Title 18. Current Electricity Hard.pdf ✅

1. A conducting wire of cross-sectional area 1 cm2 has 3  1023m–3 charge carriers. If wire carries a current of 24 mA, the drift speed of the carrier is (a) 5  10–6m/s (b) 5  10–3m/s (c) 0.5 m/s (d) 5  10–2m/s 2. A rod of certain metal is 1 m long and 0.6 cm in diameter. It’s resistance is 3  10–3. A disc of the same metal is 1 mm thick and 2 cm in diameter, what is the resistance between it’s circular faces. (a) 1.35  10–6 (b) 2.7  10–7 (c) 4.05  10–6 (d) 8.1  10–6 3. An aluminium rod of length 3.14 m is of square cross-section 3.14  3.14 mm2 . What should be the radius of 1 m long another rod of same material to have equal resistance (a) 2 mm (b) 4 mm (c) 1 mm (d) 6 mm 4. If a copper wire is stretched to make it 0.1% longer, the percentage increase in resistance will be (a) 0.2 (b) 2 (c) 1 (d) 0.1 5. The temperature co-efficient of resistance of a wire is 0.00125/ 0C. At 300 K. It’s resistance is 1. The resistance of the wire will be 2 at (a) 1154 K (b) 1127 K (c) 600 K (d) 1400 K 6. Equal potentials are applied on an iron and copper wire of same length. In order to have same current flow in the wire, the ratio         copper iron r r of their radii must be [Given that specific resistance of iron = 1.0  10–7m and that of copper = 1.7  10–8m] (a) About 1.2 (b) About 2.4 (c) About 3.6 (d) About 4.8 7. Masses of three wires are in the ratio 1 : 3 : 5 and their lengths are in the ratio 5 : 3 : 1. The ratio of their electrical resistance is (a)1 : 3 : 5 (b) 5 : 3 : 1 (c) 1 : 15 : 125 (d) 125 : 15 : 1 8. Following figure shows cross-sections through three long conductors of the same length and material, with square cross- section of edge lengths as shown. Conductor B will fit snugly within conductor A, and conductor C will fit snugly within conductor B. Relationship between their end to end resistance is (a) RA = RB = RC (b) RA>RB>RC (c) RA(a) r 4 5 (b) r 5 6 (c) r 6 7 (d) r 7 8 17. In the given figure, equivalent resistance between A and B will be (a)  3 14 (b)  14 3 (c)  14 9 (d)  9 14 18. In the combination of resistances shown in the figure the potential difference between B and D is zero, when unknown resistance (x) is (a) 4  (b) 2  (c) 3  (d) The emf of the cell is require 19. A current of 2 A flows in a system of conductors as shown. The potential difference (VA – VB) will be (a) + 2V (b) + 1V (c) – 1 V (d) – 2 V 20. Three resistances each of 4  are connected in the form of an equilateral triangle. The effective resistance between two corners is (a) 8  (b) 12  (c)  8 3 (d)  3 8 21. In the adjoining circuit, the battery E1 has as emf of 12 volt and zero internal resistance, while the battery E has an emf of 2 volt. If the galvanometer reads zero, then the value of resistance Xohm is (a) 10 (b) 100 (c) 500 (d) 200 22. In the circuit shown here E1 = E2 = E3 = 2V and R1 = R2 = 4 . The current flowing between point A and B through battery E2 is (a) Zero (b) 2 A from A to B (c) 2 A from B to A (d) None of these 23. The magnitude and direction of the current in the circuit shown will be (a) A 3 7 from a to b through e (b) A 3 7 from b and a through e (c) 1.0 A from b to a through e (d) 1.0 A from a to b through e 24. Figure represents a part of the closed circuit. The potential difference between points A and B (VA – VB) is (a) + 9 V (b) – 9 V (c) + 3 V (d) + 6 V 25. With a certain cell the balance point is obtained at 0.60 m from one end of the potentiometer. With another cell whose emf differs from that of the first by 0.1 V, the balance point is obtained at 0.55 m. Then, the two emf’s are (a) 1.2 V, 1.1 V (b) 1.2 V, 1.3 V (c) – 1.1 V, – 1.0 V (d) None of the above 26. In the following circuit E1 = 4V, R1 = 2 E2 = 6V, R2 = 2 and R3 = 4. The current i1 is (a) 1.6 A (b) 1.8 A (c) 2.25 A (d) 1 A 27. Determine the current in the following circuit (a) 1 A (b) 2.5 A (c) 0.4 A (d) 3 A 28. In the circuit shown in figure, find the current through the branch BD 10 V 2 5 V 3 E1 R1 R2 R3 E2 i2 i1 3 V 2 1 2 A A B 10 V a d c 2 3 1 4 V e b R1 R2 A B E1 E2 E3 500 A B D C E1 X E O P G 2 3 3 2 A D C B 2A B 12  4  1  1  C D A 1  3  x 3 4 6 8 A B 7
(a) 5 A (b) 0 A (c) 3 A (d) 4 A 29. The figure shows a network of currents. The magnitude of current is shown here. The current i will be (a) 3 A (b) 13 A (c) 23 A (d) – 3 A 30. Consider the circuit shown in the figure. The current i3 is equal to (a) 5 amp (b) 3 amp (c) – 3 amp (d) – 5/6 amp 31. In the following circuit diagram fig. the lengths of the wires AB and BC are same but the radius of AB is three times that of BC. The ratio of potential gradients at AB and BC will be (a) 1 : 9 (b) 9 : 1 (c) 3 : 1 (d) 1 : 3 32. In the following circuit the potential difference between P and Q is (a) 15 V (b) 10 V (c) 5 V (d) 2.5 V 33. In the following figure ammeter and voltmeter reads 2 amp and 120 volt respectively. Resistance of voltmeter is (a) 100  (b) 200  (c) 300  (d) 400  34. In the circuit shown in figure, the voltmeter reading would be (a) Zero (b) 0.5 volt (c) 1 volt (d) 2 volt 35. Voltmeters V1 and V2 are connected in series across a d.c. line. V1reads 80 V and has a per volt resistance of 200 , V2 has a total resistance of 32 k. The line voltage is (a) 120 V (b) 160 V (c) 220 V (d) 240 V 36. The resistance of 1 A ammeter is 0.018 . To convert it into 10 A ammeter, the shunt resistance required will be (a) 0.18  (b) 0.0018  (c) 0.002  (d) 0.12  37. In meter bridge the balancing length from left and when standard resistance of 1  is in right gas is found to be 20 cm. The value of unknown resistance is (a) 0.25  (b) 0.4  (c) 0.5  (d) 4  38. A galvanometer having a resistance of 8  is shunted by a wire of resistance 2 . If the total current is 1 amp, the part of it passing through the shunt will be (a) 0.25 amp (b) 0.8 amp (c) 0.2 amp (d) 0.5 amp 39. The resistivity of a potentiometer wire is 40  10–8m and its area of cross section is 8  10–6m2 . If 0.2 amp. Current is flowing through the wire, the potential gradient will be (a) 10–2 volt/m (b) 10–1 volt/m (c) 3.2  10–2 volt/m (d) 1 volt/m 40. A deniel cell is balanced on 125 cm length of a potentiometer wire. When the cell is short circuited with a 2  resistance the balancing length obtained is 100 cm. Internal resistance of the cell will be (a) 1.5  (b) 0.5  (c) 1.25  (d) 4/5  41. A potentiometer wire of length 10 m and a resistance 30  is connected in series with a battery of emf 2.5 V and internal resistance 5  and an external resistance R. If the fall of potential along the potentiometer wire is 50 V/mm, the value of R is (in ) (a) 115 (b) 80 (c) 50 (d) 100 42. A 2 volt battery, a 15  resistor and a potentiometer of 100 cm length, all are connected in series. If the resistance of potentiometer wire is 5 , then the potential gradient of the potentiometer wire is (a) 0.005 V/cm (b) 0.05 V/cm (c) 0.02 V/cm (d) 0.2 V/cm 43. In an experiment to measure the internal resistance of a cell by potentiometer, it is found that the balance point is at a length of 2 m when the cell is shunted by a 5  resistance; and is at a length of 3 m when the cell is shunted by a 10  resistance. The internal resistance of the cell is, then (a) 1.5  (b) 10  (c) 15  (d) 1  2  + 3V – A V 1  A V X 75  Y 5 R 2A P Q 15V E1 E2 C A B + – 12 V 54 i3 28 6 V 8 V 15 A 3 A 5 A i A 6 C 15 V 3 B D 30 V 3
44. A resistance of 4  and a wire of length 5 metres and resistance 5  are joined in series and connected to a cell of emf 10 V and internal resistance 1 . A parallel combination of two identical cells is balanced across 300 cm of the wire. The emf E of each cell is (a) 1.5 V (b) 3.0 V (c) 0.67 V (d) 1.33 V 45. A potentiometer has uniform potential gradient across it. Two cells connected in series (i) to support each other and (ii) to oppose each other are balanced over 6 m and 2 m respectively on the potentiometer wire. The emf’s of the cells are in the ratio of (a) 1 : 2 (b) 1 : 1 (c) 3 : 1 (d) 2 : 1 46. In the following circuit the potential difference between the points B and C is balanced against 40 cm length of potentiometer wire. In order to balance the potential difference between the points C and D, where should jockey be pressed (a) 32 cm (b) 16 cm (c) 8 cm (d) 4 cm 47. When a galvanometer is shunted with a 4 resistance, the deflection is reduced to one-fifth. If the galvanometer is further shunted with a 2 wire. the further reduction (find the ratio of decrease in current to the previous current) in the deflection will be (the main current remains the same) (a) (8/13) of the deflection when shunted with 4  only (b) (5/13) of the deflection when shunted with 4  only (c) (3/4) of the deflection when shunted with 4  only (d) (3/13) of the deflection when shunted with 4  only 48. Three batteries of emf 1V and internal resistance 1  each are connected as shown. Effective emf of combination between the points PQ is – 1  P 1  1  1 V 1 V 1 V Q R (a) Zero (b) 1V (c) 2V (d) 3 2 V 49. In the circuit shown, each resistance is 2. The potential V1 as indicated in the circuit, is equal to – 12V 5V V1 (a) 11 V (b) – 11V (c) 9 V (d) – 9 V 50. Two resistances, a 60 ohm and an unknown one are connected to a power source in a series arrangement. This way the power of the unknown resistance is 60 watt. What is the least voltage of the power source? (a) 60 Volt (b) 120 Volt (c) 140 Volt (d) 180 Volt 51. If all meters are ideal and reading of voltmeter 3 is 6V. Power supplied by voltage source is - A V A A 1 5 2 20 4 V 30 10 3 Voltge source (a) 10 Watt (b) 38 Watt (c) 20 Watt (d) 30 Watt 52. Eight resistances each of resistance 5 are connected in the circuit as shown in figure. The equivalent resistance between A and B is – A B (a)  3 8 (b)  3 16 (c)  7 15 (d)  2 19 53. In the circuit shown in figure. (a), R3 is a variable resistance. As the value R3 is changed, current I though the cell varies as shown. Obviously, the variation is asymptotic, i.e. I → 6A as R3→ . Resistances R1 and R2 are, respectively – R2 R3 I I R1 R2 36V Figure (A)  → R3 ()    → R3 ()  () Figure (B) (a) 4 , 2  (b) 2 , 4  (c) 2 , 2  (d) 1 , 4  X G + – Y + – Rh D K B A 6V 10  10  40 cm r = 1 F C 4  E G 5m 4 E 10 V, 1 5 3m