JSR INSTITUTE (PHYSICS) XII ASSINGMENT 1 (CAPACITANCE)

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Blake Ford
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1 Physics J S R ESTD:007 JSR INSTITUTE (PHYSIS) XII ASSINGMENT (APAITANE). A capacitor of capacitance, which is initially charged up to a potential difference, is connected with a battery of emf / such that the positive terminal of the battery is connected with the positive plate of the capacitor. After a long time (i) find the total charge flow through the battery (ii) find the total work done by the battery (iii) Find the heat dissipated in the circuit during the process of charging. A parallel plate capacitor has capacitance. If the charges of the plates are and 3, find the (i) charge at the inner surfaces of the pates (ii) potential difference between the plates (iii) charge flown if the plates are connected (iv) energy lost by the capacitor in (iii) (v) charge flown if any plate is earthed 3. Three are two spheres of radii R and R having charges and /, respectively. These two spheres are connected with a cell of emf volts as shown in figure. When the switch is closed, find the final charge on each sphere. 5. A solid conducting sphere of radius 0 cm is enclosed by a thin metallic shell of radius 0 cm. A charge q = 0 µ is given to the inner sphere. Find the heat generated in the process. The inner sphere is connected to the shell by a conducting wire. 6. Suppose the two plates of a capacitor have different areas. When the capacitor is charged by connecting it to a battery, do the charges on the two plates having equal magnitude, or can they be different? Explain your reasoning. 7. The charged plates of a capacitor attract each other. So work by some external force is required to pull the plates farther apart. What happens to the energy added by this work? 8. The two plates of a capacitor are given charges ±. The capacitor is then disconnected from the charging device so that the charges on the plates cannot change, and the capacitor is immersed in a tank of coil. Does the electric field between the plates increase, decrease, or remain the same? Give an explanation. How can this field be measured? 9. A capacitor of capacitance is charged to a potential difference from a cell and then disconnected from it. A charge + is now given to its positive plate. Find the potential difference across the capacitor. 0. Three identical large metallic plates are placed parallel to each other at a very small separation as shown in figure. 4. Two conducting spheres of radii 6 cm and cm each, having the same charge 3 0 8, are kept very far apart. If the spheres are connected to each other by a conducting wire, and (i) the direction and amount of charge transferred and (ii) final potential of each sphere The central plate is given a charge. What amount of charge will flow to earth when the key is pressed?. The plates of a plane capacitor are drawn apart keeping them connected to a battery. Next, the same plates are drawn apart from the same initial condition keeping the battery k

2 Physics disconnected. In which case is more work done?. Three capacitors are arranged as shown in figure. Find the equivalent capacity across the points A and B. 5. An infinite ladder is constructed by connecting several sections of µf, 4 µf capacitor combinations as shown in figure. It is terminated by a capacitor of capacitance. What value should be chosen for such that the equivalent capacitance of the ladder between A and B becomes independent of the number of sections in between? 3. In the circuit shown in figure, the potential difference between the points a and b is 4. Find the emf of the battery. Assume that before connecting the battery in the circuit, all the capacitors were uncharged. 6. Find the potential difference a b between the points () and () shown in each part of figure. 4. A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. The area of each stair is A/3, and the height is d. Find the capacitance of this arrangement. 7. What is A in the arrangement shown in figure. What is the condition such that A = Six capacitors = = 3 = 4 = 5 = 6 = are arranged as shown in figure. Determine the equivalent capacitance between A and B.

3 Physics 3 HINTS / SOLUTIONS (APAITORS) When the switch is closed, the potential difference between the spheres should be. Let q charges flow from the sphere of radius R.

4 4 Physics 6. Yes, magnitude of charge on both plates will be equal because all the electrons lost from positive plate will go to negative plate. 7. This energy is stored as electrostatic potential energy between the plates Positive plate is given a charge ; the charge distribution on different surface are shown in figure so U d ell disconnected W = = d U or Alt. solution st case d q F U = AE nd case d q remains same F doesnot change.. Since there is no capacitor in the path APB, the points A, P and B are electricity same, i.e., the input and output points and directly connected (short circuited). Thus, the entire charge will prefer to flow along the path APB. If means that the capacitors connected in the circuit will not receive any charge for storing. Thus, the equivalent capacitance of this circuit is zero d a c e d 4. The arrangement is a parallel combination of three capacitors. Each capacitor has a plate area A/3, and the separations between the plates are d, d and 3d, respectively. So, As these three capacitances are in parallel, their equivalent capacitance is given by 0. On connecting charges on outer surface = O No charges appear on inner surface of plate and So no charge on outer surface of plate. So + charge will flow to ground. + O O +. ell connected W = U W to A d 5. The equivalent capacitance of the ladder between A and B becomes indepdent of the number of sections in between. If we remove all the capacitors other than, the equivalent capacitance should also be. In the last unit, and 4 µf are in series, let equivalent capacity of 4 µf and be so and µf are in parallel. Then 6.

5 Physics 5 7. X on each capacitor = on each capacitor = 8. X A = X = A A A D B B B B P or (eliminant 3 ) R S

1) Two lightbulbs, one rated 30 W at 120 V and another rated 40 W at 120 V, are arranged in two different circuits.

1) Two lightbulbs, one rated 30 W at 120 V and another rated 40 W at 120 V, are arranged in two different circuits. a. The two bulbs are first connected in parallel to a 120 V source. i. Determine the