Page 1 Exercises For JEE Main Q 31. An ideal voltmeter V is connected to a 2.0 ? resistor and a battery with emf 5.0 V and internal resistance 0.5 ? as shown in figure : (a) What is the current in the 2.0 ? resistor? (b) What is the terminal voltage of the battery? (c) What is the reading of the voltmeter? Q 32. The potential difference across the terminals of a battery is 8.4 V when there is a current of 1.50 A in the battery from the negative to the positive terminal. When the current is 3.50 A in the reverse direction, the potential difference becomes 9.4 V. (a) What is the internal resistance of the battery? (b) What is the emf of the battery? Q 33. A battery of emf 2.0 V and internal resistance 0.10 ? is being charged with a current of 5.0 A. Find the potential difference between the terminals of the battery? Q 34. Find the currents in different resistors shown in figure. Electrical Measuring Instruments Q 35. A resistance box, a battery and a galvanometer of resistance G ohm are connected in series. If the galvanometer is shunted by resistance of S ohm, find the change in resistance in the box required to maintain the current from the battery unchanged. Q 36. Determine the resistance r if an ammeter shows a current of I = 5 A and a voltmeter 100 V. The internal resistance of the voltmeter is R = 2,500 ?. Q 37. In the circuit, a voltmeter reads 30 V when it is connected across 400 ? resistance. Calculate what the same voltmeter will read when it is connected across the 300 ? resistance? Page 2 Exercises For JEE Main Q 31. An ideal voltmeter V is connected to a 2.0 ? resistor and a battery with emf 5.0 V and internal resistance 0.5 ? as shown in figure : (a) What is the current in the 2.0 ? resistor? (b) What is the terminal voltage of the battery? (c) What is the reading of the voltmeter? Q 32. The potential difference across the terminals of a battery is 8.4 V when there is a current of 1.50 A in the battery from the negative to the positive terminal. When the current is 3.50 A in the reverse direction, the potential difference becomes 9.4 V. (a) What is the internal resistance of the battery? (b) What is the emf of the battery? Q 33. A battery of emf 2.0 V and internal resistance 0.10 ? is being charged with a current of 5.0 A. Find the potential difference between the terminals of the battery? Q 34. Find the currents in different resistors shown in figure. Electrical Measuring Instruments Q 35. A resistance box, a battery and a galvanometer of resistance G ohm are connected in series. If the galvanometer is shunted by resistance of S ohm, find the change in resistance in the box required to maintain the current from the battery unchanged. Q 36. Determine the resistance r if an ammeter shows a current of I = 5 A and a voltmeter 100 V. The internal resistance of the voltmeter is R = 2,500 ?. Q 37. In the circuit, a voltmeter reads 30 V when it is connected across 400 ? resistance. Calculate what the same voltmeter will read when it is connected across the 300 ? resistance? Q 38. Resistances R 1 and R 2 , each 60 ?, are connected in series. The potential difference between points A and B is 120 V. Find the reading of voltmeter connected between points C and D if its resistance r = 120 ?. Q 39. A moving coil galvanometer of resistance 20 ? gives a full scale deflection when a current of 1 mA is passed through it. It is to be converted into an ammeter reading 20 A on full scale. But the shunt of 0.005 ? only is available. What resistance should be connected in series with the galvanometer coil? Q 40. In a potentiometer experiment it is found that no current passes through the galvanometer when the terminals of the cell are connected across 0.52 m of the potentiometer wire. If the cell is shunted by a resistance of 5 ? a balance is obtained when the cell is connected across 0.4 m of the wire. Find the internal resistance of the cell. Q 41. A cell of emf 3.4 V and internal resistance 3 ?, is connected to an ammeter having resistance 2 ? and to an external resistance of 100 ?. When a voltmeter is connected across the 100 ?. resistance the ammeter reading is 0.04 A. Find the voltage read by the voltmeter and its resistance. Had the voltmeter been an ideal one what would have been its reading? Q 42. The potentiometer wire AB shown in figure is 40 cm long. Where the free end of the galvanometer should be connected on AB so that the galvanometer may show zero deflection? Q 43. The resistance R G of the coil of a pivotedcoil galvanometer is 9.36 ? and a current of 0.0224 A causes it to deflect full scale. We want to convert this galvanometer to an ammeter reading 20.0 A Page 3 Exercises For JEE Main Q 31. An ideal voltmeter V is connected to a 2.0 ? resistor and a battery with emf 5.0 V and internal resistance 0.5 ? as shown in figure : (a) What is the current in the 2.0 ? resistor? (b) What is the terminal voltage of the battery? (c) What is the reading of the voltmeter? Q 32. The potential difference across the terminals of a battery is 8.4 V when there is a current of 1.50 A in the battery from the negative to the positive terminal. When the current is 3.50 A in the reverse direction, the potential difference becomes 9.4 V. (a) What is the internal resistance of the battery? (b) What is the emf of the battery? Q 33. A battery of emf 2.0 V and internal resistance 0.10 ? is being charged with a current of 5.0 A. Find the potential difference between the terminals of the battery? Q 34. Find the currents in different resistors shown in figure. Electrical Measuring Instruments Q 35. A resistance box, a battery and a galvanometer of resistance G ohm are connected in series. If the galvanometer is shunted by resistance of S ohm, find the change in resistance in the box required to maintain the current from the battery unchanged. Q 36. Determine the resistance r if an ammeter shows a current of I = 5 A and a voltmeter 100 V. The internal resistance of the voltmeter is R = 2,500 ?. Q 37. In the circuit, a voltmeter reads 30 V when it is connected across 400 ? resistance. Calculate what the same voltmeter will read when it is connected across the 300 ? resistance? Q 38. Resistances R 1 and R 2 , each 60 ?, are connected in series. The potential difference between points A and B is 120 V. Find the reading of voltmeter connected between points C and D if its resistance r = 120 ?. Q 39. A moving coil galvanometer of resistance 20 ? gives a full scale deflection when a current of 1 mA is passed through it. It is to be converted into an ammeter reading 20 A on full scale. But the shunt of 0.005 ? only is available. What resistance should be connected in series with the galvanometer coil? Q 40. In a potentiometer experiment it is found that no current passes through the galvanometer when the terminals of the cell are connected across 0.52 m of the potentiometer wire. If the cell is shunted by a resistance of 5 ? a balance is obtained when the cell is connected across 0.4 m of the wire. Find the internal resistance of the cell. Q 41. A cell of emf 3.4 V and internal resistance 3 ?, is connected to an ammeter having resistance 2 ? and to an external resistance of 100 ?. When a voltmeter is connected across the 100 ?. resistance the ammeter reading is 0.04 A. Find the voltage read by the voltmeter and its resistance. Had the voltmeter been an ideal one what would have been its reading? Q 42. The potentiometer wire AB shown in figure is 40 cm long. Where the free end of the galvanometer should be connected on AB so that the galvanometer may show zero deflection? Q 43. The resistance R G of the coil of a pivotedcoil galvanometer is 9.36 ? and a current of 0.0224 A causes it to deflect full scale. We want to convert this galvanometer to an ammeter reading 20.0 A full scale. The only shunt available has a resistance of 0.0250 ?. What resistance R must be connected in series with the coil of galvanometer? Q 44. (a) A voltmeter with resistance R V is connected across the terminals of a battery of emf E and internal resistance r. Find the potential difference measured by the voltmeter. (b) If E = 7.50 V and r = 0.45 ?, find the minimum value of the voltmeter resistance R V so that the voltmeter reading is within 1.0% of the emf of the battery. (c) Explain why your answer in part (b) represents a minimum value. Q 45. (a) An ammeter with resistance R A is connected in series with a resistor R and a battery of emf e and internal resistance r. The current measured by the ammeter is I A . Find the current through the circuit if the ammeter is removed so that the battery and the resistor form a complete circuit. Express your answer in terms of I A , r, R A and R. The more "ideal" the ammeter, the smaller the difference between this current and the current I A . (b) If R = 3.80 ?, ? = 7.50 V and r = 0.45 ?, find the maximum value of the ammeter resistance R A so that I A is within 99% of the current in the circuit when the ammeter is absent. (c) Explain why your answer in part (b) represents a maximum value. Heating Effects of Current Q 46. Each of three resistors in figure has a resistance of 2.4 ? and can dissipate a maximum of 36 W without becoming excessively heated. What is the maximum power the circuit can dissipate? Q 47. A 120 V house circuit has the following light bulbs switched on : 40 W, 60 W and 75 W. Find the equivalent resistance of these bulbs. Q 48. A storage battery with emf 2.6 V loaded with external resistance produces a current 1 A. In this case, the potential difference between the terminals of the storage battery equals 2 V. Find the thermal power generated in the battery and the net power supplied by the battery for external circuit.. Q 49. In the circuit shown in figure E 1 = 7 V, E 2 = 1V, R 1 = 2 ?, R 2 = 2 ? and R 3 = 3 ? respectively. Find the power supplied by the two batteries. Q 50. Assume that the batteries in figure have negligible internal resistance. Find : Page 4 Exercises For JEE Main Q 31. An ideal voltmeter V is connected to a 2.0 ? resistor and a battery with emf 5.0 V and internal resistance 0.5 ? as shown in figure : (a) What is the current in the 2.0 ? resistor? (b) What is the terminal voltage of the battery? (c) What is the reading of the voltmeter? Q 32. The potential difference across the terminals of a battery is 8.4 V when there is a current of 1.50 A in the battery from the negative to the positive terminal. When the current is 3.50 A in the reverse direction, the potential difference becomes 9.4 V. (a) What is the internal resistance of the battery? (b) What is the emf of the battery? Q 33. A battery of emf 2.0 V and internal resistance 0.10 ? is being charged with a current of 5.0 A. Find the potential difference between the terminals of the battery? Q 34. Find the currents in different resistors shown in figure. Electrical Measuring Instruments Q 35. A resistance box, a battery and a galvanometer of resistance G ohm are connected in series. If the galvanometer is shunted by resistance of S ohm, find the change in resistance in the box required to maintain the current from the battery unchanged. Q 36. Determine the resistance r if an ammeter shows a current of I = 5 A and a voltmeter 100 V. The internal resistance of the voltmeter is R = 2,500 ?. Q 37. In the circuit, a voltmeter reads 30 V when it is connected across 400 ? resistance. Calculate what the same voltmeter will read when it is connected across the 300 ? resistance? Q 38. Resistances R 1 and R 2 , each 60 ?, are connected in series. The potential difference between points A and B is 120 V. Find the reading of voltmeter connected between points C and D if its resistance r = 120 ?. Q 39. A moving coil galvanometer of resistance 20 ? gives a full scale deflection when a current of 1 mA is passed through it. It is to be converted into an ammeter reading 20 A on full scale. But the shunt of 0.005 ? only is available. What resistance should be connected in series with the galvanometer coil? Q 40. In a potentiometer experiment it is found that no current passes through the galvanometer when the terminals of the cell are connected across 0.52 m of the potentiometer wire. If the cell is shunted by a resistance of 5 ? a balance is obtained when the cell is connected across 0.4 m of the wire. Find the internal resistance of the cell. Q 41. A cell of emf 3.4 V and internal resistance 3 ?, is connected to an ammeter having resistance 2 ? and to an external resistance of 100 ?. When a voltmeter is connected across the 100 ?. resistance the ammeter reading is 0.04 A. Find the voltage read by the voltmeter and its resistance. Had the voltmeter been an ideal one what would have been its reading? Q 42. The potentiometer wire AB shown in figure is 40 cm long. Where the free end of the galvanometer should be connected on AB so that the galvanometer may show zero deflection? Q 43. The resistance R G of the coil of a pivotedcoil galvanometer is 9.36 ? and a current of 0.0224 A causes it to deflect full scale. We want to convert this galvanometer to an ammeter reading 20.0 A full scale. The only shunt available has a resistance of 0.0250 ?. What resistance R must be connected in series with the coil of galvanometer? Q 44. (a) A voltmeter with resistance R V is connected across the terminals of a battery of emf E and internal resistance r. Find the potential difference measured by the voltmeter. (b) If E = 7.50 V and r = 0.45 ?, find the minimum value of the voltmeter resistance R V so that the voltmeter reading is within 1.0% of the emf of the battery. (c) Explain why your answer in part (b) represents a minimum value. Q 45. (a) An ammeter with resistance R A is connected in series with a resistor R and a battery of emf e and internal resistance r. The current measured by the ammeter is I A . Find the current through the circuit if the ammeter is removed so that the battery and the resistor form a complete circuit. Express your answer in terms of I A , r, R A and R. The more "ideal" the ammeter, the smaller the difference between this current and the current I A . (b) If R = 3.80 ?, ? = 7.50 V and r = 0.45 ?, find the maximum value of the ammeter resistance R A so that I A is within 99% of the current in the circuit when the ammeter is absent. (c) Explain why your answer in part (b) represents a maximum value. Heating Effects of Current Q 46. Each of three resistors in figure has a resistance of 2.4 ? and can dissipate a maximum of 36 W without becoming excessively heated. What is the maximum power the circuit can dissipate? Q 47. A 120 V house circuit has the following light bulbs switched on : 40 W, 60 W and 75 W. Find the equivalent resistance of these bulbs. Q 48. A storage battery with emf 2.6 V loaded with external resistance produces a current 1 A. In this case, the potential difference between the terminals of the storage battery equals 2 V. Find the thermal power generated in the battery and the net power supplied by the battery for external circuit.. Q 49. In the circuit shown in figure E 1 = 7 V, E 2 = 1V, R 1 = 2 ?, R 2 = 2 ? and R 3 = 3 ? respectively. Find the power supplied by the two batteries. Q 50. Assume that the batteries in figure have negligible internal resistance. Find : (a) the current in the circuit, (b) the power dissipated in each resistor and (c) the power of each battery, stating whether energy is supplied by or absorbed by it. Q 51. In the circuit shown in figure, find : (a) the rate of conversion of internal (chemical) energy to electrical energy within the battery (b) the rate of dissipation of electrical energy in the battery (c) the rate of dissipation of electrical energy in the external resistor. Q 52. Three resistors having resistances of 1.60 ?, 2.40 ? and 4.80 ? are connected in parallel to a 28.0 V battery that has negligible internal resistance. Find : (a) the equivalent resistance of the combination. (b) the current in each resistor. (c) the total current through the battery. (d) the voltage across each resistor. (e) the power dissipated in each resistor. (f) which resistor dissipates the maximum power the one with the greatest resistance or the least resistance? Explain why this should be. Q 53. (a) The power of resistor is the maximum power the resistor can safely dissipate without too rise in temperature. The power rating of a 15 k ? resistor is 5.0 W. What is the maximum allowable potential difference across the terminals of the resistor? (b) A 9.0 k ? resistor is to be connected across a 120 V potential difference. What power rating is required? Equivalent Resistance Note Attempt this after reading article 22.9. Q 54. Find the equivalent resistance between points A and B in the following circuits : Page 5 Exercises For JEE Main Q 31. An ideal voltmeter V is connected to a 2.0 ? resistor and a battery with emf 5.0 V and internal resistance 0.5 ? as shown in figure : (a) What is the current in the 2.0 ? resistor? (b) What is the terminal voltage of the battery? (c) What is the reading of the voltmeter? Q 32. The potential difference across the terminals of a battery is 8.4 V when there is a current of 1.50 A in the battery from the negative to the positive terminal. When the current is 3.50 A in the reverse direction, the potential difference becomes 9.4 V. (a) What is the internal resistance of the battery? (b) What is the emf of the battery? Q 33. A battery of emf 2.0 V and internal resistance 0.10 ? is being charged with a current of 5.0 A. Find the potential difference between the terminals of the battery? Q 34. Find the currents in different resistors shown in figure. Electrical Measuring Instruments Q 35. A resistance box, a battery and a galvanometer of resistance G ohm are connected in series. If the galvanometer is shunted by resistance of S ohm, find the change in resistance in the box required to maintain the current from the battery unchanged. Q 36. Determine the resistance r if an ammeter shows a current of I = 5 A and a voltmeter 100 V. The internal resistance of the voltmeter is R = 2,500 ?. Q 37. In the circuit, a voltmeter reads 30 V when it is connected across 400 ? resistance. Calculate what the same voltmeter will read when it is connected across the 300 ? resistance? Q 38. Resistances R 1 and R 2 , each 60 ?, are connected in series. The potential difference between points A and B is 120 V. Find the reading of voltmeter connected between points C and D if its resistance r = 120 ?. Q 39. A moving coil galvanometer of resistance 20 ? gives a full scale deflection when a current of 1 mA is passed through it. It is to be converted into an ammeter reading 20 A on full scale. But the shunt of 0.005 ? only is available. What resistance should be connected in series with the galvanometer coil? Q 40. In a potentiometer experiment it is found that no current passes through the galvanometer when the terminals of the cell are connected across 0.52 m of the potentiometer wire. If the cell is shunted by a resistance of 5 ? a balance is obtained when the cell is connected across 0.4 m of the wire. Find the internal resistance of the cell. Q 41. A cell of emf 3.4 V and internal resistance 3 ?, is connected to an ammeter having resistance 2 ? and to an external resistance of 100 ?. When a voltmeter is connected across the 100 ?. resistance the ammeter reading is 0.04 A. Find the voltage read by the voltmeter and its resistance. Had the voltmeter been an ideal one what would have been its reading? Q 42. The potentiometer wire AB shown in figure is 40 cm long. Where the free end of the galvanometer should be connected on AB so that the galvanometer may show zero deflection? Q 43. The resistance R G of the coil of a pivotedcoil galvanometer is 9.36 ? and a current of 0.0224 A causes it to deflect full scale. We want to convert this galvanometer to an ammeter reading 20.0 A full scale. The only shunt available has a resistance of 0.0250 ?. What resistance R must be connected in series with the coil of galvanometer? Q 44. (a) A voltmeter with resistance R V is connected across the terminals of a battery of emf E and internal resistance r. Find the potential difference measured by the voltmeter. (b) If E = 7.50 V and r = 0.45 ?, find the minimum value of the voltmeter resistance R V so that the voltmeter reading is within 1.0% of the emf of the battery. (c) Explain why your answer in part (b) represents a minimum value. Q 45. (a) An ammeter with resistance R A is connected in series with a resistor R and a battery of emf e and internal resistance r. The current measured by the ammeter is I A . Find the current through the circuit if the ammeter is removed so that the battery and the resistor form a complete circuit. Express your answer in terms of I A , r, R A and R. The more "ideal" the ammeter, the smaller the difference between this current and the current I A . (b) If R = 3.80 ?, ? = 7.50 V and r = 0.45 ?, find the maximum value of the ammeter resistance R A so that I A is within 99% of the current in the circuit when the ammeter is absent. (c) Explain why your answer in part (b) represents a maximum value. Heating Effects of Current Q 46. Each of three resistors in figure has a resistance of 2.4 ? and can dissipate a maximum of 36 W without becoming excessively heated. What is the maximum power the circuit can dissipate? Q 47. A 120 V house circuit has the following light bulbs switched on : 40 W, 60 W and 75 W. Find the equivalent resistance of these bulbs. Q 48. A storage battery with emf 2.6 V loaded with external resistance produces a current 1 A. In this case, the potential difference between the terminals of the storage battery equals 2 V. Find the thermal power generated in the battery and the net power supplied by the battery for external circuit.. Q 49. In the circuit shown in figure E 1 = 7 V, E 2 = 1V, R 1 = 2 ?, R 2 = 2 ? and R 3 = 3 ? respectively. Find the power supplied by the two batteries. Q 50. Assume that the batteries in figure have negligible internal resistance. Find : (a) the current in the circuit, (b) the power dissipated in each resistor and (c) the power of each battery, stating whether energy is supplied by or absorbed by it. Q 51. In the circuit shown in figure, find : (a) the rate of conversion of internal (chemical) energy to electrical energy within the battery (b) the rate of dissipation of electrical energy in the battery (c) the rate of dissipation of electrical energy in the external resistor. Q 52. Three resistors having resistances of 1.60 ?, 2.40 ? and 4.80 ? are connected in parallel to a 28.0 V battery that has negligible internal resistance. Find : (a) the equivalent resistance of the combination. (b) the current in each resistor. (c) the total current through the battery. (d) the voltage across each resistor. (e) the power dissipated in each resistor. (f) which resistor dissipates the maximum power the one with the greatest resistance or the least resistance? Explain why this should be. Q 53. (a) The power of resistor is the maximum power the resistor can safely dissipate without too rise in temperature. The power rating of a 15 k ? resistor is 5.0 W. What is the maximum allowable potential difference across the terminals of the resistor? (b) A 9.0 k ? resistor is to be connected across a 120 V potential difference. What power rating is required? Equivalent Resistance Note Attempt this after reading article 22.9. Q 54. Find the equivalent resistance between points A and B in the following circuits : (a) (b) (c) (d) (e) (f) (g) Q 55. What will be the change in the resistance of a circuit between A and F consisting of five identical conductors, if two similar conductors are added as shown by the dashed line in figure? Q 56. Find R AB in the circuit, shown in figure.Read More
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