Current Electricity-06- Subjective UnSolved

(BRUSH UP YOUR CONCEPTS) 1. Find the equivalent resistance between the points a and b of the circuit shown in figure. a 10  5  5  10  2. In the circuit shown in figure E, F, G and H are cells of emf 2, 1, 3 and 1V respectively. The resistances 2, 1, 3 and 1 Ω are their re- spective internal resistances. Calculate (a) The potential difference between B and D and (b) The potential differences across the terminals of each of the cells G and H. 1 V 3. The electric field between the plates of a parallel plate capacitor of capacitance 2.0 μF drops to one third of its initial value in 4.4 μs when the plates are connected by a thin wire. Find the resistance of the wire. 4. Find the equivalent resistance of the networks shown in figure between the points a and b. 5. Find the current in the three resistors shown in figure. 2V 2V 2V 1 2V 6. For the figure calculate the current through 3 Ω resistor and power dissipated in the entire circuit. The emf of battery is 2 volt and its internal resistance is 2/3 Ω . 7. In the circuit shown in the figure initially switch S is open and capacitor is uncharged. Internal resistances of the cells are r1 and r2 their emf’s are equal to  . The potential difference across the cell of internal resistance r1 becomes zero long time after closing the switch. Find the value of R in terms of other known physical quantities. All symbols have their usual meaning. S 8. The potential difference across the terminal of a storage battery is 10V in a closed circuit. If the external resistance is increased by 1 Ω , the potential difference increases by 1V. Further increase in the external resistance of 3 Ω produces a further increase of 2V in the potential difference. What is the emf E and internal resistance of the battery. 9. How many time constants will elapse before the power delivered by the battery drops to half of its maximum value in a charging RC circuit? 10. A potential difference of 220 V is maintained across a 12000 Ω rheo- stat as shown in figure. The voltmeter V has a resistance of 6000 Ω and point c is at one fourth of the distance from a to b. What is the reading of voltmeter ? (CHECK YOUR SKILLS) 1. A long resistor between A and B has resistance of 300 Ω and is tapped at one third points (a) What is equivalent resistance between A and B (b) If the potential difference between A and B is 320V, what will be the potential difference between B and C. (c) Will this change, if the 40 Ω resistor is disconnected ? A B A B 2. In the figure each cell has an emf of 1.5 V and internal resis- tance of 0.40 Ω . Calculate : (i) Total current (ii) Current in the 36 Ω resistor (iii) Potential difference across A & B 12  18  36  D 1.8  C 3. In the circuit shown in figure ξ1  3V, ξ2  2V, ξ3  1V and r1  r2  r3  1Ω. C (B)  1 (a) Find the potential difference between the points A and B 1 when A and B are not connected by wire ACB. (b) Now A and B are connected through a resistance less wire ACB find the current through ACB. A r2 B (c) Using results of (a) & (b). Find the effective emf of the combination between AB in case (a) and effective inter- r3 nal resistance 4. 2 Galvanometers, three resistances 10-3  , 106  , 100  and variable DC supply are given. Form the circuit required for verification of Ohm’s law. Indicate Ammeter & voltmeter. 5. The switch S shown in figure is kept closed for a long time and is then opened at t = 0. Find the current in the middle 10 Ω resistor at t = 1.0 ms. 6. The two parallel plates of a capacitor have equal and opposite charges Q. The dielectric has a dielectric constant k and resistivity ρ . Find the leakage current as a function of time. 7. A silver wire of length 10 meter and cross sectional area 10-8 m2 is suspended vertically and a weight of 10N is attached to it. Calculate the increase in its resistance given that young’s modulus of silver is 7 × 1010 N/m2 & the resistivity of silver is 1.59 × 10-8 Ω -m. Assume the density of silver remains constant during the stretching process. Neglect the change in area. 8. (a) Calculate the steady state current in the 2 Ω resistor 2 shown in the circuit in figure. The internal resistance of the battery is negligible and the capacitance of the condenser is 0.2 μF . (b) The resistors 400 Ω and 800 Ω are connected in se- ries with a 6V battery. It is desired to measure the current in the circuit. An ammeter of 10 Ω resistance is used for this purpose. What will be the reading in the ammeter ? Similarly, if a voltmeter of 10K Ω resistance is used to measure the potential dif- ference across the 400 Ω resistor, what will be the reading in the voltmeter. 9. The region between two concentric conducting spheres of radii ra & rb is filled with a material of resistivity ρ . (a) Show that the resistance between the spheres is given by, R     4π  ra rb  (b) Drive an expression for the current density as a function of radius, if the potential difference between the spheres is Vab . 10. The capacitors shown in figure have been charged to a potential difference of V volts, so that it carries a charge CV with both the switches S1 and S2 remaining open. Switch S1 is closed at t = 0. At t = R1Cswitch S1 is opened and S2 is closed. Find the charge on the capacitor at t = R1C + R2C. R1 R2

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