Page 1 Exercises For JEE Main Subjective Questions Note You can take approximations in the answers. Equivalent Capacitance Q 1. A parallel-plate capacitor has capacitance of 1.0 F. If the plates are 1.0 mm apart, what is the area of the plates? Q 2. Two parallel-plate vacuum capacitors have areas A 1 and A 2 and equal plate spacing d. Show that when the capacitors are connected in parallel, the equivalent capacitance is the same as for a single capacitor with plate area A 1 + A 2 and spacing d. Q 3. What is the capacitance of the capacitor, shown in figure? Q 4. (a) Two spheres have radii a and b and their centres are at a distance d apart. Show that the capacitance of this system is; 0 4 C 1 1 2 a b d ?? ? ?? provided that d is large compared with a and b. (b) Show that as d approaches infinity the above result reduces to that of two isolated spheres in series. Q 5. Find equivalent capacitance between points A and B (a) (b) (c) General Problems on Capacitors Q 6. A capacitor has a capacitance of 7.28 ?F. What amount of charge must be placed on each of its plates to make the potential difference between its plates equal to 25.0 V? Q 7. A parallel-plate air capacitor of capacitance 245 pF has a charge of magnitude 0.148 ?C on each plate. The plates are 0.328 mm apart (a) What is the potential difference between the plates? (b) What is the area of each plate? (c) What is the surface charge density on each plate? Q 8. Two parallel plates have equal and opposite charges. When the space between the plates is evacuated, the electric field is E = 3.20 × 10 5 V/m When the space is filled with dielectric, the electric field is E = 2.50 × 10 5 V/m Page 2 Exercises For JEE Main Subjective Questions Note You can take approximations in the answers. Equivalent Capacitance Q 1. A parallel-plate capacitor has capacitance of 1.0 F. If the plates are 1.0 mm apart, what is the area of the plates? Q 2. Two parallel-plate vacuum capacitors have areas A 1 and A 2 and equal plate spacing d. Show that when the capacitors are connected in parallel, the equivalent capacitance is the same as for a single capacitor with plate area A 1 + A 2 and spacing d. Q 3. What is the capacitance of the capacitor, shown in figure? Q 4. (a) Two spheres have radii a and b and their centres are at a distance d apart. Show that the capacitance of this system is; 0 4 C 1 1 2 a b d ?? ? ?? provided that d is large compared with a and b. (b) Show that as d approaches infinity the above result reduces to that of two isolated spheres in series. Q 5. Find equivalent capacitance between points A and B (a) (b) (c) General Problems on Capacitors Q 6. A capacitor has a capacitance of 7.28 ?F. What amount of charge must be placed on each of its plates to make the potential difference between its plates equal to 25.0 V? Q 7. A parallel-plate air capacitor of capacitance 245 pF has a charge of magnitude 0.148 ?C on each plate. The plates are 0.328 mm apart (a) What is the potential difference between the plates? (b) What is the area of each plate? (c) What is the surface charge density on each plate? Q 8. Two parallel plates have equal and opposite charges. When the space between the plates is evacuated, the electric field is E = 3.20 × 10 5 V/m When the space is filled with dielectric, the electric field is E = 2.50 × 10 5 V/m (a) What is the dielectric constant? (b) What is the charge density on each surface of the dielectric? Q 9. A 4.00 ?F capacitor and a 6.00 ?F capacitor are connected in parallel across a 660 V supply line. (a) Find the charge on each capacitor and the voltage across each. (b) The charged capacitors are disconnected from the line and from each other, and then reconnected to each other with terminals of unlike sign together. Find the final charge on each and the voltage across each. Q 10. A 5.80 ?F parallel-plate air capacitor has a plate separation of 5.00 mm and is charged to a potential difference of 400 V. Calculate the energy density in the region between the plates, in J/m 3 . Q 11. The dielectric to be used in a parallel-plate capacitor has a dielectric constant of 3.60 and a dielectric strength of 1.60 × 10 7 V/m. The capacitor is to have a capacitance of 1.25 × 10 -9 F and must be able to withstand a maximum potential difference of 5500 V. What is the minimum area the plates of the capacitor may have? Q 12. Two condensers are in parallel and the energy of the combination is 0.1 J, when the difference of potential between terminals is 2 V. With the same two condensers in series, the energy is 1.6 ×10 -2 J for the same difference of potential across the series combination. What are the capacities? Q 13. A circuit has section AB as shown in figure. The emf of the source equals E = 10 V, the capacitor capacitances are equal to C 1 = 1.0 ?F and C 2 = 2.0 ?F, and the potential difference V A -V B = 5.0 V Find the voltage across each capacitor. Q 14. Several 10 pF capacitors are given, each capable of withstanding 100 V. How would you construct: (a) a unit possessing a capacitance of 2 pF and capable of withstanding 500 V? (b) a unit possessing a capacitance of 20 pF and capable of withstanding 300 V? Q 15. Two, capacitors A and B are connected in series across a 100 V supply and it is observed that the potential difference across them are 60 V and 40 V. A capacitor of 2 ?F capacitance is now connected in parallel with A and the potential difference across B rises to 90 V. Determine the capacitance of A and B. Q 16. A 10.0 ?F parallel-plate capacitor with circular plates is connected to a 12.0 V battery. (a) What is the charge on each plate? (b) How much charge would be on the plates if their separation were doubled while the capacitor remained connected to the battery? (c) How much charge would be on the plates if the capacitor were connected to the 12.0 V battery after the radius of each plate was doubled without changing their separation? Q 17. A 450 ?F capacitor is charged to 295 V. Then a wire is connected between the plates. How many joule of thermal energy are produced as the capacitor discharges if all of the energy that was stored goes into heating the wire? Q 18. The plates of a parallel-plate capacitor in vacuum are 5.00 mm apart and 2.00 m 2 in area. A potential difference of 10,000 V is applied across the capacitor. Compute Page 3 Exercises For JEE Main Subjective Questions Note You can take approximations in the answers. Equivalent Capacitance Q 1. A parallel-plate capacitor has capacitance of 1.0 F. If the plates are 1.0 mm apart, what is the area of the plates? Q 2. Two parallel-plate vacuum capacitors have areas A 1 and A 2 and equal plate spacing d. Show that when the capacitors are connected in parallel, the equivalent capacitance is the same as for a single capacitor with plate area A 1 + A 2 and spacing d. Q 3. What is the capacitance of the capacitor, shown in figure? Q 4. (a) Two spheres have radii a and b and their centres are at a distance d apart. Show that the capacitance of this system is; 0 4 C 1 1 2 a b d ?? ? ?? provided that d is large compared with a and b. (b) Show that as d approaches infinity the above result reduces to that of two isolated spheres in series. Q 5. Find equivalent capacitance between points A and B (a) (b) (c) General Problems on Capacitors Q 6. A capacitor has a capacitance of 7.28 ?F. What amount of charge must be placed on each of its plates to make the potential difference between its plates equal to 25.0 V? Q 7. A parallel-plate air capacitor of capacitance 245 pF has a charge of magnitude 0.148 ?C on each plate. The plates are 0.328 mm apart (a) What is the potential difference between the plates? (b) What is the area of each plate? (c) What is the surface charge density on each plate? Q 8. Two parallel plates have equal and opposite charges. When the space between the plates is evacuated, the electric field is E = 3.20 × 10 5 V/m When the space is filled with dielectric, the electric field is E = 2.50 × 10 5 V/m (a) What is the dielectric constant? (b) What is the charge density on each surface of the dielectric? Q 9. A 4.00 ?F capacitor and a 6.00 ?F capacitor are connected in parallel across a 660 V supply line. (a) Find the charge on each capacitor and the voltage across each. (b) The charged capacitors are disconnected from the line and from each other, and then reconnected to each other with terminals of unlike sign together. Find the final charge on each and the voltage across each. Q 10. A 5.80 ?F parallel-plate air capacitor has a plate separation of 5.00 mm and is charged to a potential difference of 400 V. Calculate the energy density in the region between the plates, in J/m 3 . Q 11. The dielectric to be used in a parallel-plate capacitor has a dielectric constant of 3.60 and a dielectric strength of 1.60 × 10 7 V/m. The capacitor is to have a capacitance of 1.25 × 10 -9 F and must be able to withstand a maximum potential difference of 5500 V. What is the minimum area the plates of the capacitor may have? Q 12. Two condensers are in parallel and the energy of the combination is 0.1 J, when the difference of potential between terminals is 2 V. With the same two condensers in series, the energy is 1.6 ×10 -2 J for the same difference of potential across the series combination. What are the capacities? Q 13. A circuit has section AB as shown in figure. The emf of the source equals E = 10 V, the capacitor capacitances are equal to C 1 = 1.0 ?F and C 2 = 2.0 ?F, and the potential difference V A -V B = 5.0 V Find the voltage across each capacitor. Q 14. Several 10 pF capacitors are given, each capable of withstanding 100 V. How would you construct: (a) a unit possessing a capacitance of 2 pF and capable of withstanding 500 V? (b) a unit possessing a capacitance of 20 pF and capable of withstanding 300 V? Q 15. Two, capacitors A and B are connected in series across a 100 V supply and it is observed that the potential difference across them are 60 V and 40 V. A capacitor of 2 ?F capacitance is now connected in parallel with A and the potential difference across B rises to 90 V. Determine the capacitance of A and B. Q 16. A 10.0 ?F parallel-plate capacitor with circular plates is connected to a 12.0 V battery. (a) What is the charge on each plate? (b) How much charge would be on the plates if their separation were doubled while the capacitor remained connected to the battery? (c) How much charge would be on the plates if the capacitor were connected to the 12.0 V battery after the radius of each plate was doubled without changing their separation? Q 17. A 450 ?F capacitor is charged to 295 V. Then a wire is connected between the plates. How many joule of thermal energy are produced as the capacitor discharges if all of the energy that was stored goes into heating the wire? Q 18. The plates of a parallel-plate capacitor in vacuum are 5.00 mm apart and 2.00 m 2 in area. A potential difference of 10,000 V is applied across the capacitor. Compute (a) the capacitance (b) the charge on each plate, and (c) the magnitude of the electric field in the space between them. Q 19. Three capacitors having capacitances of 8.4 ?F, 8.2 ?F and 4.2 ?F are connected in series across a 36 V potential difference. (a) What is the charge on 4.2 ?F capacitor? (b) What is the total energy stored in all three capacitors? (c) The capacitors are disconnected from the potential difference without allowing them to discharge. They are then reconnected in parallel with each other, with the positively charged plates connected together. What is the voltage across each capacitor in the parallel combination? (d) What is the total energy now stored in the capacitors? Q 20. Find the charges on 6 ?F and 4 ?F capacitors. Q 21. In figure, C 1 = C 5 = 8.4 ?F and C 2 = C 3 = C 4 = 4.2 ?F. The applied potential is V ab = 220 V (a) What is the equivalent capacitance of the network between points a and b ? (b) Calculate the charge on each capacitor and the potential difference across each capacitor. Q 22. Two condensers A and B each having slabs of dielectric constant K = 2 are connected in series. When they are connected across 230 V supply, potential across A is 130 V and that across B is 100 V. If the dielectric in the condenser of smaller capacitance is replaced by one for which K = 5, what will be the values of potential difference across them? Q 23. A capacitor of capacitance C 1 = 1.0 ?F charged upto a voltage V = 110 Vis connected in parallel to the terminals of a circuit consisting of two uncharged capacitors connected in series and possessing the capacitance C 2 = 2.0 ?F and C 3 = 3.0 ?F. What charge will flow through the connecting wires? Q 24. In figure, the battery has a potential difference of 20 V. Find : (a) the equivalent capacitance of all the capacitors across the battery and Page 4 Exercises For JEE Main Subjective Questions Note You can take approximations in the answers. Equivalent Capacitance Q 1. A parallel-plate capacitor has capacitance of 1.0 F. If the plates are 1.0 mm apart, what is the area of the plates? Q 2. Two parallel-plate vacuum capacitors have areas A 1 and A 2 and equal plate spacing d. Show that when the capacitors are connected in parallel, the equivalent capacitance is the same as for a single capacitor with plate area A 1 + A 2 and spacing d. Q 3. What is the capacitance of the capacitor, shown in figure? Q 4. (a) Two spheres have radii a and b and their centres are at a distance d apart. Show that the capacitance of this system is; 0 4 C 1 1 2 a b d ?? ? ?? provided that d is large compared with a and b. (b) Show that as d approaches infinity the above result reduces to that of two isolated spheres in series. Q 5. Find equivalent capacitance between points A and B (a) (b) (c) General Problems on Capacitors Q 6. A capacitor has a capacitance of 7.28 ?F. What amount of charge must be placed on each of its plates to make the potential difference between its plates equal to 25.0 V? Q 7. A parallel-plate air capacitor of capacitance 245 pF has a charge of magnitude 0.148 ?C on each plate. The plates are 0.328 mm apart (a) What is the potential difference between the plates? (b) What is the area of each plate? (c) What is the surface charge density on each plate? Q 8. Two parallel plates have equal and opposite charges. When the space between the plates is evacuated, the electric field is E = 3.20 × 10 5 V/m When the space is filled with dielectric, the electric field is E = 2.50 × 10 5 V/m (a) What is the dielectric constant? (b) What is the charge density on each surface of the dielectric? Q 9. A 4.00 ?F capacitor and a 6.00 ?F capacitor are connected in parallel across a 660 V supply line. (a) Find the charge on each capacitor and the voltage across each. (b) The charged capacitors are disconnected from the line and from each other, and then reconnected to each other with terminals of unlike sign together. Find the final charge on each and the voltage across each. Q 10. A 5.80 ?F parallel-plate air capacitor has a plate separation of 5.00 mm and is charged to a potential difference of 400 V. Calculate the energy density in the region between the plates, in J/m 3 . Q 11. The dielectric to be used in a parallel-plate capacitor has a dielectric constant of 3.60 and a dielectric strength of 1.60 × 10 7 V/m. The capacitor is to have a capacitance of 1.25 × 10 -9 F and must be able to withstand a maximum potential difference of 5500 V. What is the minimum area the plates of the capacitor may have? Q 12. Two condensers are in parallel and the energy of the combination is 0.1 J, when the difference of potential between terminals is 2 V. With the same two condensers in series, the energy is 1.6 ×10 -2 J for the same difference of potential across the series combination. What are the capacities? Q 13. A circuit has section AB as shown in figure. The emf of the source equals E = 10 V, the capacitor capacitances are equal to C 1 = 1.0 ?F and C 2 = 2.0 ?F, and the potential difference V A -V B = 5.0 V Find the voltage across each capacitor. Q 14. Several 10 pF capacitors are given, each capable of withstanding 100 V. How would you construct: (a) a unit possessing a capacitance of 2 pF and capable of withstanding 500 V? (b) a unit possessing a capacitance of 20 pF and capable of withstanding 300 V? Q 15. Two, capacitors A and B are connected in series across a 100 V supply and it is observed that the potential difference across them are 60 V and 40 V. A capacitor of 2 ?F capacitance is now connected in parallel with A and the potential difference across B rises to 90 V. Determine the capacitance of A and B. Q 16. A 10.0 ?F parallel-plate capacitor with circular plates is connected to a 12.0 V battery. (a) What is the charge on each plate? (b) How much charge would be on the plates if their separation were doubled while the capacitor remained connected to the battery? (c) How much charge would be on the plates if the capacitor were connected to the 12.0 V battery after the radius of each plate was doubled without changing their separation? Q 17. A 450 ?F capacitor is charged to 295 V. Then a wire is connected between the plates. How many joule of thermal energy are produced as the capacitor discharges if all of the energy that was stored goes into heating the wire? Q 18. The plates of a parallel-plate capacitor in vacuum are 5.00 mm apart and 2.00 m 2 in area. A potential difference of 10,000 V is applied across the capacitor. Compute (a) the capacitance (b) the charge on each plate, and (c) the magnitude of the electric field in the space between them. Q 19. Three capacitors having capacitances of 8.4 ?F, 8.2 ?F and 4.2 ?F are connected in series across a 36 V potential difference. (a) What is the charge on 4.2 ?F capacitor? (b) What is the total energy stored in all three capacitors? (c) The capacitors are disconnected from the potential difference without allowing them to discharge. They are then reconnected in parallel with each other, with the positively charged plates connected together. What is the voltage across each capacitor in the parallel combination? (d) What is the total energy now stored in the capacitors? Q 20. Find the charges on 6 ?F and 4 ?F capacitors. Q 21. In figure, C 1 = C 5 = 8.4 ?F and C 2 = C 3 = C 4 = 4.2 ?F. The applied potential is V ab = 220 V (a) What is the equivalent capacitance of the network between points a and b ? (b) Calculate the charge on each capacitor and the potential difference across each capacitor. Q 22. Two condensers A and B each having slabs of dielectric constant K = 2 are connected in series. When they are connected across 230 V supply, potential across A is 130 V and that across B is 100 V. If the dielectric in the condenser of smaller capacitance is replaced by one for which K = 5, what will be the values of potential difference across them? Q 23. A capacitor of capacitance C 1 = 1.0 ?F charged upto a voltage V = 110 Vis connected in parallel to the terminals of a circuit consisting of two uncharged capacitors connected in series and possessing the capacitance C 2 = 2.0 ?F and C 3 = 3.0 ?F. What charge will flow through the connecting wires? Q 24. In figure, the battery has a potential difference of 20 V. Find : (a) the equivalent capacitance of all the capacitors across the battery and (b) the charge stored on that equivalent capacitance. Find the charge on (c) capacitor 1, (d) capacitor 2, and (e) capacitor 3. Q 25. In figure, battery B supplies 12 V Find the charge on each capacitor (a) first when only switch S 1 is closed and (b) later when S 2 is also closed. (Take C 1 =1.0 ?F,C 2 =2.0 ?F, C 3 =3.0 ?F and C 4 = 4.0 ?F) Q 26. When switch S is thrown to the left in figure, the plates of capacitor 1 acquire a potential difference V o . Capacitors 2 and 3 are initially uncharged. The switch is now thrown to the right. What are the final charges q 1 , q 2 and q 3 on the capacitors? Q 27. A parallel-plate capacitor has plates of area A and separation d and is charged to a potential difference V. The charging battery is then disconnected, and the plates are pulled apart until their separation is 2d. Derive expression in terms of A, d and V for (a) the new potential difference (b) the initial and final stored energies, U i and U f and (c) the work required to increase the separation of plates from d to 2d. C-R Circuits Q 28. In the circuit shown in figure E 1 = 2E 2 =20 V, R 1 = R 2 = 10 k? and C = 1 ?F. Find the current through R 1 , R 2 and C when : (a) S has been kept connected to A for a long time. (b) The switch is suddenly shifted to B. Q 29. (a) What is the steady state potential of point a with respect to point b in figure when switch S is open? Page 5 Exercises For JEE Main Subjective Questions Note You can take approximations in the answers. Equivalent Capacitance Q 1. A parallel-plate capacitor has capacitance of 1.0 F. If the plates are 1.0 mm apart, what is the area of the plates? Q 2. Two parallel-plate vacuum capacitors have areas A 1 and A 2 and equal plate spacing d. Show that when the capacitors are connected in parallel, the equivalent capacitance is the same as for a single capacitor with plate area A 1 + A 2 and spacing d. Q 3. What is the capacitance of the capacitor, shown in figure? Q 4. (a) Two spheres have radii a and b and their centres are at a distance d apart. Show that the capacitance of this system is; 0 4 C 1 1 2 a b d ?? ? ?? provided that d is large compared with a and b. (b) Show that as d approaches infinity the above result reduces to that of two isolated spheres in series. Q 5. Find equivalent capacitance between points A and B (a) (b) (c) General Problems on Capacitors Q 6. A capacitor has a capacitance of 7.28 ?F. What amount of charge must be placed on each of its plates to make the potential difference between its plates equal to 25.0 V? Q 7. A parallel-plate air capacitor of capacitance 245 pF has a charge of magnitude 0.148 ?C on each plate. The plates are 0.328 mm apart (a) What is the potential difference between the plates? (b) What is the area of each plate? (c) What is the surface charge density on each plate? Q 8. Two parallel plates have equal and opposite charges. When the space between the plates is evacuated, the electric field is E = 3.20 × 10 5 V/m When the space is filled with dielectric, the electric field is E = 2.50 × 10 5 V/m (a) What is the dielectric constant? (b) What is the charge density on each surface of the dielectric? Q 9. A 4.00 ?F capacitor and a 6.00 ?F capacitor are connected in parallel across a 660 V supply line. (a) Find the charge on each capacitor and the voltage across each. (b) The charged capacitors are disconnected from the line and from each other, and then reconnected to each other with terminals of unlike sign together. Find the final charge on each and the voltage across each. Q 10. A 5.80 ?F parallel-plate air capacitor has a plate separation of 5.00 mm and is charged to a potential difference of 400 V. Calculate the energy density in the region between the plates, in J/m 3 . Q 11. The dielectric to be used in a parallel-plate capacitor has a dielectric constant of 3.60 and a dielectric strength of 1.60 × 10 7 V/m. The capacitor is to have a capacitance of 1.25 × 10 -9 F and must be able to withstand a maximum potential difference of 5500 V. What is the minimum area the plates of the capacitor may have? Q 12. Two condensers are in parallel and the energy of the combination is 0.1 J, when the difference of potential between terminals is 2 V. With the same two condensers in series, the energy is 1.6 ×10 -2 J for the same difference of potential across the series combination. What are the capacities? Q 13. A circuit has section AB as shown in figure. The emf of the source equals E = 10 V, the capacitor capacitances are equal to C 1 = 1.0 ?F and C 2 = 2.0 ?F, and the potential difference V A -V B = 5.0 V Find the voltage across each capacitor. Q 14. Several 10 pF capacitors are given, each capable of withstanding 100 V. How would you construct: (a) a unit possessing a capacitance of 2 pF and capable of withstanding 500 V? (b) a unit possessing a capacitance of 20 pF and capable of withstanding 300 V? Q 15. Two, capacitors A and B are connected in series across a 100 V supply and it is observed that the potential difference across them are 60 V and 40 V. A capacitor of 2 ?F capacitance is now connected in parallel with A and the potential difference across B rises to 90 V. Determine the capacitance of A and B. Q 16. A 10.0 ?F parallel-plate capacitor with circular plates is connected to a 12.0 V battery. (a) What is the charge on each plate? (b) How much charge would be on the plates if their separation were doubled while the capacitor remained connected to the battery? (c) How much charge would be on the plates if the capacitor were connected to the 12.0 V battery after the radius of each plate was doubled without changing their separation? Q 17. A 450 ?F capacitor is charged to 295 V. Then a wire is connected between the plates. How many joule of thermal energy are produced as the capacitor discharges if all of the energy that was stored goes into heating the wire? Q 18. The plates of a parallel-plate capacitor in vacuum are 5.00 mm apart and 2.00 m 2 in area. A potential difference of 10,000 V is applied across the capacitor. Compute (a) the capacitance (b) the charge on each plate, and (c) the magnitude of the electric field in the space between them. Q 19. Three capacitors having capacitances of 8.4 ?F, 8.2 ?F and 4.2 ?F are connected in series across a 36 V potential difference. (a) What is the charge on 4.2 ?F capacitor? (b) What is the total energy stored in all three capacitors? (c) The capacitors are disconnected from the potential difference without allowing them to discharge. They are then reconnected in parallel with each other, with the positively charged plates connected together. What is the voltage across each capacitor in the parallel combination? (d) What is the total energy now stored in the capacitors? Q 20. Find the charges on 6 ?F and 4 ?F capacitors. Q 21. In figure, C 1 = C 5 = 8.4 ?F and C 2 = C 3 = C 4 = 4.2 ?F. The applied potential is V ab = 220 V (a) What is the equivalent capacitance of the network between points a and b ? (b) Calculate the charge on each capacitor and the potential difference across each capacitor. Q 22. Two condensers A and B each having slabs of dielectric constant K = 2 are connected in series. When they are connected across 230 V supply, potential across A is 130 V and that across B is 100 V. If the dielectric in the condenser of smaller capacitance is replaced by one for which K = 5, what will be the values of potential difference across them? Q 23. A capacitor of capacitance C 1 = 1.0 ?F charged upto a voltage V = 110 Vis connected in parallel to the terminals of a circuit consisting of two uncharged capacitors connected in series and possessing the capacitance C 2 = 2.0 ?F and C 3 = 3.0 ?F. What charge will flow through the connecting wires? Q 24. In figure, the battery has a potential difference of 20 V. Find : (a) the equivalent capacitance of all the capacitors across the battery and (b) the charge stored on that equivalent capacitance. Find the charge on (c) capacitor 1, (d) capacitor 2, and (e) capacitor 3. Q 25. In figure, battery B supplies 12 V Find the charge on each capacitor (a) first when only switch S 1 is closed and (b) later when S 2 is also closed. (Take C 1 =1.0 ?F,C 2 =2.0 ?F, C 3 =3.0 ?F and C 4 = 4.0 ?F) Q 26. When switch S is thrown to the left in figure, the plates of capacitor 1 acquire a potential difference V o . Capacitors 2 and 3 are initially uncharged. The switch is now thrown to the right. What are the final charges q 1 , q 2 and q 3 on the capacitors? Q 27. A parallel-plate capacitor has plates of area A and separation d and is charged to a potential difference V. The charging battery is then disconnected, and the plates are pulled apart until their separation is 2d. Derive expression in terms of A, d and V for (a) the new potential difference (b) the initial and final stored energies, U i and U f and (c) the work required to increase the separation of plates from d to 2d. C-R Circuits Q 28. In the circuit shown in figure E 1 = 2E 2 =20 V, R 1 = R 2 = 10 k? and C = 1 ?F. Find the current through R 1 , R 2 and C when : (a) S has been kept connected to A for a long time. (b) The switch is suddenly shifted to B. Q 29. (a) What is the steady state potential of point a with respect to point b in figure when switch S is open? (b) Which point, a or b, is at the higher potential? (c) What is the final potential of point b with respect to ground when switch S is closed? (d) How much does the charge on each capacitor change when S is closed? Q 30. (a) What is the potential of point a with respect to point b in figure, when switch S is open? (b) Which point, a or b, is at the higher potential? (c) What is the final potential of point b with respect to ground when switch S is closed? (d) How much charge flows through switch S when it is closed? Q 31. In the circuit shown in figure, the battery is an ideal one with emf V. The capacitor is initially uncharged. The switch S is closed at time t = 0. (a) Find the charge Q on the capacitor at time t. (b) Find the current in AB at time t. What is its limiting value as t ? ?? Solutions 1. = 1.1 × 10 8 m 2 2. C = C 1 + C 2 (in parallel) or A = A 1 + A 2 3. C = C LHS + C RHSRead More

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