure shows a charge array known as an electric quadrupole. For a point on the axis of the quadrupole, obtain the dependence of potential on r for r/a>>, and contrast your results with that due to an electric dipole, and an electric monopole ( i.e, a single charge) 0.. A point charge of +0 C is at distance of 5cm directly above the centre of square of side 0 cm as shown in figure. What is the magnitude of the electric flux through the square?
7 {Ans : Nm C ]..A charge of 8mc is located at the origin. Calculated the work in taking a small charge of (0,0,3 cm) to a point Q (0, 4cm, 0), via a point R (0, 6cm, 9cm) 0 9 C from a point P [Ans :.J].. An electrical technician requires a capacitance of F in his circuit across a potential difference of kv. A large number of F capacitors are available to him each of which can withstand a potential difference of not more than 400 V. Suggest a possible arrangement that requires the minimum number of capacitors. [Ans: 6 rows with 3 capacitors in each row] 3. (a) A 900pF capacitor is charged by 00V battery. How much electrostatic energy is stored by the capacitor? (b) The capacitor is disconnected to another 900pF capacitor. What is the electrostatic energy stored by the system?
8 A system has two electric charges q A.5 0 C and q B.5 0 C located at the points A (0,0,5 cm) and B (0,0, +5 cm) respectively. Calculate the electric dipole moment of the system. What is its direction? Ans. 7.5 x 08, +Z axis 5. A 0 F capacitor is charged by a 30 V d.c supply and then connected across an uncharged 50 F capacitor. Calculate (i) the final potential difference across the combination, and (ii) the initial and final energies. How will you account for the difference in Energy? 6. Find : (i) the equivalent capacitance and (ii) the total energy stored in the system of capacitor given in the network. The charging battery has an emf of 4V.
9 7. In the figure shown, calculate the total flux of the electrostatic field through the spheres S and S. The wire AB, shown here has a linear charge density, given by = kx where x is the distance measured along the wire from the end A 8. Two point charges C and 0 8 C are separated by a distance of 0 cm in air as shown in the figure (i) Find at what distance from point A would the electric potential be zero (ii) Also calculate the electrostatic potential energy of the system.
10 9. Calculate the equivalent capacitance between the points A and B of the circuit given below. If a battery of emf 0 V is connected between the points A and B, Calculate the total charge in circuit. 30. What is the function of dielectric in a capacitor? Calculate the equivalent capacitance of the combination between the points P and Q as shown in figure. 3. Define the capacitance of a parallel plate capacitor. Two parallel plated PQ and RS are kept distance d apart. Area of each plate is A The space between them is filled with three dielectric slabs of identical size having dielectric constants K, K and K respectively as shown in figure. Find the capacitance of the capacitor. 3
11 A 0 [Ans: C ( K K K ) ] 3 3 d 3. Define electric potential. Deduce an expression for the electric potential at a point distant r from a point charge (Q > 0) 33. A capacitor half filled with dielectric of dielectric constant 4 has a capacitance 0 F without dielectric. [Ans: C 4 F ] 0. What is the capacitance 34. Capacitance of an air filled parallel plate capacitor is 0 F filled with dielectric slab of dielectric constant 4?. What will its capacitance become when it is half
12 35. Calculate capacitance of capacitor as shown [Ans : 0 K K K K d A ] 36. Calculate capacitance of capacitor as shown [Ans : 0 K K d A ]
13 37. Calculate capacitance of capacitor as shown 0 [Ans : A K K K 3 d K K 3 ] 38. In the arrangement of capacitors shown here, the energy stored in the 6 F capacitor is E. Find the following: (i) Energy stored in the F capacitor (ii) Energy stored in the 3 F capacitor (iii) Total energy drawn from the battery [Ans : E, 8 E, E]
14 39. In a certain region of space the electric field is along the z direction through out. The magnitude of electric field is 5 however, not constant but increases uniformly along the positive z direction at the rate of 0 0 NC per meter. 7 What are the forces and torque experienced by a system having a total dipole moment equal to 0 0 Cm in the negative z direction? 40. Consider a uniform electric field E =3 0 3 N/C i a. What is the flux of this field. Through a square of 0 cm on a side whose plane is parallel to the yz plane? b. What is the flux through the same square if the normal to its plane makes a [Ans : a. 30 Nm C b. 5 Nm / C ] 60 angle with the x axis? 4. An oil drop of excess electrons is held stationary under constant electric field of oil drop experiment. The density of the oil is.6 g. cm Estimate the radius of the drop. 9 [ g 9.8 ms, e.60 0 C ] 4 0 NC in Millikan
15 4 [ Ans : mm ] 4. Obtain the equivalent capacitance of the network in adjoining figure. For a 300 v supply, determine the charge and voltage across ech capacitor. [Ans : C Q eq 00/3pF, Q Q C, V 0 8 V C,V 3 00V, 50V, Q C, V 4 00V] An electron falls through a distance of.5 cm in a uniform electric field of magnitude.0 0 NC. The direction of the field is reversed keeping its magnitude unchanged and proton falls through the same distance. Compute the time of fall in each case. Contrast the situation with that of free fall under gravity
16 44.. Two charges 0 C are placed 5.0 mm apart. Determine the electric field at (i) a point P on the axis of the dipole 5 cm away from its centre. O on the side of the positive charges and (ii) a point Q, 5 cm away from O on a line passing through O and normal to the axis of the dipole Draw electric field lines between the plates of a parallel plate capacitor with (i) air and (i) dielectric as the medium A parallel plate capacitor with air as dielectric is connected to a power supply and charged to a potential differencev 0. After disconnecting from power supply, a sheet of insulating material is inserted between the plates. Completely filling the space between them. How will its (i) capacity, (ii) electric field and (iii) energy change? Given that the capacity of capacitor with air and medium is C and permittivity for air and medium are and respectively Derive an expression for the electric potential at a point along the axial line of an electric dipole. at a point due to a point charge, the values of electric field intensity and potential are 3 N/C and 6 J/C respectively. Calculate (i) magnitude of the charge and (ii) distance of the charge from the point of observation Figures a and b shows the field lines of a positive and negative point charge respectively. a. Give the signs of the potential difference V V. V V P Q B A b. Give the sign of the potential energy difference of a small negative charge between the points Q and P, A and B. c. Give the sign of the work done by the field in moving a small positive charge from Q and P d. Give the sign of the work done by the external agency in moving a small negative charge from B to A
17 e. Does the kinetic energy of a small negative charge increase or decrease in going from B to A
18 LJPS Gurgaon. The variation of Potential difference V with length l in case of two potentiometers P and Q is as shown. Which one of these two will you prefer for comparing emfs of two primary cell. Class XIIPhysics  Assignment Topic:  Current Electricity 5. The metallic conductor is at temperature.the temperature of the metallic conductor is increased to How will the product of its resistivity and conductivity change? 6. The electric lamps A and B are marked 0V00W and 0V 60W. How will the product of its resistivity and conductivity change?. 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. 7. A carbon resistor is marked in coloured bands of red, black, orange and silver. What is the resistance and tolerance value of the resistor? 3. Two conductors one having resistor R and another R are connected in turn across a d.c. source If the rate of heat produced in the two conductors is Q andq respectively, what is the value of Q? Q 8. A uniform wire of resistance 0ohm is cut into two equal parts. These parts are now connected in parallel. What will be the resistance of the combination? 4. How does the drift velocity of electrons in a metallic conductor change, if the length of the conductor is doubled by stretching it, keeping the applied potential difference constant? 9. If a wire of resistivity is stretched to thrice its initial length, what will be its new resistivity? 0. The sequence of bands marked on a carbon resistor are: Red, Red, Red, Silver. Write the value of resistance with tolerance?
19 . Nichrome and Copper wires of the same length and same radius are connected in series. Current I is passed through them. Why does the nichrome wire get heated first? 9. Under which conditions will the current I andi be in the directions as shown in the diagram here?. Two bulbs whose resistances are in the ratio of : are connected in parallel to a source of constant voltage, what will be the ratio of power dissipation in these? 0 Determine the equivalent resistance of network shown. 3. If the temperature of a good conductor increases, how does the relaxation time of electron in the conductor change? 4. If the length of a wire conductor is doubled by stretching it, keeping the p.d across it constant by what factor does the drift speed of electrons change? 5. How can we increase the sensitivity of a potentiometer?. You are given n resistors, each of resistance r. These are first connected to get minimum possible resistance. In the second case, these are again connected differently to get maximum possible resistance. Complete the ratio between the minimum and maximum values of resistance so obtained.. Two primary cells of e.m.f E ande ( E E )are connected to the potentiometer wire AB as shown in Figure. Find ratio of E /E =? 6. When is the Wheatstone s bridge most sensitive? 7. Define conductivity of a material. Give its S.I units? 3. Define the term temperature coefficient of resistivity Show graphically the variation of resistivity with temperature for nichrome. 8. Three identical resistors R R andr are connected to, 3 a battery in figure. What will be the ratio of voltages across R andr [Ans: : ] 4. 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?
20 5. A carbon resistor has the following color bands drawn on it. Find its value. Define the term resistivity of a material. Give its unit. 9. Find the value of current in the circuit shown. 6. The circuit shown in the diagram contains a battery B, a rheostat Rh and identical lamps P and Q. What will happen to the brightness of the lamps, if the resistance through the rheostat is increased? Give reason. 30. Two hollow spheres of radius r andr are given. The space between them is filled with material resistivity as shown. Calculate its resistance. 7. The voltage current graphs for two resistors of the same material and same radii with length L andl are shown in the figure. If L L, state with reason, which of these graphs represents voltage current change for L 3. VI graph for a metallic wire at two different temperatures T andt is as shown in the following figure. Which of the two temperatures is higher and why? 8. Potential difference across terminals of cell were measured (in volts) against different currents ( in ampere) flowing through the cell. A graph was drawn which was a straight line ABC. Using the data given in the graph determine, (i) the e.m.f and (ii) the internal resistance of the cell. 3. Calculate the equivalent resistance of the resistance network between the points A and B as shown in the figure, when switch S is closed. [Ans: 9.6 ohm]
21 33. In the arrangement of conductors, find the equivalent resistance between A and B [Ans: R=3 Ω] 38. Calculate R in the following circuit ab [Ans:.5 ohm] 34. Determine the current in each branch of the network shown in figure. 39. At room temperature (7.0 C, and resistance of heating element is 00 Ω. What is the temperature of the element if the resistance is found to be 7Ω, given that the temperature coefficient of the material of the resistor is ] C [Ans: 07 C 35. Current flows through a wire varies with time t in second as I = (t + 4) A. How much charge passes through a cross section of the wire in seconds? [ Ans : C] 40. A silver wire has a resistance of.ωat 7.5 C resistance of.7ω at 00 C, and a. Determine the temperature coefficient of resistivity of silver? [Ans: C ] 36. With switch S open, the network of the resistors, shown here drawn a current I from the battery. How many times will this current become on closing the Switch S? 4. Determine the current drawn from V supply with internal resistance 0.5 Ω by the infinite network shown in figure. Each resistor has Ω resistance. 37. Find the resistance of the network shown in figure between points A and B [Ans: 4ohm} 4.The resistance of the platinum wire of a platinum resistance thermometer at the ice point is 5 Ω and at steam point is 5.3 Ω. When the thermometer is inserted in a hot
22 bath, the resistance of the platinum wire is Ω. Calculate the temperature of the bath. 43.A 0 m long wire of uniform cross section and 0 Ω. resistance is used in a potentiometer. The wire is connected in series with a battery of 5 V along with an external resistance of 480 Ω. If an unknown e.m.f E is balanced at 6.0 m length of the wire calculate :(i) the potential gradient of the potentiometer wire (ii) the value of unknown e.m.f E. 46. Potentiometer wire, PQ of m length is connected to a standard cell E, Another cell E of e.m.f.0v is connected as shown in the circuit diagram with a resistance r. and a switch S. When switch S is open, null positions is obtained at a distance of 5 cm from P. Calculate (i) potential gradient of the potentiometer wire and (ii) e.m.f of the cell E (iii) When switch S is closed, will null point move towards P or towards Q? Give reason cells of identical e.m.f E, internal resistance r are connected in series to a variable resistor. The following graph shows the variation of terminal voltage of the combination with the current output: (i) What is the e.m.f of each cell used? (ii) For what current from the cells, does maximum power dissipation occur in the circuit? (iii) Calculate the internal resistance of each cell. 47. In the potentiometer circuit shown, the balance (null) point is at X. State with reason, where the balance point will be shifted when. Resistance R is increased, keeping all parameters unchanged.. Resistance S is increased, keeping R constant. 3. Cell P is replaced by another cell whose e.m.f is lower than that of cell Q 45. 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 I from the zero end of the meter 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 I from zero end of the meter bridge wire. Obtain a formula for Xth terms of I and S. I, 48. What is meant by the sensitivity of a potentiometer? A battery E of 4V and a variable resistance R are h connected in series with the wire AB of the potentiometer. The length of the wire of the potentiometer is meter. When a cell E of e.m.f.5 volt is connected between points A and C, no current flows through E. Length of AC = 60 cm.
23 i)find the potential difference between the ends A and B of the potentiometer? ii) Would the method work, if the battery E is replaced by a cell of emf of V? 49. The potentiometer wire of length 00cm has a resistance of 0 Ω. It is connected in series with a resistance 5 Ω and an accumulator of e.m.f 3V having negligible resistance. A source of.v is balanced against a length L of the potentiometer wire. Find the value of L. 5. Two cells of e.m.f E and E ( E > E ) are connected as shown below. When a potentiometer is connected between A and B, the balancing length of potentiometer is 300 cm. On connecting the same potentiometer is 300 cm. On connecting the same potentiometer between A and C, the balancing length is 00cm. Calculate the ratio of E and E [Ans: E / E = 3/] 50. In the given circuit diagram E and E are.0v and 4.0V respectively and resistances r, r and R are.0 Ω.,.0 Ω. and 5.0 Ω. respectively. Calculate the value of current and indicate its direction. Also calculate the potential difference between the points (i) B and A and (ii) A and C. 53. Find the value of 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 AB to be 0.0 Ω/cm [Ans: X = 3 Ω, I =.8A] [Ans (a) /4A, anticlockwise direction (b) (i) 7/ volt (ii) 5/ volt] 5. Find the value of the unknown resistance X, in the following circuit, if no current flows through the section AO. Also calculate the current drawn by the circuit from the battery of e.m.f 6 V and negligible internal resistance. [Ans : 6 Ω, I = A] 54. Find the current drawn from a cell of e.m.f.5 V and internal resistance 0.5 Ω connected to the electrical network given below.
24 55. Calculate (i) the equivalent resistance between A and B of the electrical network given below, and (ii) the current drawn by the network, if a battery of e.m.f 8V, internal resistance Ω is connected across the points A and B. [ Ans : Ω, I =.6 A] 58. Determine the current in each branch of the network shown in figure [Ans: I 4 / 7 A, I 6 / 7 A, I 4 / 7 A, I 6 / 7 A, I / 7 A, I 0 / 7 A AB BC CD AD BD 56. AB is one meter long uniform wire of 0 Ω resistance.. The other data are shown in the circuit diagram given below: Calculate (i) Potential gradient along AB, and (ii) length AO of the wire, when the galvanometer shows no deflection [ Ans: (i) 0.8V/m (ii) 0.3V Length AO = 37.5 cm] 59. Figure shows a potentiometer circuit for comparison of two resistances. The balance point with a standard resistor R = 0.0 Ω is found to be 58.3 cm, while that with the unknown resistance X is 68.5 cm. Determine the value of X. What might you do if you failed to find a balance point with the given cell of e.m.f E? [Ans: X=.75 Ω or.8 Ω] 60. A battery of 0 V and negligible internal resistance is connected across the diagonally opposite corners of a cubical network consisting of resistors each of resistance of the network and the current along each edge of the cube. 57. Calculate the current drawn from the battery in the given network sketched here. [Ans : A]
25 6. A resistance of R Ω draws current from a potentiometer. The potentiometer has a total resistance R 0 Ω. A voltage V supplied to the potentiometer. Derive an expression for the voltage across R when the sliding contact is in the middle of the potentiometer 6. A uniform wire of resistance 36 Ω is bent in the form of a circle. Calculate the effective resistance across the points A and B.
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