Page 1 Exercises For JEE Main Subjective Questions Current Q 1. How many electrons per second pass through a section of wire carrying a current of 0.7 A? Q 2. A current of 3.6 A flows through an automobile headlight. How many coulombs of charge flow through the headlight in 3.0 h? Q 3. A current of 7.5 A is maintained in wire for 45 s. In this time (a) How much charge and (b) How many electrons flow through the wire? Q 4. In the Bohr model, the electron of a hydrogen atom moves in a circular orbit of radius 5.3 × 10 11 m with a speed of 2.2 × 10 6 m/s. Determine its frequency f and the current I in the orbit. Q 5. The current in a wire varies with time according to the relation I = 55A  (0.65 A/s 2 ) t 2 . (a) How many coulombs of charge pass a crosssection of the wire in the time interval between t = 0 and t = 8.0 s ? (b) What constant current would transport the same charge in the same time interval? Q 6. When a wire carries a current of 1.20 A, the drift velocity is 1.20 × 10 4 m/s. What is the drift velocity when the current is 6.00 A? Q 7. Find the velocity of charge leading to 1 A current which flows in a copper conductor of cross section 1 cm 2 and length 10 km. Free electron density of copper is 8.5 × 10 2 /m 3 . How long will it take the electric charge to travel from one end of the conductor to the other? Q 8. A typical copper wire have 2 × 10 21 free electrons in 1 cm of its length. Suppose that the drift speed of the electrons along the wire is 0.05 cm/s. How many electrons would pass through a given crosssection of the wire each second? How large a current would be flowing in the wire? Resistivity and Resistance Q 9. In household wiring, copper wire 2.05 mm in diameter is often used. Find the resistance of a 24.0 m length of this wire. Resistivity of copper is 0.017 ? ?m. Q 10. You need to produce a set of cylindrical copper wires 3.50 m long that will have a resistance of 0.125 ?, each. What will be the mass of each of these wires? Specific resistance of copper = 1.72 × 10 8 ?m, density of copper = 8.9 × 10 3 kg/m 3 . Q 11. Two coils connected in series have resistance of 600 ? and 300 ? at 20° C and temperature co efficient of 0.001 and 0.004(°C) 1 respectively. Find resistance of the combination at a temperature of 50° C. What is the effective temperature coefficient of combination? Q 12. An aluminium wire 7.5 m long is connected in parallel with a copper wire 6 m long. When a current of 5 A is passed through the combination, it is found that the current in the aluminium wire is 3 A. The diameter of the aluminium wire is 1 mm. Determine the diameter of the copper wire. Resistivity of copper is 0.017 ? ?m and that of the aluminium is 0.028 ? ?m. Q 13. The potential difference between two points in a wire 75.0 cm apart is 0.938 V, when the current density is 4.40 × 10 7 A/m 2 . What is Page 2 Exercises For JEE Main Subjective Questions Current Q 1. How many electrons per second pass through a section of wire carrying a current of 0.7 A? Q 2. A current of 3.6 A flows through an automobile headlight. How many coulombs of charge flow through the headlight in 3.0 h? Q 3. A current of 7.5 A is maintained in wire for 45 s. In this time (a) How much charge and (b) How many electrons flow through the wire? Q 4. In the Bohr model, the electron of a hydrogen atom moves in a circular orbit of radius 5.3 × 10 11 m with a speed of 2.2 × 10 6 m/s. Determine its frequency f and the current I in the orbit. Q 5. The current in a wire varies with time according to the relation I = 55A  (0.65 A/s 2 ) t 2 . (a) How many coulombs of charge pass a crosssection of the wire in the time interval between t = 0 and t = 8.0 s ? (b) What constant current would transport the same charge in the same time interval? Q 6. When a wire carries a current of 1.20 A, the drift velocity is 1.20 × 10 4 m/s. What is the drift velocity when the current is 6.00 A? Q 7. Find the velocity of charge leading to 1 A current which flows in a copper conductor of cross section 1 cm 2 and length 10 km. Free electron density of copper is 8.5 × 10 2 /m 3 . How long will it take the electric charge to travel from one end of the conductor to the other? Q 8. A typical copper wire have 2 × 10 21 free electrons in 1 cm of its length. Suppose that the drift speed of the electrons along the wire is 0.05 cm/s. How many electrons would pass through a given crosssection of the wire each second? How large a current would be flowing in the wire? Resistivity and Resistance Q 9. In household wiring, copper wire 2.05 mm in diameter is often used. Find the resistance of a 24.0 m length of this wire. Resistivity of copper is 0.017 ? ?m. Q 10. You need to produce a set of cylindrical copper wires 3.50 m long that will have a resistance of 0.125 ?, each. What will be the mass of each of these wires? Specific resistance of copper = 1.72 × 10 8 ?m, density of copper = 8.9 × 10 3 kg/m 3 . Q 11. Two coils connected in series have resistance of 600 ? and 300 ? at 20° C and temperature co efficient of 0.001 and 0.004(°C) 1 respectively. Find resistance of the combination at a temperature of 50° C. What is the effective temperature coefficient of combination? Q 12. An aluminium wire 7.5 m long is connected in parallel with a copper wire 6 m long. When a current of 5 A is passed through the combination, it is found that the current in the aluminium wire is 3 A. The diameter of the aluminium wire is 1 mm. Determine the diameter of the copper wire. Resistivity of copper is 0.017 ? ?m and that of the aluminium is 0.028 ? ?m. Q 13. The potential difference between two points in a wire 75.0 cm apart is 0.938 V, when the current density is 4.40 × 10 7 A/m 2 . What is (a) The magnitude of E in the wire? (b) the resistivity of the material of which the wire is made? Q 14. A rectangular block of metal of resistivity p has dimensions d × 2d × 3d. A potential difference V is applied between two opposite faces of the block. (a) To which two faces of the block should the potential difference V be applied to give the maximum current density? What is the maximum current density? (b) To which two faces of the block should the potential difference V be applied to give the maximum current? What is this maximum current? Q 15. An electrical conductor designed to carry large currents has a circular crosssection 2.50 mm in diameter and is 14.0 m long. The resistance between its ends is 0.104 ?. (a) What is the resistivity of the material? (b) If the electric field magnitude in the conductor is 1.28 V/m, what is the total current? (c) If the material has 8.5 × 10 28 free electrons per cubic metre, find the average drift speed under the conditions of part (b). Q 16. It is desired to make a 20.0 ? coil of wire which has a zero thermal coefficient of resistance. To do this, a carbon resistor of resistance R 1 is placed in series with an iron resistor of resistance R 2 . The proportions of iron and carbon are so chosen that R 1 + R 2 = 20.00 ? for all temperatures near 20° C. How large are R 1 and R 2 ? Given ? C = 0.5 × 10 3 K 1 and ? Fe = 5.0 × 10 3 K 1 . Resistors in Series and Parallel (Kirchhoff's Laws) Q 17. Find the current supplied by the battery in the circuit shown in figure. Q 18. Calculate battery current and equivalent resistance of the network shown in figure. Q 19. Compute total circuit resistance and battery current as shown in figure. Page 3 Exercises For JEE Main Subjective Questions Current Q 1. How many electrons per second pass through a section of wire carrying a current of 0.7 A? Q 2. A current of 3.6 A flows through an automobile headlight. How many coulombs of charge flow through the headlight in 3.0 h? Q 3. A current of 7.5 A is maintained in wire for 45 s. In this time (a) How much charge and (b) How many electrons flow through the wire? Q 4. In the Bohr model, the electron of a hydrogen atom moves in a circular orbit of radius 5.3 × 10 11 m with a speed of 2.2 × 10 6 m/s. Determine its frequency f and the current I in the orbit. Q 5. The current in a wire varies with time according to the relation I = 55A  (0.65 A/s 2 ) t 2 . (a) How many coulombs of charge pass a crosssection of the wire in the time interval between t = 0 and t = 8.0 s ? (b) What constant current would transport the same charge in the same time interval? Q 6. When a wire carries a current of 1.20 A, the drift velocity is 1.20 × 10 4 m/s. What is the drift velocity when the current is 6.00 A? Q 7. Find the velocity of charge leading to 1 A current which flows in a copper conductor of cross section 1 cm 2 and length 10 km. Free electron density of copper is 8.5 × 10 2 /m 3 . How long will it take the electric charge to travel from one end of the conductor to the other? Q 8. A typical copper wire have 2 × 10 21 free electrons in 1 cm of its length. Suppose that the drift speed of the electrons along the wire is 0.05 cm/s. How many electrons would pass through a given crosssection of the wire each second? How large a current would be flowing in the wire? Resistivity and Resistance Q 9. In household wiring, copper wire 2.05 mm in diameter is often used. Find the resistance of a 24.0 m length of this wire. Resistivity of copper is 0.017 ? ?m. Q 10. You need to produce a set of cylindrical copper wires 3.50 m long that will have a resistance of 0.125 ?, each. What will be the mass of each of these wires? Specific resistance of copper = 1.72 × 10 8 ?m, density of copper = 8.9 × 10 3 kg/m 3 . Q 11. Two coils connected in series have resistance of 600 ? and 300 ? at 20° C and temperature co efficient of 0.001 and 0.004(°C) 1 respectively. Find resistance of the combination at a temperature of 50° C. What is the effective temperature coefficient of combination? Q 12. An aluminium wire 7.5 m long is connected in parallel with a copper wire 6 m long. When a current of 5 A is passed through the combination, it is found that the current in the aluminium wire is 3 A. The diameter of the aluminium wire is 1 mm. Determine the diameter of the copper wire. Resistivity of copper is 0.017 ? ?m and that of the aluminium is 0.028 ? ?m. Q 13. The potential difference between two points in a wire 75.0 cm apart is 0.938 V, when the current density is 4.40 × 10 7 A/m 2 . What is (a) The magnitude of E in the wire? (b) the resistivity of the material of which the wire is made? Q 14. A rectangular block of metal of resistivity p has dimensions d × 2d × 3d. A potential difference V is applied between two opposite faces of the block. (a) To which two faces of the block should the potential difference V be applied to give the maximum current density? What is the maximum current density? (b) To which two faces of the block should the potential difference V be applied to give the maximum current? What is this maximum current? Q 15. An electrical conductor designed to carry large currents has a circular crosssection 2.50 mm in diameter and is 14.0 m long. The resistance between its ends is 0.104 ?. (a) What is the resistivity of the material? (b) If the electric field magnitude in the conductor is 1.28 V/m, what is the total current? (c) If the material has 8.5 × 10 28 free electrons per cubic metre, find the average drift speed under the conditions of part (b). Q 16. It is desired to make a 20.0 ? coil of wire which has a zero thermal coefficient of resistance. To do this, a carbon resistor of resistance R 1 is placed in series with an iron resistor of resistance R 2 . The proportions of iron and carbon are so chosen that R 1 + R 2 = 20.00 ? for all temperatures near 20° C. How large are R 1 and R 2 ? Given ? C = 0.5 × 10 3 K 1 and ? Fe = 5.0 × 10 3 K 1 . Resistors in Series and Parallel (Kirchhoff's Laws) Q 17. Find the current supplied by the battery in the circuit shown in figure. Q 18. Calculate battery current and equivalent resistance of the network shown in figure. Q 19. Compute total circuit resistance and battery current as shown in figure. Q 20. Compute the value of battery current i shown in figure. All resistances are in ohm. Q 21. Calculate the potentials of points A, B, C and D as shown in Fig. (a). What would be the new potential values if connections of 6 V battery are reversed as shown in Fig. (b)? All resistances are in ohm. Q 22. Give the magnitude and polarity of the following voltages in the circuit of figure : (i) V 1 (ii) V 2 (iii) V 3 (iv) V 32 (v) V 12 (vi) V 13 Q 23. The emf E and the internal resistance r of the battery shown in figure are 4.3 V and 1.0 ? respectively. The external resistance R is 50 ?. The resistances of the ammeter and voltmeter are 2.0 ? and 200 ?, respectively. Page 4 Exercises For JEE Main Subjective Questions Current Q 1. How many electrons per second pass through a section of wire carrying a current of 0.7 A? Q 2. A current of 3.6 A flows through an automobile headlight. How many coulombs of charge flow through the headlight in 3.0 h? Q 3. A current of 7.5 A is maintained in wire for 45 s. In this time (a) How much charge and (b) How many electrons flow through the wire? Q 4. In the Bohr model, the electron of a hydrogen atom moves in a circular orbit of radius 5.3 × 10 11 m with a speed of 2.2 × 10 6 m/s. Determine its frequency f and the current I in the orbit. Q 5. The current in a wire varies with time according to the relation I = 55A  (0.65 A/s 2 ) t 2 . (a) How many coulombs of charge pass a crosssection of the wire in the time interval between t = 0 and t = 8.0 s ? (b) What constant current would transport the same charge in the same time interval? Q 6. When a wire carries a current of 1.20 A, the drift velocity is 1.20 × 10 4 m/s. What is the drift velocity when the current is 6.00 A? Q 7. Find the velocity of charge leading to 1 A current which flows in a copper conductor of cross section 1 cm 2 and length 10 km. Free electron density of copper is 8.5 × 10 2 /m 3 . How long will it take the electric charge to travel from one end of the conductor to the other? Q 8. A typical copper wire have 2 × 10 21 free electrons in 1 cm of its length. Suppose that the drift speed of the electrons along the wire is 0.05 cm/s. How many electrons would pass through a given crosssection of the wire each second? How large a current would be flowing in the wire? Resistivity and Resistance Q 9. In household wiring, copper wire 2.05 mm in diameter is often used. Find the resistance of a 24.0 m length of this wire. Resistivity of copper is 0.017 ? ?m. Q 10. You need to produce a set of cylindrical copper wires 3.50 m long that will have a resistance of 0.125 ?, each. What will be the mass of each of these wires? Specific resistance of copper = 1.72 × 10 8 ?m, density of copper = 8.9 × 10 3 kg/m 3 . Q 11. Two coils connected in series have resistance of 600 ? and 300 ? at 20° C and temperature co efficient of 0.001 and 0.004(°C) 1 respectively. Find resistance of the combination at a temperature of 50° C. What is the effective temperature coefficient of combination? Q 12. An aluminium wire 7.5 m long is connected in parallel with a copper wire 6 m long. When a current of 5 A is passed through the combination, it is found that the current in the aluminium wire is 3 A. The diameter of the aluminium wire is 1 mm. Determine the diameter of the copper wire. Resistivity of copper is 0.017 ? ?m and that of the aluminium is 0.028 ? ?m. Q 13. The potential difference between two points in a wire 75.0 cm apart is 0.938 V, when the current density is 4.40 × 10 7 A/m 2 . What is (a) The magnitude of E in the wire? (b) the resistivity of the material of which the wire is made? Q 14. A rectangular block of metal of resistivity p has dimensions d × 2d × 3d. A potential difference V is applied between two opposite faces of the block. (a) To which two faces of the block should the potential difference V be applied to give the maximum current density? What is the maximum current density? (b) To which two faces of the block should the potential difference V be applied to give the maximum current? What is this maximum current? Q 15. An electrical conductor designed to carry large currents has a circular crosssection 2.50 mm in diameter and is 14.0 m long. The resistance between its ends is 0.104 ?. (a) What is the resistivity of the material? (b) If the electric field magnitude in the conductor is 1.28 V/m, what is the total current? (c) If the material has 8.5 × 10 28 free electrons per cubic metre, find the average drift speed under the conditions of part (b). Q 16. It is desired to make a 20.0 ? coil of wire which has a zero thermal coefficient of resistance. To do this, a carbon resistor of resistance R 1 is placed in series with an iron resistor of resistance R 2 . The proportions of iron and carbon are so chosen that R 1 + R 2 = 20.00 ? for all temperatures near 20° C. How large are R 1 and R 2 ? Given ? C = 0.5 × 10 3 K 1 and ? Fe = 5.0 × 10 3 K 1 . Resistors in Series and Parallel (Kirchhoff's Laws) Q 17. Find the current supplied by the battery in the circuit shown in figure. Q 18. Calculate battery current and equivalent resistance of the network shown in figure. Q 19. Compute total circuit resistance and battery current as shown in figure. Q 20. Compute the value of battery current i shown in figure. All resistances are in ohm. Q 21. Calculate the potentials of points A, B, C and D as shown in Fig. (a). What would be the new potential values if connections of 6 V battery are reversed as shown in Fig. (b)? All resistances are in ohm. Q 22. Give the magnitude and polarity of the following voltages in the circuit of figure : (i) V 1 (ii) V 2 (iii) V 3 (iv) V 32 (v) V 12 (vi) V 13 Q 23. The emf E and the internal resistance r of the battery shown in figure are 4.3 V and 1.0 ? respectively. The external resistance R is 50 ?. The resistances of the ammeter and voltmeter are 2.0 ? and 200 ?, respectively. (a) Find the readings of the two meters. (b) The switch is thrown to the other side. What will be the readings of the two meters now? Q 24. Find the current in each branch of the circuit shown in figure. Q 25. An electrical circuit is shown in figure. Calculate the potential difference across the resistor of 400 ?, as will be measured by the voltmeter V of resistance 400 ? either by applying Kirchhoff s rules or otherwise. Q 26. In the circuit shown in figure V 1 and V 2 are two voltmeters of resistances 3000 ? and 2000 ? respectively. In addition R 1 = 2000 ?, R 2 = 3000 ? and E = 200 V. (a) Find the reading of voltmeters V 1 and V 2 when (i) switch S is open (ii) switch S is closed (b) Current through S, when it is closed (Disregard the resistance of battery) Q 27. Find the net emf of the three batteries shown in figure. Q 28. In figure, E 1 = 12 V and E 2 = 8 V. Page 5 Exercises For JEE Main Subjective Questions Current Q 1. How many electrons per second pass through a section of wire carrying a current of 0.7 A? Q 2. A current of 3.6 A flows through an automobile headlight. How many coulombs of charge flow through the headlight in 3.0 h? Q 3. A current of 7.5 A is maintained in wire for 45 s. In this time (a) How much charge and (b) How many electrons flow through the wire? Q 4. In the Bohr model, the electron of a hydrogen atom moves in a circular orbit of radius 5.3 × 10 11 m with a speed of 2.2 × 10 6 m/s. Determine its frequency f and the current I in the orbit. Q 5. The current in a wire varies with time according to the relation I = 55A  (0.65 A/s 2 ) t 2 . (a) How many coulombs of charge pass a crosssection of the wire in the time interval between t = 0 and t = 8.0 s ? (b) What constant current would transport the same charge in the same time interval? Q 6. When a wire carries a current of 1.20 A, the drift velocity is 1.20 × 10 4 m/s. What is the drift velocity when the current is 6.00 A? Q 7. Find the velocity of charge leading to 1 A current which flows in a copper conductor of cross section 1 cm 2 and length 10 km. Free electron density of copper is 8.5 × 10 2 /m 3 . How long will it take the electric charge to travel from one end of the conductor to the other? Q 8. A typical copper wire have 2 × 10 21 free electrons in 1 cm of its length. Suppose that the drift speed of the electrons along the wire is 0.05 cm/s. How many electrons would pass through a given crosssection of the wire each second? How large a current would be flowing in the wire? Resistivity and Resistance Q 9. In household wiring, copper wire 2.05 mm in diameter is often used. Find the resistance of a 24.0 m length of this wire. Resistivity of copper is 0.017 ? ?m. Q 10. You need to produce a set of cylindrical copper wires 3.50 m long that will have a resistance of 0.125 ?, each. What will be the mass of each of these wires? Specific resistance of copper = 1.72 × 10 8 ?m, density of copper = 8.9 × 10 3 kg/m 3 . Q 11. Two coils connected in series have resistance of 600 ? and 300 ? at 20° C and temperature co efficient of 0.001 and 0.004(°C) 1 respectively. Find resistance of the combination at a temperature of 50° C. What is the effective temperature coefficient of combination? Q 12. An aluminium wire 7.5 m long is connected in parallel with a copper wire 6 m long. When a current of 5 A is passed through the combination, it is found that the current in the aluminium wire is 3 A. The diameter of the aluminium wire is 1 mm. Determine the diameter of the copper wire. Resistivity of copper is 0.017 ? ?m and that of the aluminium is 0.028 ? ?m. Q 13. The potential difference between two points in a wire 75.0 cm apart is 0.938 V, when the current density is 4.40 × 10 7 A/m 2 . What is (a) The magnitude of E in the wire? (b) the resistivity of the material of which the wire is made? Q 14. A rectangular block of metal of resistivity p has dimensions d × 2d × 3d. A potential difference V is applied between two opposite faces of the block. (a) To which two faces of the block should the potential difference V be applied to give the maximum current density? What is the maximum current density? (b) To which two faces of the block should the potential difference V be applied to give the maximum current? What is this maximum current? Q 15. An electrical conductor designed to carry large currents has a circular crosssection 2.50 mm in diameter and is 14.0 m long. The resistance between its ends is 0.104 ?. (a) What is the resistivity of the material? (b) If the electric field magnitude in the conductor is 1.28 V/m, what is the total current? (c) If the material has 8.5 × 10 28 free electrons per cubic metre, find the average drift speed under the conditions of part (b). Q 16. It is desired to make a 20.0 ? coil of wire which has a zero thermal coefficient of resistance. To do this, a carbon resistor of resistance R 1 is placed in series with an iron resistor of resistance R 2 . The proportions of iron and carbon are so chosen that R 1 + R 2 = 20.00 ? for all temperatures near 20° C. How large are R 1 and R 2 ? Given ? C = 0.5 × 10 3 K 1 and ? Fe = 5.0 × 10 3 K 1 . Resistors in Series and Parallel (Kirchhoff's Laws) Q 17. Find the current supplied by the battery in the circuit shown in figure. Q 18. Calculate battery current and equivalent resistance of the network shown in figure. Q 19. Compute total circuit resistance and battery current as shown in figure. Q 20. Compute the value of battery current i shown in figure. All resistances are in ohm. Q 21. Calculate the potentials of points A, B, C and D as shown in Fig. (a). What would be the new potential values if connections of 6 V battery are reversed as shown in Fig. (b)? All resistances are in ohm. Q 22. Give the magnitude and polarity of the following voltages in the circuit of figure : (i) V 1 (ii) V 2 (iii) V 3 (iv) V 32 (v) V 12 (vi) V 13 Q 23. The emf E and the internal resistance r of the battery shown in figure are 4.3 V and 1.0 ? respectively. The external resistance R is 50 ?. The resistances of the ammeter and voltmeter are 2.0 ? and 200 ?, respectively. (a) Find the readings of the two meters. (b) The switch is thrown to the other side. What will be the readings of the two meters now? Q 24. Find the current in each branch of the circuit shown in figure. Q 25. An electrical circuit is shown in figure. Calculate the potential difference across the resistor of 400 ?, as will be measured by the voltmeter V of resistance 400 ? either by applying Kirchhoff s rules or otherwise. Q 26. In the circuit shown in figure V 1 and V 2 are two voltmeters of resistances 3000 ? and 2000 ? respectively. In addition R 1 = 2000 ?, R 2 = 3000 ? and E = 200 V. (a) Find the reading of voltmeters V 1 and V 2 when (i) switch S is open (ii) switch S is closed (b) Current through S, when it is closed (Disregard the resistance of battery) Q 27. Find the net emf of the three batteries shown in figure. Q 28. In figure, E 1 = 12 V and E 2 = 8 V. (a) What is the direction of the current in the resistor? (b) Which battery is doing positive work? (c) Which point, A or B, is at the higher potential? Q 29. In figure, circuit section AB absorbs energy at the rate of 5.0 W when a current i = 1.0 A passes through it in the indicated direction. (a) What is the potential difference between points A and B ? (b) Emf device X does not have internal resistance. What is its emf? (c) What is its polarity (the orientation of its positive and negative terminals)? Q 30. In figure, if the potential at point P is 100 V, what is the potential at point Q ? Solutions Subjective Questions 1. q ne i tt ?? ? 19 it (0.7)(1) n e 1.6 10 ? ?? ? = 4.375 × 10 18 2. q = it = (3.6) (3 × 60 × 60) = 38880 C 3. (a) q = it = (7.5) (45) = 337.5 C (b) 19 q 337.5 n e 1.6 10 ? ?? ? = 2.1 × 10 21 4. 6 11 v 2.2 10 f 2 r (2 )(5.3 10 ) ? ? ?? ? ? ? = 6.6 × 10 16 HzRead More
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