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Physics Week 3(Sem. 2) Name____________________________ Chapter Summary ElectricityElectric Potential and Circuits negative terminal. The field exerts a force on the free electrons in the wire, and they respond by moving through the wire. The resulting from of charge is called an electric current. The current is defined as the amount of charge per unit time that crosses an area of the wire. Thus the equation for current is Electric Potential A positive point charge +q creates an electric potential, thus has the ability to do work. The force exerted on the test charge varies with the distance between the charges. The work done on the test charge can be calculated using If the rate of flow is not constant then the equation gives the average current. The units are Coulombs per second or the ampere (A‐amp). The potential difference between A and B (VB –VA) can now be determined, since the ΔV=WAB/q0. The equation then becomes If the charges move around a circuit in the same direction at all times, the current is said to be direct current (DC). This is the kind of current that batteries produce. In contrast, when the charges move one way and then the opposite way the current is said to be alternating current (AC). So generators at power plants, the electrical companies and microphones produce alternating current. As point B is located farther and farther away from the charge q, rB becomes larger and the kq/rB goes to zero. So the equation then becomes: This equation is the potential of a point charge. If the charge is positive then the potential will be increased for the system. If the charge is negative then the potential of the system will be decreased. In circuits the negatively charged electrons go around the circuit from the negative side of the battery toward the positive side. However, it is customary to not use the flow of electrons to indicate the current. The direction of conventional current goes from higher potential to lower potential. The symbol I stands for conventional current. Electromotive Force Ohm’s Law The maximum potential difference because of the positive and negative charges in a battery is called the electromotive force (EMF) of the battery. The maximum EMF of a car battery is a 12 V or 12 J/C. The typical EMF of a D cell battery is 1.5 V. The current that a battery can push through a wire is analogous to the water flow that a pump can push through a pipe. Stronger pumps lead to larger flow rates, and similarly a stronger (greater) battery leads to a larger electric current. Therefore the electric current is found to be directly proportional to the voltage. Thus a 12 V battery leads to twice the current of a 6V battery. Water flow is also determined by the length and diameter of the pipe Current Due to this potential difference the battery creates an electric field directed from the positive toward the Ms. N. May through which it travels. Current, much like water, is also determined by the length and diameter of the wire it travels through. For wires that are longer and thinner they provide larger resistance to current flow. Conversely, shorter wires with larger diameters have less resistance. Therefore it stands to reason that current is inversely proportional to the resistance. Through this Ohm’s law was developed Resistance and Resistivity Resistance of a wire to flowing current is determined by length, cross sectional area, and type of material. Therefore the equation to calculate the resistance of a wire can be employed Where R is the resistance in Ohm’s (Ω), is the resistivity of the material (Ω m), L is length of the wire, and A is the cross sectional area perpendicular to the flow (m2). All conductors (metals) have fairly low resistivity’s. Nonconductors, such as rubber, have high resistivity’s. Silicon and germanium are semi metals and have intermediate values for their resistivity’s. The resistivity of a material depends on temperature. In metals, the resistivity increases with increasing temperature, whereas in semi‐metals the reverse is true. For many materials and limited temperature ranges, it is possible to express the temperature dependence of the resistivity as Where is the resistivity of the material (Ω m), T is temperature (oC), and α is the temperature coefficient of resistivity (oC‐1). When the resistivity increases with increasing temperature, α is positive, as it is for metals. The formula can be rearranged to use resistance 1 Where R is resistance in Ohm’s (Ω), V is voltage in volts(V), and I is current in amperes(A). Ms. N. May 1 There is a special class of materials whose resistivity suddenly goes to zero below a certain temperature (Tc) called the critical temperature. This temperature is typically very close to absolute zero. Below this temperature, such materials are called superconductors. The name derives from the fact that with zero resistivity, these materials offer no resistance to electric current and are, therefore, perfect conductors. One of the remarkable properties of zero resistivity is that once a current is established in a super conducting ring, it continues indefinitely without the need of an EMF. Currents have persisted in superconductors for many years without measureable decay. In contrast, the current in a nonsuperconducting material drops to zero almost immediately after the EMF is removed. Many metals become superconductors only at very low temperatures, such as aluminum (Tc =1.18K), tim (Tc=3.72K), lead (Tc=7.20K), and niobium (Tc=9.25K). Recently, ceramic materials have been developed that undergo the transition to the superconducting state at much higher temperatures (Tc= 133.5K). The development of superconductors that occur at higher temperatures, like room temperature, presents benefits in MRI, computer chips, and cheaper electrical power (smaller motors). Ms. N. May Ms. N. May Ms. N. May 6048 - 1 - Page 1 Name: ____________________________________________ 1) 2) An electron is accelerated from rest through a potential difference of 200. volts. The work done on the electron is A) 320. eV C) 3.20 x 10-17 eV B) 200. eV D) 8.00 x 10-17 eV If 10. joules of work must be done to move 2.0 coulombs of charge from point A to point B in an electric field, the potential difference between points A and B is A) 20. V B) 12 V C) 5.0 V D) 10. V An alpha particle with a charge of +2 elementary charges is accelerated in a vacuum through a potential difference of 10,000. volts. What is the energy acquired by the particle? A) 40,000 eV B) 2.0 eV 4) 3) C) 20,000 eV D) 3.2 x 10-15 eV The diagram below represents a source connected to two large, parallel metal plates. The electric field intensity between the plates is 3.75 x 104 newtons per coulomb. Compared to the work done in moving an electron from point A to point B to point C, the work done in moving an electron directly from point A to point C is A) greater 5) The electron volt is a unit of A) B) C) D) 6) charge energy current potential difference A) decrease B) remain the same C) increase 11) The graph below shows the relationship between current and potential difference for four resistors, A, B, C, and D. resistance electric current charge potential difference a high resistance a low resistance a potential difference a magnetic field A wire carries a current of 6.0 amperes. How much charge passes a point in the wire in 120 seconds? A) 360. C B) 20. C 9) If the diameter of a wire were to increase, its electrical resistance would Which condition must exist between two points in a conductor in order to maintain a flow of charge? A) B) C) D) 8) C) the same 10) The number of electrons that pass a certain point in a conductor in a given amount of time is defined as A) B) C) D) 7) B) less C) 720. C D) 6.0 C A flow rate of 1 coulomb per 0.1 second is measured in a wire. What is the electrical current in the wire? A) 1 A B) 10 A C) 100 A D) 0.1 A Which resistor has the greatest resistance? A) B B) D C) A D) C 6048 - 1 - Page 2 12) In a flashlight, a battery provides a total of 3.0 volts to a bulb. If the flashlight bulb has an operating resistance of 5.0 ohms, what is the current through the bulb? A) 1.7 A B) 1.5 A 13) 15) 16) 17) 18) The graph below shows the relationship between the potential difference across a metallic conductor and the electric current through the conductor at constant temperature T1 . An electric iron draws a current of 5 amperes and has a resistance of 20 ohms. The amount of energy used by the iron in 40 seconds is A) 20,000 J B) 4,000 J 14) C) 0.60 A D) 0.30 A 19) C) 100 J D) 500 J What is the resistance at 20.DC of a 2.0-meter length of tungsten wire with a cross-sectional area of 7.9 x 10-7 meter2 ? A) 4.0 x 10-2 O C) 5.7 x 10-1 O B) 7.1 x 10-2 O D) 1.4 x 10-1 O An electric iron operating at 120 volts draws 10. amperes of current. How much heat energy is delivered by the iron in 30. seconds? A) 3.0 x 102 J C) 3.6 x 104 J B) 1.2 x 103 J D) 3.6 x 103 J Which graph best represents the relationship between potential difference and current for the same conductor maintained at a higher constant temperature, T2 ? A) If 4.8 x 10-17 joule of work is required to move an electron between two points in an electric field, what is the electric potential difference between these points? A) 4.8 x 102 V C) 3.0 x 102 V B) 4.8 x 10-17 V D) 1.6 x 10-19 V What is the resistance at 20DC of a 1.50-meter-long aluminum conductor that has a cross-sectional area of 1.13 x 10-6 meter2 ? A) 1.33 x 106 O C) 1.87 x 10-3 O B) 2.28 x 10-2 O D) 3.74 x 10-2 O B) For which quantities are values needed to calculate the amount of energy supplied to an operating toaster? A) B) C) D) applied voltage and resistance, only applied voltage, current drawn, and operation time applied voltage, current drawn, and resistance applied voltage and operation time, only C) D) 6048 - 1 - Page 3 20) A 100.-ohm resistor and an unknown resistor are connected in series to a 10.0-volt battery. If the potential drop across the 100.-ohm resistor is 4.00 volts, what is the resistance of the unknown resistor? A) 200. O B) 100. O 21) 23) C) 60. C D) 120 C B) C) remains the same D) is doubled An operating electric heater draws a current of 10. amperes and has a resistance of 12 ohms. How much energy does the heater use in 60. seconds? A) 120 J B) 1,200 J 24) A) A 6.0-ohm resistor that obeys Ohm's Law is connected to a source of variable potential difference. When the applied voltage is decreased from 12 V to 6.0 V, the current passing through the resistor A) is halved B) is quadrupled C) C) 72,000 J D) 7,200 J A device operating at a potential difference of 1.5 volts draws a current of 0.20 ampere. How much energy is used by the device in 60. seconds? A) 12 J B) 8.0 J Several pieces of copper wire, all having the same length but different diameters, are kept at room temperature. Which graph best represents the resistance, R, of the wires as a function of their cross-sectional areas, A? C) 50.0 O D) 150. O The current through a light bulb is 2.0 amperes. How many coulombs of electric charge pass through the light bulb in one minute? A) 240 C B) 2.0 C 22) 25) D) C) 4.5 J D) 18 J 26) The graph below represents the relationship between the potential difference (V) across a resistor and the current (I) through the resistor. Through which entire interval does the resistor obey Ohm's law? A) BC B) AD C) AB D) CD 6048 - 1 - Page 4 27) 28) Which graph best represents the relationship between the electrical power and the current in a resistor that obeys Ohm's Law? Which graph best represents the relationship between resistance and length of a copper wire of uniform crosssectional area at constant temperature? A) A) B) B) C) C) D) D) In order to measure the current through an electrical device, an ammeter is placed in series with the device. Compared to the electrical device, the ammeter should have a much A) B) C) D) 29) 30) lower permeability higher resistance lower resistance higher permeability 31) A) increases B) remains the same C) decreases 32) A 0.500-meter length of wire with a cross-sectional area of 3.14 x 10-6 meters squared is found to have a resistance of 2.53 x 10-3 ohms. According to the resistivity chart, the wire could be made of A) copper B) nichrome A complete circuit is left on for several minutes, causing the connecting copper wire to become hot. As the temperature of the wire increases, the electrical resistance of the wire C) aluminum D) silver 33) The current traveling from the cathode to the screen in a television picture tube is 5.0 x 10-5 ampere. How many electrons strike the screen in 5.0 seconds? A) 1.0 x 105 C) 1.6 x 1015 B) 6.3 x 1018 D) 3.1 x 1024 During a thunderstorm, a lightning strike transfers 12 coulombs of charge in 2.0 x 10-3 second. What is the average current produced in this strike? A) 6.0 x 103 A C) 1.7 x 10-4 A B) 9.6 x 103 A D) 2.4 x 10-2 A 6048 - 1 - Page 5 34) A physics student is given three 12-ohm resistors with instructions to create the circuit that would have the lowest possible resistance. The correct circuit would be a A) B) C) D) 35) parallel circuit with an equivalent resistance of 4.0 O parallel circuit with an equivalent resistance of 36 O series circuit with an equivalent resistance of 36 O series circuit with an equivalent resistance of 4.0 O decreases and the current through it increases decreases and the current through it decreases increases and the current through it decreases increases and the current through it increases Which graph best represents the relationship between potential difference across a metallic conductor and the resulting current through the conductor at a constant temperature? C) 0.15 W D) 0.015 W A) C) aluminum D) silver A 330.-ohm resistor is connected to a 5.00-volt battery. What is the current through the resistor? A) 1,650 mA B) 15.2 mA 40) 42) Pieces of aluminum, copper, gold, and silver wire each have the same length and the same cross-sectional area. Which wire has the lowest resistance at 20DC? A) gold B) copper 39) A) increase B) remain the same C) decrease C) 10. C D) 33 C In a series circuit containing two lamps, the battery supplies a potential difference of 1.5 volts. If the current in the circuit is 0.10 ampere, at what rate does the circuit use energy? A) 15 W B) 1.5 W 38) As the temperature of the nichrome is decreased, the brightness of the lamp will A current of 3.0 amperes is flowing in a circuit. How much charge passes a given point in the circuit in 30. seconds? A) 0.10 C B) 90. C 37) The diagram below represents a lamp, a 10-volt battery, and a length of nichrome wire connected in series. An incandescent light bulb is supplied with a constant potential difference of 120 volts. As the filament of the bulb heats up, its resistance A) B) C) D) 36) 41) B) C) 335 mA D) 0.152 mA Two identical resistors connected in parallel have an equivalent resistance of 40. ohms. What is the resistance of each resistor? A) 160 O B) 40. O C) 20. O D) 80. O C) D) 43) A wire carries a current of 2.0 amperes. How many electrons pass a given point in this wire in 1.0 second? A) 2.0 x 1019 C) 1.3 x 1018 B) 2.0 x 1018 D) 1.3 x 1019 6048 - 1 - Page 6 44) A manufacturer recommends that the longer the extension cord used with an electric drill, the thicker (heavier gauge) the extension cord should be. This recommendation is made because the resistance of a wire varies 50) A) inversely with length and directly with cross-sectional area B) directly with length and inversely with cross-sectional area C) inversely with both length and cross-sectional area D) directly with both length and cross-sectional area 45) 46) 48) A) 1.6 x 10-21 J C) 1.0 x 102 J B) 1.6 x 10-17 J D) 1.6 x 10-19 J B) A 10.-meter length of wire with a cross-sectional area of 3.0 x 10-6 square meter has a resistance of 9.4 x 10-2 ohm at 20D Celsius. The wire is most likely made of C) C) aluminum D) copper An immersion heater has a resistance of 5.0 ohms while drawing a current of 3.0 amperes. How much electrical energy is delivered to the heater during 200. seconds of operation? A) 1.5 x 104 J C) 3.0 x 103 J B) 6.0 x 103 J D) 9.0 x 103 J An operating electric iron draws a current of 5 amperes and has a resistance of 20 ohms. What is the amount of energy used by the iron in 40 seconds? A) 1 x 102 J C) 5 x 102 J 2 x 104 J D) 4 x 103 J B) 49) A) How much work is required to move a single electron through a potential difference of 100. volts? A) silver B) tungsten 47) Which graph best represents the relationship between the potential difference across a conductor and the current through the conductor at constant temperature? D) 51) A) decreasing the applied potential difference and increasing the length of wire B) decreasing the applied potential difference and decreasing the length of wire C) increasing the applied potential difference and increasing the length of wire D) increasing the applied potential difference and decreasing the length of wire In an electric field, 0.90 joule of work is required to bring 0.45 coulomb of charge from point A to point B. What is the electric potential difference between points A and B? A) 0.41 V B) 2.0 V Which changes would cause the greatest increase in the rate of flow of charge through a conducting wire? C) 0.50 V D) 5.0 V 52) 53) A 12-volt automobile battery has 8.4 x 103 coulombs of electric charge. The amount of electrical energy stored in the battery is approximately A) 7.0 x 102 J C) 1.0 x 105 J B) 1.4 x 10-3 J D) 8.4 x 103 J Which physical quantity is correctly paired with its unit? A) B) C) D) electric potential difference and joules/coulomb electric current and amperes/coulomb power and wattdseconds energy and newtondseconds 6048 - 1 - Page 7 54) 55) How much electrical energy is required to move a 4.00-microcoulomb charge through a potential difference of 36.0 volts? A) 1.44 x 10-4 J C) 9.00 x 106 J B) 1.11 x 10-7 J D) 144 J How much work is done in moving 5.0 coulombs of charge against a potential difference of 12 volts? A) 2.4 J B) 12 J 56) 57) A) B) C) D) 59) switch source of potential difference magnetic field source voltmeter A 10.-ohm resistor and a 20.-ohm resistor are connected in series to a voltage source. When the current through the 10.-ohm resistor is 2.0 amperes, what is the current through the 20.-ohm resistor? A) 1.0 A B) 4.0 A 60) C) 12.0 m D) 8.00 m What must be inserted between points A and B to establish a steady electric current in the incomplete circuit represented in the diagram below? If the diameter of a wire were decreased, its electrical resistance would A) increase B) remain the same C) decrease C) 60. J D) 30. J A 12.0-meter length of copper wire has a resistance of 1.50 ohms. How long must an aluminum wire with the same cross-sectional area be to have the same resistance? A) 7.32 m B) 19.7 m 58) Compared to insulators, metals are better conductors of electricity because metals contain more free A) negative ions B) positive ions 61) A proton starts from rest and gains 8.35 x 10-14 joule of kinetic energy as it accelerates between points A and B in an electric field. Based on the given situation, calculate the potential difference between points A and B in the electric field. [Show all work, including the equation and substitution with units.] 63) A 1.00-meter length of nichrome wire with a cross-sectional area of 7.85 x 10-7 meter2 is connected to a 1.50-volt battery. (a) Calculate the resistance of the wire. [Show all work, including the equation and substitution with units.] (b) Determine the current in the wire. C) protons D) electrons The diagram below represents part of an electric circuit containing three resistors. What is the equivalent resistance of this part of the circuit? A) 1.5 O B) 19 O 62) C) 2.0 A D) 0.50 A C) 0.67 O D) 6.3 O 6048 - 1 - Page 8 64) A student conducted an experiment to determine the resistance of a lightbulb. As she applied various potential differences to the bulb, she recorded the voltages and corresponding currents and constructed the graph below. 65) According to the given graph, as the potential difference increased, the resistance of the lightbulb A) increased B) changed, but there is not enough information to know which way C) decreased A long copper wire was connected to a voltage source. The voltage was varied and the current through the wire measured, while temperature was held constant. The collected data are represented by the graph below. Using the graph, determine the resistance of the copper wire. 66) An electron is accelerated through a potential difference of 2.5 x 104 volts in the cathode ray tube of a computer monitor. Calculate the work, in joules, done on the electron. [Show all work, including the equation and substitution with units.] 67) What is the magnitude of the charge, in coulombs, of a lithium nucleus containing three protons and four neutrons?