Current and Resistance


 Dorcas Sparks
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1 PHYS102 Previous Exam Problems CHAPTER 26 Current and Resistance Charge, current, and current density Ohm s law Resistance Power Resistance & temperature 1. A current of A is passed through a lamp (light bulb) for 2.00 minutes using a 6.00V power supply. How much energy is dissipated by this lamp during the 2.00 minutes? (Ans: 216 J) 2. Two wires (figure 1) are made of the same material. If the current density through segment S 1 is J 1 = 6400 A/m 2 and the current density through segment S 2 is J 2 = 1239 A/m 2, what is the diameter D 2 of segment S 2? (Ans 5.0 cm) 3. Wires A and B are made from the same material. Wire A has twice the diameter and half the length of wire B. If the resistance of wire A is 20 Ω, what is the resistance of wire B? (Ans: 160 Ω) 4. A 10V battery is applied across a 15W device. How much charge goes through the device in 4.0 hours? (Ans: C) 5. A 40W and a 60W light bulbs are designed for use with the same voltage. What is the ratio of the resistance of the 60W bulb to the resistance of the 40W bulb? (Ans: 0.67) 6. A 100W bulb is designed to operate with a 120V line voltage. If the line voltage decreases, and the bulb consumes only 90 W, find the final voltage in the line. Assume that the resistance is constant. (Ans: 114 V) 7. A heater of unknown resistance is plugged into a 120V line. The charge passing through it in one hour is 4800 C. What is the resistance of the heater? (Ans: 90 Ω) 8. In a simple circuit, a voltage of 5 V is applied across a 10 Ω resistance. How much energy is dissipated in the resistor in 2 minutes? (Ans: 300 J) 9. What diameter must a copper wire have if its resistance is to be the same as that of an equal length of an aluminum wire with a 3.26mm diameter? [resistivity of aluminum = Ω.m, resistivity of copper = Ω.m] (Ans: 2.6 mm) 10. The resistivity of a nichrome wire is Ω.m. Calculate the length of wire needed for a 1200 W electric heater that is connected across a 120V potential difference. [The wire s radius is 0.40 mm] (Ans: 6.0 m) 11. A heating coil is immersed in a 0.2kg of cold water. The coil is connected to a 12V supply and a current of 5 A flows for 140 seconds. Calculate the temperature increase of the water. [specific heat of water is 4200 J/(kg.K)] (Ans: 10 K) Dr. M. F. AlKuhaili PHYS 102 Chapter 26 Page 1
2 12. A 20% increase in the resistance of a copper wire was noticed when its temperature was raised above room temperature. Find the final temperature of the wire if the temperature coefficient of resistivity for copper is /K. [assume that the room temperature = 290 K] (Ans: 340 K) 13. A potential difference of 9.0 V is applied across the length of a cylindrical conductor with radius 2.0 mm. Calculate the magnitude of the current density if the conductor has a resistance of 90 Ω. (Ans: A/m 2 ) 14. A current of 5.0 A exists in a 10Ω resistor for 5.0 min. How many electrons pass through any cross section of the resistor in this time? (Ans: ) 15. An electric device, which heats water by immersing a resistance wire in the water, generates 153 J of heat per second when an electric potential difference of 12 V is applied across its ends. What is the resistance of the heater wire? (Ans: 0.94 Ω) 16. In one hour, how many electrons pass between the terminals of a 12V car battery when a 96W headlight is used? (Ans: ) 17. A resistance operated at 110 V has a power output of 100 W. What is the percentage increase of the power if the voltage increases to 121 V. (Assume that the resistance stays constant) (Ans: 21% ) 18. A cylindrical wire of radius R = 2.0 mm has a uniform current density J = A/m 2. What is the current through the portion of the wire between radial distances R/3 and R/2? (see figure 3) (Ans: 0.35 A) 19. At 40 o C, the resistance of a gold wire is 80 Ω. What is the resistance of the same wire at 60 o C? [α gold = / o C] (Ans: 85 Ω) 20. At what temperature would the resistance of a conductor be double its resistance at 30 o C? [The temperature coefficient of resistivity of the conductor is K 1 ] (Ans: 80 o C) 21. A solid piece made of copper has the shape and dimensions shown in figure 4. Determine the resistance for the current that flows through the solid in the zdirection. [resistivity of copper = Ω.m] (Ans: Ω) 22. A 1200W heater is used to heat 2.0 kg of water from 30 o C to 80 o C. What is the minimum time in which this can be done? [specific heat of water = kj/(kg.k)] (Ans: 348 s) 23. A cylindrical copper conductor is 10 cm long and has a resistivity of ρ = Ω.m. If a potential difference of 100 V is applied across the conductor, what is the magnitude of the resulting current density in the conductor? (Ans: A/m 2 ) 24. A conducting wire has a length of 3.0 m and a resistance of 0.35 Ω. When a potential difference is applied to the ends of the wire, a current of 1.8 A is produced in it. What is the magnitude of the electric field inside the wire? (Ans: 0.21 V/m) 25. An electric current of 0.35 A passes through a cylindrical copper wire with a cross sectional area of m 2. What is the magnitude of the electric filed inside the wire? [Resistivity of copper = Ω.m]. (Ans: V/m) 26. Electric charges flow through a wire shaped as shown in figure 5. The crosssectional areas of the two sections are A 1 = 4 mm 2 and A 2 = 1 mm 2, respectively. What is the drift speed of the electrons in the narrow section of the wire if their speed is 0.08 m/s in the wider region? (Ans: 0.32 m/s) Dr. M. F. AlKuhaili PHYS 102 Chapter 26 Page 2
3 27. Figure 6 represents a section of a circular conductor of nonuniform diameter carrying a current of 10.0 A. The cross sectional area A 1 has a radius of cm. If the crosssectional area A 2 has a radius twice of that of crosssectional area A 1, what is the current density at A 2? (Ans: 4.97 A/cm 2 ) 28. What would be the uniform crosssectional area of a wire made out of 1.50 g of a metal having a resistance of Ω, and all of the metal was used to make the wire? [Take the density of the metal to be 8.92 g/cm 3 and resistivity Ω.m]. (Ans: m 2 ) 29. A light bulb is rated at 0.40 A and 3.0 V. At 20 o C, the bulb filament has a resistance of 2.0 Ω. If the filament is made of tungsten, whose temperature coefficient of resistivity is /K, what is the temperature of the filament when bulb is on? (Ans: 631 o C) 30. The resistivity of silver is Ω.m, and that of aluminum is Ω.m. Two wires, one made of silver and the other made of aluminum, have the same dimensions and are connected to the same battery. What is the ratio of the current passing in the silver wire to that passing in the aluminum wire? (Ans: 1.9) 31. A wire having a resistance of 3 Ω is stretched so that its length becomes three times its original length. Its volume remains unchanged. What is the resistance of the stretched wire? (Ans: 27 Ω) 32. At T = 20 o C, the length of a wire is 10 m, and its cross sectional area is 0.50 mm 2. A potential difference of 1.0 V is maintained across the ends of the wire. The resistance of the wire changes by 0.30 Ω for a temperature change of 50 o C. What is the temperature coefficient of resistivity of the wire? [At T = 20 o C, the resistivity is Ω.m] (Ans: o C 1 ) 33. A resistance thermometer made from platinum has a resistance of 50.0 Ω at 20 C. When immersed in a vessel containing melting indium, its resistance increases to 76.8 Ω. Find the melting point of indium. [For platinum, α = (C ) 1 )] (Ans: 157 o C) 34. A certain resistor dissipates W when connected to a 3.00 V potential difference. When connected to a 1.00V potential difference, how much will this resistor dissipate? (Ans: W) 35. A copper wire is to be designed to carry a current of 3 A with a power loss of W/m. What is the required radius of the wire? [resistivity of copper is Ω.m] (Ans: 0.49 cm) 36. Figure 8 shows a current entering a solid conducting cone made of a metal with faces having diameters mm and mm. If the magnitude of current density at the mm diameter face is A/m 2, find the magnitude of current density at the mm diameter face. (Ans: 1260 A/m 2 ) 37. A wire consists of two segments made of copper and iron, as shown in figure 9. A current of 10 A is sent through the wire. Find ratio of electric field in the iron segment to electric field in the copper segment E iron/e copper. [ρ iron= Ω.m and ρ copper= Ω.m] (Ans: 2.5) 38. A conducting wire is used as a heating element using a constant potential difference of 110 V. From the moment the heater is first turned on to the moment the wire reaches its maximum temperature, the current in the wire drops by 20% from its initial value. What is the temperature change in the wire assuming that the length and the cross sectional area of the wire remain constant during heating? [The temperature coefficient of resistivity for the wire is α = / C] (Ans: 625 C o ) 39. A light bulb dissipates 100 W of electric power when connected to a 120V potential difference. By what percentage does the bulb power output increases when the potential difference increases to 140V? [Assume that bulb resistance does not change] (Ans: 36%) Dr. M. F. AlKuhaili PHYS 102 Chapter 26 Page 3
4 40. A 5.00mV voltage is applied to a copper rod, initially at 20.0 o C, resulting in a current I o. When the rod is heated to a temperature T x, the current is reduced to I o/3. If the temperature coefficient of resistivity of copper is α = K 1, what is the temperature (T x) of the rod? Assume that the dimensions of the rod do not change. (Ans: 508 C) 41. A copper (Cu) rod and an aluminum (Al) rod of the same length and different cross sectional areas are connected in series as shown in figure 10. The resistivities and cross sectional areas are: ρ Cu = Ω.m, ρ Al = Ω.m, A Al = cm 2, A Cu =0.200 cm 2. What is the ratio of the magnitude of the electric field along the aluminum rod to that along the copper rod (E Al / E Cu)? (Ans: 0.814) 42. Figure 8 shows a current I = 1.0 A entering a truncated solid cone made of a conducting metal. The electron drift speed at the 3.0 mm diameter end of the cone is m/s. What is the electron drift speed at the 1.5 mm diameter end of the wire? (Ans: m/s) A B C D E Conceptual Problems 1. A certain wire has resistance R. Another wire, of the same material, has half the length and half the diameter of the first wire. The resistance of the second wire is: A. 2R B. R/2 C. R D. R/4 E. 4R 2. If a wire is stretched uniformly to ntimes its original length, its resistance changes by a factor of: A. n 2 B. n C. 1/n D. 2n E. no change 3. The potential difference across the ends of a wire is doubled in magnitude. If Ohm s law is obeyed, which one of the following statements concerning the resistance of the wire is true? A. The resistance is not changed. B. The resistance is one half of its original value. C. The resistance is twice its original value. D. The resistance increases by a factor of four. E. The resistance decreases by a factor of four. 4. Two wires are made of different materials and carry the same current. The current density in both is the same only if: A. their radii are the same. B. the potential differences across them are the same. C. their lengths are the same. D. both their lengths and radii are the same. E. the electric fields in them are the same. Dr. M. F. AlKuhaili PHYS 102 Chapter 26 Page 4
5 5. Copper wire 1 has length L 1 and diameter d 1. Another copper wire 2 has length L 2 and diameter d 2. At constant temperature, the second conductor has smaller resistance if: A. d2>d1 and L2<L1. B. d2=d1 and L2>L1. C. d2<d1 and L2<L1. D. d2<d1 and L2=L1. E. d2>d1 and L2>L1. 6. Figure 2 shows three cylindrical copper conductors along with their face areas and length. Rank them according to the current through tem, greatest first, when the same potential difference V is applied across their lengths. A. 1, 3 and 2. B. 1, 2 and 3. C. 3, 2 and 1. D. 2, 1 and 3. E. 1, 3 and Conduction electrons move to the right in a certain wire. This indicates that: A) the current density and electric field both point left. B) the current density points right and the electric field points left. C) the current density points left but the direction of the electric field is unknown. D) the current density and electric field both point right. E) the current density points left and the electric field points right. 8. A copper wire has an initial resistance of 100 Ω, and is connected to a 5.0 V battery. The temperature coefficient of resistivity of copper is α = ( C) 1. If the wire is cooled by 50 C : A. The power dissipated in the wire will increase by 68 mw. B. The power dissipated in the wire will decrease by 68 mw. C. The power dissipated in the wire will increase by 47 mw. D. The power dissipated in the wire will decrease by 47 mw. E. The power dissipated will not change. 9. Two cylindrical resistors R 1 and R 2 are made from the same material and have the same length. When connected across the same battery, R 1 dissipates twice as much power as R 2. The ratio of the diameter of resistor R 1 to that of R 2 is: 10. Two light bulbs operate from a 120V voltage source. Bulb A has a power rating of 25.0 W, and bulb B has a power rating of 100 W. Which of the following statements is correct? A. Resistance of A is larger than resistance of B. B. Resistance of A is smaller than resistance of B. C. The current through A is higher than the current through B. D. The resistances of the two bulbs are the same. E. The currents through the two bulbs are the same. Dr. M. F. AlKuhaili PHYS 102 Chapter 26 Page 5
6 11. A metal wire of resistance R is cut into three equal pieces that are then connected side by side to form a new wire the length of which is equal to onethird the original length. What is the resistance of the new wire? A. R/9 B. R/3 C. R D. 3R E. 9R 12. Resistor 1 has twice the resistance of resistor 2. They are connected in parallel to a battery. If the power dissipated in R 1 is P 1 and the power dissipated in R 2 is P 2, then P 1/P 2 is: A B. 1.0 C D. 4.0 E A potential difference V is applied across a cylindrical metallic wire of radius r and length L. Both V and L are doubled, but r is halved. Which of the following statements is correct? A. The power dissipated will decrease by a factor of 2. B. The power dissipated will increase by a factor of 4. C. The power dissipated will increase by a factor of 2. D. The power dissipated will increase by a factor of 8. E. The power dissipated will decrease by a factor of The two segments of wire in figure 7 have equal diameters but different resistivities ρ 1 and ρ 2. Current I passes through this wire. If ρ 2/ ρ 1 = ½, what is the ratio of E 2/E 1 of the electric field strengths in the two segments? A. 1/2 B. 1/4 C. 1 D. 4 E A metallic wire has the smallest resistance when it is A. thick, short and cool B. thin, long and hot C. thick, long and hot D. thin, short and cool E. thin, short and hot 16. Figure 11 shows four situations in which positive and negative charges move horizontally, and gives the rate at which each charge moves. Rank the situations according to the net current through the regions, greatest first. A. a and b and c tie, then d B. a, then d, then c, then b C. a, then d, then b, then c D. a, then c, then d, then b E. a, then c, then b, then d Dr. M. F. AlKuhaili PHYS 102 Chapter 26 Page 6
7 17. A cylindrical conducting wire has radius ri and length Li. Its dimensions are changed to rf and Lf. Which of the following changes results in the least resistance? A. rf = 2ri and Lf = Li/2 B. rf = 2ri and Lf = 2Li C. rf = 2ri and Lf = Li D. rf = ri/2 and Lf = Li/2 E. rf = ri/2 and Lf = 2Li 18. The electric potential V(x) versus the position x along a copper wire carrying current is shown in figure 12. The wire consists of three sections, A, B, and C that differ in radius. Rank the three sections according to the magnitude of the current density, least first. A) C, A, B B) A, B, C C) C, B, A D) B, A, C E) A, C, B Dr. M. F. AlKuhaili PHYS 102 Chapter 26 Page 7
8 Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Dr. M. F. AlKuhaili PHYS 102 Chapter 26 Page 8
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