Physics Exam 3 (2025 VERSION) Questions with Accurate Answers Get an A.

Physics Exam 3 (2025 VERSION) Questions with Accurate Answers Get an A. An electric device delivers a current of 5.0 A to a device. How many electrons flow through this device in 10 s? (e = 1.60 × 10-19 C) A) 0.20 B) 20 C) 2.0 D) 3.1 x 10^20 E) 31 x 10^20 Answer: D In a certain electroplating process gold is deposited by using a current of 14.0 A for 19 minutes. A gold ion, Au+, has a mass of approximately 3.3 × 10-22 g. How many grams of gold are deposited by this process? A) 33 g B) 16 g C) 22 g D) 28 g E) 97 g Answer: A The figure shows a 2.0-cm diameter roller that turns at 90 rpm. A 4.0-cm wide plastic film is being wrapped onto the roller, and this plastic carries an excess electric charge having a uniform surface charge density of 5.0 nC/cm2. What is the current of the moving film? A) 190 nA B) 23 μA C) 30 nA D) 11 μA Answer: A The heater element of a particular 120-V toaster is a 8.9-m length of nichrome wire, whose diameter is 0.86 mm. The resistivity of nichrome at the operating temperature of the toaster is 1.3 × 10-6 Ω · m. If the toaster is operated at a voltage of 120 V, how much power does it draw? A) 720 W B) 700 W C) 750 W D) 770 W E) 800 W Answer: A The current supplied by a battery as a function of time is I(t) = (0.88 A)e-t/(6.0 hr). What is the total number of electrons transported from the positive electrode to the negative electrode from the time the battery is first used until it is essentially dead? (e = 1.60 × 10-19 C) A) 1.2 × 10^23 B) 4.4 × 10^22 C) 5.3 × 10^23 D) 3.3 × 10^19 Answer: A The voltage and power ratings of a particular light bulb, which are its normal operating values, are 110 V and 60 W. Assume the resistance of the filament of the bulb is constant and is independent of operating conditions. If the light bulb is operated at a reduced voltage and the power drawn by the bulb is 36 W, what is the operating voltage of the bulb? A) 66 V B) 72 V C) 78 V D) 85 V E) 90 V Answer: D A gold wire that is 1.8 mm in diameter and 15 cm long carries a current of 260 mA. How many electrons per second pass a given cross section of the wire? (e = 1.60 × 10-19 C) A) 1.6 × 10^18 B) 1.6 × 10^17 C) 1.5 × 10^23 D) 3.7 × 10^15 E) 6.3 × 10^15 Answer: A The voltage and power ratings of a particular light bulb, which are its normal operating values, are 110 V and 60 W. Assume the resistance of the filament of the bulb is constant and is independent of operating conditions. If the light bulb is operated with a current that is 50% of the current rating of the bulb, what is the actual power drawn by the bulb? A) 10 W B) 15 W C) 20 W D) 25 W E) 30 W Answer: B In an electroplating process, copper (ionic charge +2e, atomic weight 63.6 g/mol) is deposited using a current of 10.0 A. What mass of copper is deposited in 10.0 minutes? Avogadroʹs number is 6.022 × 1023 molecules/mol and e = 1.60 × 10-19 C. A) 3.96 g B) 2.52 g C) 0.99 g D) 2.52 g E) 1.98 g Answer: E A 400-W computer (including the monitor) is turned on for 8.0 hours per day. If electricity costs 10¢ per kWh, how much does it cost to run the computer annually for a typical 365-day year? A) $120 B) $1200 C) $15 D) $17 E) $150 Answer: A If a current of 2.4 A is flowing in a cylindrical wire of diameter 2.0 mm, what is the average current density in this wire? A) 7.6 × 105 A/m2 B) 5.2 × 10-6 A/m2 C) 1.9 × 105 A/m2 D) 3.6 × 105 A/m2 E) 21 × 10-6 A/m2 Answer: A The resistivity of gold is 2.44 × 10-8 Ω · m at room temperature. A gold wire that is 1.8 mm in diameter and 11 cm long carries a current of 170 mA. How much power is dissipated in the wire? A) 0.030 mW B) 0.0076 mW C) 0.013 mW D) 0.019 mW E) 0.025 mW Answer: A A proton beam that carries a total current of 1.3 mA has 10.0 mm diameter. The current density in the proton beam increases linearly with distance from the center. This is expressed mathematically as J(r) = J0 (r/R), where R is the radius of the beam and J0 is the current density at the edge. Determine the value of J0. A) 25 A/m2 B) 6.2 A/m2 C) 12 A/m2 D) 17 A/m2 Answer: A A 1500-W heater is connected to a 120-V line. How much heat energy does it produce in 2.0 hours? A) 1.5 kJ B) 3.0 kJ C) 0.18 MJ D) 11 MJ E) 18 MJ Answer: D A certain fuse ʺblowsʺ if the current in it exceeds 1.0 A, at which instant the fuse melts with a current density of 620 A/cm2. What is the diameter of the wire in the fuse? A) 0.45 mm B) 0.63 mm C) 0.68 mm D) 0.91 mm Answer: A A certain electric furnace consumes 24 kW when it is connected to a 240-V line. What is the resistance of the furnace? A) 1.0 kΩ B) 10 Ω C) 2.4 Ω D) 0.42 Ω E) 100 Ω Answer: C If the current density in a wire or radius R is given by J = kr, 0 r R, what is the current in the wire? A) 2πkR^3/3 B) 3πkR^3/2 C) kR^3/3 D) kR^2 E) kR^2/2 Answer: A A light bulb is connected to a 110-V source. What is the resistance of this bulb if it is a 100-W bulb? A) 100 Ω B) 8.0 mΩ C) 6.0 mΩ D) 120 Ω E) 240 Ω Answer: D A silver wire has a cross sectional area A = 2.0 mm2. A total of 9.4 × 10^18 electrons pass through the wire in 3.0 s. The conduction electron density in silver is 5.8 × 10^28 electrons/m3 and e = 1.60 × 10-19 C. What is the drift velocity of these electrons? A) 2.7 × 10-5 m/s B) 9.1 × 10-5 m/s C) 5.2 × 10-5 m/s D) 1.1 × 10-5 m/s E) 7.4 × 10-5 m/s Answer: A A 110-V hair dryer is rated at 1200 W. What current will it draw when operating from a 110-V electrical outlet? A) 90 mA B) 1.0 A C) 5.0 A D) 11 A E) 14 A Answer: D How much current will be flowing through a 40.0 m length of cylindrical metal wire with radius 0.0 mm if it is connected to a source supplying 16.0 V? The resistivity of this metal is 1.68 × 10-8 Ω · m. A) 1200 A B) 9.5 × 108 A C) 68 nA D) 710 A Answer: A The diameter of a 12-gauge copper wire is 0.081 in. The maximum safe current it can carry (in order to prevent fire danger in building construction) is 20 A. At this current, what is the drift velocity of the electrons? The number of electron carriers in 1.0 cm3 of copper is 8.5 × 10^22 and e = 1.60 × 10-19 C. A) 0.044 mm/s B) 0.44 mm/s C) 0.44 cm/s D) 0.44 m/s E) 4.4 cm/s Answer: B When a voltage difference is applied to a piece of metal wire, a 5.0-mA current flows through it. If this metal wire is now replaced with a silver wire having twice the diameter of the original wire, how much current will flow through the silver wire? The lengths of both wires are the same, and the voltage difference remains unchanged. (The resistivity of the original metal is 1.68 × 10-8 Ω · m, and the resistivity of silver is 1.59 × 10-8 Ω · m.) A) 21 mA B) 19 mA C) 11 mA D) 5.3 mA Answer: A Building codes usually limit the current carried by a No. 14 copper wire to 15 A. Many household circuits are wired with this size wire. What is the drift velocity of the electrons in this case? The diameter of this wire is 1.6 mm. Assume one conduction electron per atom in copper. The atomic weight of copper is 63.3 g/mol and its density is 8900 kg/m3. Avogadroʹs number is 6.022 × 1023 molecules/mol and e = 1.60 × 10-19 C. A) 5.51 × 10-4 m/s B) 4.56 × 10-4 m/s C) 1.65 × 10-3 m/s D) 4.44 × 10-2 m/s E) 4.89 × 10-5 m/s Answer: A Calculate the current through a 10.0-m long 22 gauge (having radius 0.321 mm) nichrome wire if it is connected to a 12.0-V battery. The resistivity of nichrome is 100 × 10-8 Ω · m. A) 17.5 A B) 30.9 A C) 61.8 A D) 388 mA E) 776 mA Answer: D The resistivity of gold is 2.44 × 10-8 Ω · m at room temperature. A gold wire that is 0.9 mm in diameter and 14 cm long carries a current of 940 mA. What is the electric field in the wire? A) 0.036 V/m B) 0.0090 V/m C) 0.028 V/m D) 0.046 V/m E) 0.090 V/m Answer: A Nichrome wire, often used for heating elements, has resistivity of 1.0 × 10-6 Ω · m at room temperature. What length of No. 30 wire (of diameter 0.250 mm) is needed to wind a resistor that has 50 ohms at room temperature? A) 3.66 m B) 2.45 m C) 0.61 m D) 6.54 m E) 22.4 m Answer: B A silver wire with resistivity 1.59 × 10-8 Ω · m carries a current density of 4.0 A/mm2.What is the magnitude of the electric field inside the wire? A) 0.064 V/m B) 2.5 V/m C) 0.040 V/m D) 0.10 V/m Answer: A What must be the diameter of a cylindrical 120-m long metal wire if its resistance is to be 6.0 Ω? The resistivity of this metal is 1.68 × 10-8 Ω · m. A) 0.065 mm B) 0.65 mm C) 0.65 cm D) 0.325 mm E) 0.0325 mm Answer: B A tube of mercury with resistivity 9.84 × 10-7 Ω · m has an electric field inside the column of mercury of magnitude 23 N/C that is directed along the length of the tube. How much current is flowing through this tube if its diameter is 1.0 mm? A) 18 A B) 180 A C) 29 A D) 280 A Answer: A A 2.0 mm diameter wire of length 20 m has a resistance of 0.25 Ω. What is the resistivity of the wire? A) 5.0 × 10-7 Ω · m B) 3.9 × 10-8 Ω · m C) 4.0 × 10-7 Ω · m D) 16 × 10-8 Ω · m E) 0.25 Ω · m Answer: B What length of a certain metal wire of diameter 0.15 mm is needed for the wire to have a resistance of 15 Ω? The resistivity of this metal is 1.68 × 10-8 Ω · m. A) 16 mm B) 16 cm C) 1.6 m D) 16 m E) 160 m Answer: D Chapter 28 Circuits The emf and the internal resistance of a battery are as shown in the figure. If a current of 8.3 A is drawn from the battery when a resistor R is connected across the terminals ab of the battery, what is the power dissipated by the resistor R? A) 440 W B) 700 W C) 620 W D) 530 W E) 790 W Answer: A The emf and the internal resistance of a battery are as shown in the figure. When the terminal voltage Vab is equal to 17.4 V, what is the current through the battery, including its direction? A) 6.8 A, from b to a B) 8.7 A, from b to a C) 6.8 A, from a to b D) 8.7 A, from a to b E) 16 A, from b to a Answer: A The emf and the internal resistance of a battery are shown in the figure. If a current of 7.8 A is established through the battery from b to a, what is the terminal voltage Vab of the battery? A) ‐30 V B) 80 V C) 30 V D) ‐80 V E) zero Answer: A In the circuit shown in the figure, an ideal ohmmeter is connected across ab with the switch S open. All the connecting leads have negligible resistance. The reading of the ohmmeter will be closest to A) 7.5 Ω. B) 10 Ω. C) 30 Ω. D) 40 Ω. E) 60 Ω. Answer: A In the figure a current of 6.0 A is drawn from the battery. What is the terminal voltage Vab of the battery? A) 0.00 V B) +12 V C) +24 V D) ‐12 V E) ‐24 V Answer: A In the figure, when the terminal voltage Vab of the battery is equal to 20 V, how much current passes through the battery, including its direction? A) 4 A, from a to b B) 5 A, from a to b C) 6 A, from a to b D) 4 A, from b to a E) 5 A, from b to a Answer: A Three resistors having resistances of 4.0 Ω, 6.0 Ω, and 10.0 Ω are connected in parallel. If the combination is connected in series with an ideal 12-V battery and a 2.0-Ω resistor, what is the current through the 10.0-Ω resistor? A) 0.59 A B) 2.7 A C) 6.4 A D) 11.2 A E) 16 A Answer: A For the circuit shown in the figure, the current in the 8-Ω resistor is 0.50 A, and all quantities are accurate to 2 significant figures. What is the current in the 2-Ω resistor? A) 2.25 A B) 0.75 A C) 4.5 A D) 9.5 A E) 6.4 A Answer: D Thirteen resistors are connected across points A and B as shown in the figure. If all the resistors are accurate to 2 significant figures, what is the equivalent resistance between points A and B? A) 4.0 Ω B) 6.0 Ω C) 8.0 Ω D) 10 Ω E) 12 Ω Answer: C For the circuit shown in the figure, all quantities are accurate to 3 significant figures. What is the power dissipated in the 2-Ω resistor? A) 5.33 W B) 8.0 W C) 6.67 W D) 2.67 W E) 3.56 W Answer: E Four resistors are connected across an 8-V DC battery as shown in the figure. The current through the 9-Ω resistor is closest to A) 1 A. B) 0.7 A. C) 0.5 A. D) 0.9 A. E) 2 A. Answer: B A galvanometer coil having a resistance of 20 Ω and a full-scale deflection at 1.0 mA is connected in series with a 4980 Ω resistance to build a voltmeter. What is the maximum voltage that this voltmeter can read? A) 3.0 V B) 1.0 V C) 50 V D) 5.0 V E) 10 V Answer: D When four identical resistors are connected to an ideal battery of voltage V = 10 V as shown in the figure, the current I is equal to 0.20 A. What is the value of the resistance R of the resistors? A) 20 Ω B) 40 Ω C) 30 Ω D) 50 Ω E) 10 Ω Answer: C When a 20.0-ohm resistor is connected across the terminals of a 12.0-V battery, the voltage across the terminals of the battery falls by 0.300 V. What is the internal resistance of this battery? A) 3.60 Ω B) 1.56 Ω C) 0.98 Ω D) 0.30 Ω E) 0.51 Ω Answer: E Two identical resistors of resistance R = 24 Ω and a variable resistor Rx are connected to an ideal battery of voltage V as shown in the figure. What should be the value of the variable resistance Rx to make the voltage across the two parallel resistors equal to V/5. A) 4.0 Ω B) 24 Ω C) 8.0 Ω D) 16 Ω E) 40 Ω Answer: C A galvanometer has an internal resistance of 100 Ω and deflects full-scale at 2.00 mA. What size resistor should be added to the galvanometer to convert it to a milliammeter capable of reading up to 4.00 mA, and how should this resistor be connected to the galvanometer? A) 50.0 Ω in series with the galvanometer B) 50.0 Ω in parallel with the galvanometer C) 75.0 Ω in parallel with the galvanometer D) 100 Ω in series with the galvanometer E) 100 Ω in parallel with the galvanometer Answer: E For the circuit shown in the figure, I = 0.50 A and R = 12 Ω. What is the value of the emf ε? A) 18 V B) 24 V C) 6.0 V D) 12 V E) 48 V Answer: B What is the maximum current that can be drawn from a 1.50-V battery with an internal resistance of 0.30 ohm? A) 2.5 A B) 5.0 A C) 0.45 A D) 0.20 A E) 4.5 A Answer: B Chapter 29 A galvanometer has a coil with a resistance of 24.0 Ω, and a current of 180 μA causes it to deflect full scale. If this galvanometer is to be used to construct an ammeter that can read up to 10.0 A, what shunt resistor is required? A) 123 μΩ B) 234 μΩ C) 342 μΩ D) 432 μΩ E) 423 μΩ Answer: D When a 100-Ω resistor is connected across the terminals of a battery of emf ε and internal resistance r, the battery delivers 0.794 W of power to the 100-Ω resistor. When the 100-Ω resistor is replaced by a 200-Ω resistor, the battery delivers 0.401 W of power to the 200-Ω resistor. What are the emf and internal resistance of the battery? A) ε = 10.0 V, r = 5.02 Ω B) ε = 4.50 V, r = 4.00 Ω C) ε = 9.00 V, r = 2.04 Ω D) ε = 9.00 V, r = 1.01 Ω E) ε = 12.0 V, r = 6.00 Ω Answer: D For the circuit shown in the figure, what current does the ideal ammeter read? A) 0.033 A B) 0.078 A C) 0.23 A D) 0.12 A Answer: A For the circuit shown in the figure, what is the current through resistor R1? A) 0.071 A B) 0.13 A C) 0.029 A D) 0.016 A Answer: A A galvanometer has an internal resistance of 100 Ω and deflects full-scale at a current of 2.00 mA. What size resistor should be added to it to convert it to a millivoltmeter capable of reading up to 400 mV, and how should this resistor be connected to the galvanometer? A) 50.0 Ω in series with the galvanometer B) 50.0 Ω in parallel with the galvanometer C) 75.0 Ω in parallel with the galvanometer D) 100 Ω in series with the galvanometer E) 100 Ω in parallel with the galvanometer Answer: D For the circuit shown in the figure, what is the current through resistor R3? A) 0.043 A B) 1.5 A C) 0.028 A D) 0.086 A Answer: A For the circuit shown in the figure, all quantities are accurate to 2 significant figures. What is the value of the current I1? A) 0.32 A B) 0.11 A C) 0.29 A D) 0.61 A E) 0.89 A Answer: D (a) Just after closing the switch S, what is the current in the 15.0-Ω resistor? A) 0.00 A B) 1.67 A C) 2.50 A D) 3.33 A E) 5.00 A (b) After the switch S has been closed for a very long time, what is the potential difference across the 28.0-μF capacitor? A) 0.00 V B) 25.0 V C) 3.33 V D) 37.5 V E) 50.0 V Answer: (a) A (b) B A galvanometer with a resistance of 40.0 Ω deflects full scale at a current of 2.0 mA. What resistance should be used with this galvanometer in order to construct a voltmeter that can read a maximum of 50 V? A) 25 kΩ B) 27 kΩ C) 29 kΩ D) 31 kΩ E) 35 kΩ Answer: A A multiloop circuit is shown in the figure. It is not necessary to solve the entire circuit. The current I2 is closest to A) -6 A. B) 6 A. C) 8 A. D) -8 A. E) zero. Answer: A A multiloop circuit is shown in the figure. It is not necessary to solve the entire circuit. Compared to the polarity shown in the figure, the emf ε1 is closest to A) -5 V. B) 5 V. C) 45 V. D) 51 V. E) -51 V. Answer: A For the circuit shown in the figure, the switch S is initially open and the capacitor voltage is 80V. The switch is then closed at time t = 0. How long after closing the switch will the current in the resistor be 7.0 μA? A) 87 s B) 95 s C) 78 s D) 69 s E) 61 s Answer: A A 6.0-μF capacitor is connected in series with= 5.0 MΩ resistor, and this combination is connected across an ideal 15-V DC battery. What is the current in the circuit when the capacitor has reached 20% of its maximum charge? A) 6.5 μA B) 2.4 μA C) 1.3 μA D) 4.7 μA E) 9.1 μA Answer: B A multiloop circuit is shown in the figure. Some circuit quantities are not labeled. It is not necessary to solve the entire circuit. The current I1 is closest to A) zero. B) +0.2 A. C) +0.4 A. D) -0.2 A. E) -0.4 A. Answer: B For the circuit shown in the figure, the switch S is initially open and the capacitor voltage is 80V. The switch is then closed at time t = 0. What is the charge on the capacitor when the current in the circuit is 33 μA? A) 1100 μC B) 1000 μC C) 960 μC D) 890 μC E) 830 μC Answer: A A multiloop circuit is shown in the figure. Some circuit quantities are not labeled. It is not necessary to solve the entire circuit. The emf ε is closest to A) +3 V. B) +19 V. C) -3 V. D) -10 V. E) -1 V. Answer: B A multiloop circuit is shown in the figure. Some circuit quantities are not labeled. It is not necessary to solve the entire circuit. The current I2 is closest to A) +0.1 A. B) +0.3 A. C) +0.5 A. D) -0.1 A. E) -0.3 A. Answer: E A 4.0-mF capacitor is discharged through a 4.0-kΩ resistor. How long will it take for the capacitor to lose half its initial stored energy? A) 9.2 s B) 2.7 s C) 10.2 s D) 5.5 s E) 1.6 s Answer: D An uncharged 1.0-μF capacitor is connected in series with a 23-kΩ resistor, an ideal 7.0-V battery, and an open switch. What is the voltage across the capacitor 11 ms after closing the switch? A) 2.7 V B) 1.6 V C) 2.6 V D) 0.62 V Answer: A A beam of electrons is accelerated through a potential difference of 10 kV before entering a region having uniform electric and magnetic fields that are perpendicular to each other and perpendicular to the direction in which the electron is moving. If the magnetic field in this region has a value of 0.010 T, what magnitude of the electric field is required if the particles are to be undeflected as they pass through the region? A) 2.3 × 103 V/m B) 7.9 × 103 V/m C) 5.9 × 105 V/m D) 6.0 × 105 V/m E) 7.2 × 106 V/m Answer: C An L-shaped metal machine part is made of two equal-length segments that are perpendicular to each other and carry a 4.50-A current as shown in the figure. This part has a total mass of 3.80 kg and a total length of 3.00 m, and it is in an external 1.20 -T magnetic field that is oriented perpendicular to the plane of the part, as shown. What is the magnitude of the NET magnetic force that the field exerts on the part? A) 8.10 N B) 11.5 N C) 16.2 N D) 22.9 N E) 32.4 N Answer: B An electron moving with a velocity v= 5.0 × 107 m/s i ^ enters a region of space where perpendicular electric and a magnetic fields are present. The electric field is E = j^. What magnetic field will allow the electron to go through the region without being deflected? A) B = +2.0 × 10-4 T j^ B) B = ‐2.0 × 10-4 T j^ C) B = +2.0 × 10-4 T k ^ D) B = ‐2.0 × 10-4 T k ^ E) B = +5.0 × 10-4 T Answer: C An electron traveling toward the north with speed 4.0 × 105 m/s enters a region where the Earthʹs magnetic field has the magnitude 5.0 × 10-5 T and is directed downward at 45° below horizontal. What is the magnitude of the force that the Earthʹs magnetic field exerts on the electron? (e = 1.60 × 10-19 C) A) 2.3 × 10-18 N B) 3.2 × 10-18 N C) 2.3 × 10-19 N D) 3.2 × 10-19 N E) 2.3 × 10-20 N Answer: A The figure shows a velocity selector that can be used to measure the speed of a charged particle. A beam of particles is directed along the axis of the instrument. A parallel plate capacitor sets up an electric field E, which is oriented perpendicular to a uniform magnetic field B. If the plates are separated by 2.0 mm and the value of the magnetic field is 0.60 T, what voltage between the plates will allow particles of speed 5.0 × 10^5 m/s to pass straight through without deflection? A) 600 V B) 1900 V C) 3800 V D) 190 V E) 94 V Answer: A A uniform magnetic field of magnitude 0.80 T in the negative z direction is present in a region of space, as shown in the figure. A uniform electric field is also present and is set at 76,000 V/m in the +y direction. An electron is projected with an initial velocity v0 = 9.5 × 104 m/s in the +x direction. The y component of the initial force on the electron is closest to which of the following quantities? (e = 1.60 × 10-19 C) A) ‐2.4 × 10-14 N B) +2.4 × 10-14 N C) ‐1.0 × 10-14 N D) +1.0 × 10-14 N E) zero Answer: A For the circuit shown in the figure, the switch S is initially open and the capacitor is uncharged. The switch is then closed at time t = 0. How many seconds after closing the switch will the energy stored in the capacitor be equal to 50.2 mJ? A) 81 s B) 65 s C) 97 s D) 110 s E) 130 s Answer: A A particle with charge -5.00 C initially moves at v = (1.00 i^ + 7.00 j^) m/s. If it encounters a magnetic field B = 10.00 T k ^ , find the magnetic force vector on the particle. A) (-350 i^ + 50.0 j^) N B) (-350i ^- 50.0 j^) N C) (350i ^+ 50.0 j^) N D) (350i ^- 50.0 j^) N Answer: A A wire segment 1.2 m long carries a current I = 3.5 A and is oriented as shown in the figure. A uniform magnetic field of magnitude 0.50 T pointing toward the ‐x direction is present as shown. The +z-axis points directly into the page. What is the magnetic force vector on the wire segment? A) +1.6 N j ^ B) ‐1.6 N k ^ C) +1.6 N k ^ D) (+1.3 j ^ ‐ 1.6 k ^ ) N E) (‐1.3 j ^+ 1.6 k ^ N Answer: C A uniform magnetic field of magnitude 0.80 T in the negative z-direction is present in a region of space, as shown in the figure. A uniform electric field is also present. An electron that is projected with an initial velocity v0 = 9.1 × 104 m/s in the positive x-direction passes through the region without deflection. What is the electric field vector in the region? A) -73 kV/m j^ B) +73 kV/m i ^ C) +110 kV/m i^ D) +110 kV/m j^ E) -110 kV/m j ^ Answer: A An electron moving perpendicular to a uniform magnetic field of 3.2 × 10-2 T moves in a circle of radius 0.40 cm. How fast is this electron moving? (mel = 9.11 × 10-31 kg. e = 1.60 × 10-19 C) A) 2.2 × 107 m/s B) 1.9 × 10-2 m/s C) 1.9 × 10-30 m/s D) 3.0 × 106 m/s E) 8.0 × 106 m/s Answer: A A 4.0-μF capacitor that is initially uncharged is connected in series with a 4.0-kΩ resistor and an ideal 17.0-V battery. How much energy is stored in the capacitor 17 ms after the battery has been connected? A) 250,000 nJ B) 15,000 kJ C) 25 μJ D) 890 nJ Answer: A A proton starting from rest travels through a potential of 1.0 kV and then moves into a uniform 0.040-T magnetic field. What is the radius of the protonʹs resulting orbit? (mproton =1.67 × 10-27 kg, e = 1.60 × 10-19 C) A) 0.080 m B) 0.11 m C) 0.14 m D) 0.17 m E) 0.19 m Answer: B A wire segment 1.2 m long carries a current I = 3.5 A, and is oriented as shown in the figure. The +x-axis points directly into the page. A uniform magnetic field of magnitude 0.50 T pointing toward the ‐x direction is present as shown. What is the magnetic force vector on the wire segment? A) (+1.1 j ^ ‐ 1.8 k ^ ) N B) (‐1.1 j^ + 1.8 k ^ ) N C) (‐1.1 j^ ‐ 1.8 k ^ ) N D) (+1.8 j ^ ‐ 1.1 k ^ ) N E) (‐1.8 j^ + 1.1 k ^ ) N Answer: D A charged particle of mass 0.0020 kg is subjected to a 6.0 T magnetic field which acts at a right angle to its motion. If the particle moves in a circle of radius 0.20 m at a speed of 5.0 m/s, what is the magnitude of the charge on the particle? A) 0.0083 C B) 120 C C) 0.00040 C D) 2500 C Answer: A A long straight very thin wire on the y-axis carries a 10-A current in the positive y-direction. A circular loop 0.50 m in radius, also of very thin wire and lying in the yz-plane, carries a 9.0-A current, as shown. Point P is on the positive x-axis, at a distance of 0.50 m from the center of the loop. What is the magnetic field vector at point P due to these two currents? (μ0 =4π × 10-7 T · m/A) A) zero B) ‐8.0 × 10-6 T k ^ C) (+4.0 × 10-6 T) i ^ ‐ (4.0 × 10-6 T) k ^ D) (‐4.0 × 10-6 T) i^ ‐ (4.0 × 10-6 T) k ^ E) (‐4.0 × 10-6 T) i^ ‐ (8.0 × 10-6 T) k Answer: D In a mass spectrometer, a singly-charged particle (charge e) has a speed of 1.0 × 106 m/s and enters a uniform magnetic field of 0.20 T. The radius of the circular orbit of the particle is 0.020 m. What is the mass of this particle? (e = 1.60 × 10-19 C) A) 3.2 × 10-28 kg B) 6.4 × 10-28 kg C) 1.7 × 10-27 kg D) 4.5 × 10-27 kg E) 3.1 × 10-31 kg Answer: B A rectangular loop of wire carrying a 4.0-A current is placed in a magnetic field of 0.60 T. The magnitude of the torque acting on this wire when the plane of the loop makes a 30° angle with the field is measured to be 1.1 N · m. What is the area of this loop? A) 0.20 m2 B) 0.40 m2 C) 0.26 m2 D) 0.80 m2 E) 0.53 m2 Answer: E A doubly charged ion (charge 2e) with velocity 6.9 × 106 m/s moves in a circular path of diameter 60.0 cm in a magnetic field of 0.80 T in a mass spectrometer. What is the mass of this ion? (e = 1.60 × 10-19 C) A) 11 × 10-27 kg B) 6.7 × 10-27 kg C) 4.5 × 10-27 kg D) 3.3 × 10-27 kg E) 8.2 × 10-27 kg Answer: A A circular loop of diameter 10 cm, carrying a current of 0.20 A, is placed inside a magnetic field B = 0.30 T k ^ . The normal to the loop is parallel to a unit vector n ^= -0.60 i^ - 0.80 j^. Calculate the magnitude of the torque on the loop due to the magnetic field. A) 4.7 × 10-4 N · m B) 2.8 × 10-4 N · m C) 0.60 × 10-4 N · m D) 1.2 × 10-4 N · m E) zero Answer: A An electron enters a magnetic field of 0.75 T with a velocity perpendicular to the direction of the field. At what frequency does the electron traverse a circular path? (mel = 9.11 × 10-31 kg, e= 1.60 × 10-19 C) A) 2.1 × 1010 Hz B) 4.8 × 10-7 Hz C) 2.1 × 1014 Hz D) 4.8 × 10-11 Hz Answer: A Two coaxial circular coils of radius R = 15 cm, each carrying 4.0 A in the same direction, are positioned a distance d = 20 cm apart, as shown in the figure. Calculate the magnitude of the magnetic field halfway between the coils along the line connecting their centers. (μ0 = 4π ×10-7 T · m/A) A) 0.90 × 10-5 T B) 3.9 × 10-5 T C) 1.9 × 10-5 T D) 6.3 × 10-5 T E) 9.2 × 10-5 T Answer: C Alpha particles (charge = +2e, mass = 6.68 × 10-27 kg, e = 1.60 × 10-19 C) are accelerated in a cyclotron to a final orbit radius of 0.90 m. The magnetic field in the cyclotron is 0.30 T. The period of the circular motion of the alpha particles is closest to A) 0.44 μs. B) 0.67 μs. C) 0.87 μs. D) 1.1 μs. E) 1.3 μs. Answer: A A rigid rectangular loop, which measures 0.30 m by 0.40 m, carries a current of 5.5 A, as shown in the figure. A uniform external magnetic field of magnitude 2.9 T in the negative x direction is present. Segment CD is in the xz-plane and forms a 35° angle with the z-axis, as shown. Find the magnitude of the external torque needed to keep the loop in static equilibrium. A) 1.1 N · m B) 0.73 N · m C) 1.3 N · m D) 1.4 N · m E) 1.6 N · m Answer: A A straight wire that is 0.60 m long is carrying a current of 2.0 A. It is placed in a uniform magnetic field of strength 0.30 T. If the wire experiences a force of 0.18 N, what angle does the wire make with respect to the magnetic field? A) 25° B) 30° C) 35° D) 60° E) 90° Answer: B A wire carrying a current is shaped in the form of a circular loop of radius 3.0 mm. If the magnetic field strength that this current produces at the center of the loop is 1.1 mT, what is the magnitude of the current that flows through the wire? (μ0 = 4π × 10-7 T · m/A) A) 5.3 A B) 16 A C) 9.1 A D) 23 A Answer: A A thin copper rod that is 1.0 m long and has a mass of 0.050 kg is in a magnetic field of 0.10 T. What minimum current in the rod is needed in order for the magnetic force to cancel the weight of the rod? A) 1.2 A B) 2.5 A C) 4.9 A D) 7.6 A E) 9.8 A Answer: C A circular loop of wire of radius 10 cm carries a current of 6.0 A. What is the magnitude of the magnetic field at the center of the loop? (μ0 = 4π × 10-7 T · m/A) A) 3.8 × 10-5 T B) 3.8 × 10-7 T C) 1.2 × 10-5 T D) 1.2 × 10-7 T E) 3.8 × 10-8 T Answer: A A wire carries a 4.0-A current along the +x-axis through a magnetic field B = (5.0 i ^ + 7.0 j ^ ) T. If the wire experiences a force of 30 N k ^ as a result, how long is the wire? A) 1.1 m B) 0.87 m C) 1.5 m D) 0.63 m Answer: A A circular coil of wire of 200 turns and diameter 2.0 cm carries a current of 4.0 A. It is placed in a magnetic field of 0.70 T with the plane of the coil making an angle of 30° with the magnetic field. What is the magnetic torque on the coil? A) 0.15 N · m B) 0.088 N · m C) 0.29 N · m D) 0.40 N · m E) 0.076 N · m Answer: A A rectangular loop of wire measures 1.0 m by 1.0 cm. If a 7.0 -A current flows through the wire, what is the magnitude of the magnetic force on the centermost 1.0-cm segment of the 1.0-m side of the loop? (μ0 = 4π × 10-7 T · m/A) A) 9.8 × 10-6 N B) 7.8 × 10-7 N C) 9.8 × 10-8 N D) 4.9 × 10-6 N Answer: A A round loop of diameter 12 cm, carrying a current of 0.40 A, is placed inside a magnetic field B = 0.20 T i ^+ 0.40 T j^ . The normal to the loop is parallel to the unit vector n ^= -0.60 i^ - 0.80 j^. What is the potential energy of the loop? A) ‐4.5 × 10-3 J B) +2.0 × 10-3 J C) ‐2.0 × 10-3 J D) ‐2.3 × 10-3 J E) +4.5 × 10-3 J Answer: B A very long straight wire carries a 12-A current eastward and a second very long straight wire carries a 14-A current westward. The wires are parallel to each other and are 42 cm apart. Calculate the force on a 6.4 m length of one of the wires. (μ0 = 4π × 10-7 T · m/A) A) 8.0 × 10-7 N B) 5.1 × 10-4 N C) 8.0 × 10-5 N D) 5.1 × 10-6 N E) 2.2 × 10-4 N Answer: B A rigid circular loop has a radius of 0.20 m and is in the xy-plane. A clockwise current I is carried by the loop, as shown. The magnitude of the magnetic moment of the loop is 0.75 A · m2. A uniform external magnetic field, B = 0.20 T in the positive x-direction, is present. An external torque changes the orientation of the loop from one of lowest potential energy to one of highest potential energy. The work done by this external torque is closest to A) 0.20 J B) 0.30 J C) 0.40 J D) 0.50 J E) 0.60 J Answer: B Three very long, straight, parallel wires each carry currents of 4.00 A, directed out of the page as shown in the figure. The wires pass through the vertices of a right isosceles triangle of side 2.00 cm. What is the magnitude of the magnetic field at point P at the midpoint of the hypotenuse of the triangle? A) 4.42 × 10-6 T B) 1.77 × 10-5 T C) 5.66 × 10-5 T D) 1.26 × 10-4 T E) 1.77 × 10-6 T Answer: C At what distance from the central axis of a long straight thin wire carrying a current of 5.0 A is the magnitude of the magnetic field due to the wire equal to the strength of the Earthʹs magnetic field of about 5.0 × 10-5 T? (μ0 = 4π × 10-7 T · m/A) A) 1.0 cm B) 2.0 cm C) 3.0 cm D) 4.0 cm E) 5.0 cm Answer: B The figure shows two long, parallel current-carrying wires. The wires carry equal currents I1 = I2 = 20 A in the directions indicated and are located a distance d = 0.5 m apart. Calculate the magnitude and direction of the magnetic field at the point P that is located an equal distance d from each wire. (μ0 = 4π × 10-7 T · m/A) A) 8 μT downward B) 8 μT upward C) 4 μT downward D) 4 μT upward E) 4 μT to the right Answer: B A very long thin wire produces a magnetic field of 0.0050 × 10-4 T at a distance of 3.0 mm. from the central axis of the wire. What is the magnitude of the current in the wire? (μ0 = 4π × 10-7 T · m/A) A) 7.5 mA B) 1.7 mA C) 3300 mA D) 24,000 mA Answer: A Two long parallel wires carry currents of 10 A in opposite directions. They are separated by 40 cm. What is the magnitude of the magnetic field in the plane of the wires at a point that is 20 cm from one wire and 60 cm from the other? (μ0 = 4π × 10-7 T · m/A) A) 1.5 μT B) 3.3 μT C) 6.7 μT D) 33 μT E) 67 μT Answer: C The magnetic field at a distance of 2 cm from a current carrying wire is 4 μT. What is the magnetic field at a distance of 4 cm from the wire? A) 1/2 μT B) 1 μT C) 2 μT D) 4 μT E) 8 μT Answer: C A long straight very thin wire on the y-axis carries a 10-A current in the positive y-direction. A circular loop 0.50 m in radius, also of very thin wire and lying in the yz-plane, carries a 9.0-A current, as shown. Point P is on the positive x-axis, at a distance of 0.50 m from the center of the loop. What is the magnetic field vector at point P due to these two currents? (μ0 =4π × 10-7 T · m/A) A) zero B) ‐8.0 × 10-6 T k ^ C) (+4.0 × 10-6 T) i ^ ‐ (4.0 × 10-6 T) k ^ D) (‐4.0 × 10-6 T) i^ ‐ (4.0 × 10-6 T) k ^ E) (‐4.0 × 10-6 T) i^ ‐ (8.0 × 10-6 T) k ^ Answer: D A long straight wire on the z-axis carries a current of 6.0 A in the positive direction. A circular loop in the xy-plane, of radius 10 cm, carries a 1.0-A current, as shown in the figure. Point P, at the center of the loop, is 25 cm from the z-axis. An electron is projected from P with a velocity of 1.0 × 106 m/s in the negative x-direction. What is the y component of the force on the electron? (e = 1.60 × 10-19 C, μ0 = 4π × 10-7 T · m/A) A) ‐1.0 × 10-18 N B) +1.0 × 10-18 N C) ‐2.0 × 10-18 N D) +2.0 × 10-18 N E) zero Answer: A As shown in the figure, a wire is bent into the shape of a tightly closed omega (Ω), with a circular loop of radius 4.0 cm and two long straight sections. The loop is in the xy-plane, with the center at the origin. The straight sections are parallel to the x-axis. The wire carries a 5.0-A current, as shown. What is the magnitude of the magnetic field at the center of the loop? (μ0 = 4π × 10-7 T · m/A) A) 25 μT B) 40 μT C) 54 μT D) 80 μT E) 104 μT Answer: C As shown in the figure, an insulated wire is bent into a circular loop of radius 6.0 cm and has two long straight sections. The loop is in the xy-plane, with the center at the origin. The straight sections are parallel to the z-axis. The wire carries a current of 8.0 A. What is the magnitude of the magnetic field at the origin? (μ0 = 4π × 10-7 T · m/A) A) 75 μT B) 81 μT C) 88 μT D) 110 μT E) 120 μT Answer: C A type of transmission line for electromagnetic waves consists of two parallel conducting plates (assumed infinite in width) separated by a distance a. Each plate carries the same uniform surface current density of 16.0 A/m, but the currents run in opposite directions. What is the magnitude of the magnetic field between the plates at a point 1.00 mm from one of the plates if a = 0.800 cm? (μ0 = 4π × 10-7 T · m/A) A) 3.20 × 10-3 T B) 1.00 × 10-5 T C) 4.63 × 10-5 T D) 2.01 × 10-5 T E) 7.07 × 10-4 T Answer: D A long, straight wire with 3.0 A current flowing through it produces magnetic field strength 1.0 T at its surface. If the wire has a radius R, where within the wire is the field strength equal to 36.0% of the field strength at the surface of the wire? Assume that the current density is uniform throughout the wire. (μ0 = 4π × 10-7 T · m/A) A) 0.36 R B) 0.060 R C) 0.64 R D) 0.030 R Answer: A The figure shows the cross-section of a hollow cylinder of inner radius a = 5.0 cm and outer radius b = 7.0 cm. A uniform current density of 1.0 A/ cm2 flows through the cylinder parallel to its axis. Calculate the magnitude of the magnetic field at a distance of d = 10 cm from the axis of the cylinder. (μ0 = 4π × 10-7 T · m/A) A) 0.00 T B) 1.5 × 10-4 T C) 2.5 × 10-4 T D) 4.5 × 10-4 T E) 0.50 × 10-4 T Answer: B A hollow cylinder with an inner radius of 4.0 mm and an outer radius of 30 mm conducts a 3.0-A current flowing parallel to the axis of the cylinder. If the current density is uniform throughout the wire, what is the magnitude of the magnetic field at a point 12 mm from its center? (μ0 = 4π × 10-7 T · m/A) A) 7.2 × 10-6 T B) 8.0 × 10-6 T C) 8.9 × 10-7 T D) 7.1 × 10-8 T Answer: A Chapter 30 Electromagnetic Induction A tube with a 3.0-mm radius has ions flowing through it along its length. To determine the rate at which the charge is being moved through the tube, the magnetic field just outside the tube is measured and found to be 44.0 × 10-4 T. If the only contributor to the magnetic field is the moving ions, and if the walls of the container are very thin and do not screen magnetism, what is the magnitude of the current flowing through the tube? (μ0 = 4π × 10-7 T · m/A) A) 66 A B) 132 A C) 829 A D) 415 A Answer: A A solenoid with 400 turns has a radius of 0.040 m and is 40 cm long. If this solenoid carries a current of 12 A, what is the magnitude of the magnetic field near the center of the solenoid? (μ0 = 4π × 10-7 T · m/A) A) 16 mT B) 4.9 mT C) 15 mT D) 6.0 mT E) 9.0 mT Answer: C Two long parallel wires carry currents of 20 A and 5.0 A in opposite directions. The wires are separated by 0.20 m. What is the magnitude of the magnetic field midway between the two wires? (μ0 = 4π × 10-7 T · m/A) A) 1.0 × 10-5 T B) 2.0 × 10-5 T C) 3.0 × 10-5 T D) 4.0 × 10-5 T E) 5.0 × 10-5 T Answer: E A solenoid having N turns and carrying a current of 2.000 A has a length of 34.00 cm. If the magnitude of the magnetic field generated at the center of the solenoid is 9.000 mT, what is the value of N? (μ0 = 4π × 10-7 T · m/A) A) 860.0 B) 1591 C) 2318 D) 3183 E) 1218 Answer: E An LR circuit contains an ideal 60-V battery, a 51-H inductor having no resistance, a 21-Ω resistor, and a switch S, all in series. Initially, the switch is open and has been open for a very long time. At time t = 0 s, the switch is suddenly closed. When the voltage across the resistor is equal to the voltage across the inductor, what is the current in the circuit? A) 1.4 A B) 0.57 A C) 1.1 A D) 0.86 A E) 1.7 A Answer: A The coil in a 60-Hz ac generator has 125 turns, each having an area of 3.0 × 10-2 m2 and is rotated in a uniform 0.12-T magnetic field. What is the peak output voltage of this generator? A) 170 V B) 120 V C) 200 V D) 110 V E) 220 V Answer: A A cylindrical insulated wire of diameter 5.0 mm is tightly wound 200 times around a cylindrical core to form a solenoid with adjacent coils touching each other. When a 0.10 A current is sent through the wire, what is the magnitude of the magnetic field on the axis of the solenoid near its center? (μ0 = 4π × 10-7 T · m/A) A) 6.6 × 10-5 T B) 2.5 × 10-5 T C) 1.3 × 10-5 T D) 3.6 × 10-5 T E) 9.8 × 10-5 T Answer: B A solenoid is wound with 970 turns on a form 4.0 cm in diameter and 50 cm long. The windings carry a current I in the sense that is shown in the figure. The current produces a magnetic field, of magnitude 4.3 mT, near the center of the solenoid. Find the current in the solenoid windings. (μ0 = 4π × 10-7 T · m/A) A) 1.8 A B) 1.5 A C) 1.3 A D) 2.2 A E) 2.0 A Answer: A Suppose that you wish to construct a simple ac generator having an output of 12 V maximum when rotated at 60 Hz. A uniform magnetic field of 0.050 T is available. If the area of the rotating coil is 100 cm2, how many turns do you need? A) 8 B) 16 C) 32 D) 64 E) 128 Answer: D An LR circuit contains an ideal 60-V battery, a 42-H inductor having no resistance, a 24-Ω resistor, and a switch S, all in series. Initially, the switch is open and has been open for a very long time. At time t = 0 s, the switch is suddenly closed. How long after closing the switch will the potential difference across the inductor be 24 V? A) 1.6 s B) 1.4 s C) 1.8 s D) 1.9 s E) 2.1 s Answer: A A solenoid of length 18 cm consists of closely spaced coils of wire wrapped tightly around a wooden core. The magnetic field strength is 2.0 mT inside the solenoid near its center when a certain current flows through the coils. If the coils of the solenoid are now pulled apart slightly, stretching it to 21 cm without appreciably changing the size of the coils, what does the magnetic field become near the center of the solenoid when the same current flows through the coils? (μ0 = 4π × 10-7 T · m/A) A) 1.7 mT B) 3.4 mT C) 0.85 mT D) 2.0 mT Answer: A A toroidal solenoid has a central radius of 0.50 m and a cross-sectional diameter of 10 cm. When a current passes through the coil of the solenoid, the magnetic field inside the solenoid at its CENTER has a magnitude of 2.0 μT. What is the largest value of the magnetic field inside the solenoid when this current is flowing? (μ0 = 4π × 10-7 T · m/A) A) 3.5 μT B) 1.8 μT C) 2.2 μT D) 0.50 μT E) 2.8 μT Answer: C You are designing a generator to have a maximum emf of 8.0 V. If the generator coil has 200 turns and a cross-sectional area of 0.030 m2, what should be the frequency of the generator in a uniform magnetic field of 0.030 T? A) 7.1 Hz B) 7.5 Hz C) 8.0 Hz D) 22 Hz E) 44 Hz Answer: A A 1000-turn toroidal solenoid has a central radius of 4.2 cm and is carrying a current of 1.7 A. What is the magnitude of the magnetic field inside the solenoid at the central radius? ( μ0 = 4π × 10-7 T · m/A) A) 8.1 mT B) 51 mT C) 16 mT D) 81 mT E) zero Answer: A A series LR circuit contains an emf source of 14 V having no internal resistance, a resistor, a 34 H inductor having no appreciable resistance, and a switch. If the emf across the inductor is 80% of its maximum value 4.0 s after the switch is closed, what is the resistance of the resistor? A) 14 Ω B) 1.9 Ω C) 1.5 Ω D) 5.0 Ω Answer: B What resistance should be added in series with a 3.0-H inductor to complete an LR circuit with a time constant of 4.0 ms? A) 0.75 k Ω B) 12 Ω C) 0.75 Ω D) 2.5 Ω Answer: A A rectangular coil having N turns and measuring 15 cm by 25 cm is rotating in a uniform 1.6-T magnetic field with a frequency of 75 Hz. The rotation axis is perpendicular to the direction of the field. If the coil develops a sinusoidal emf of maximum value 56.9 V, what is the value of N? A) 2 B) 4 C) 6 D) 8 E) 10 Answer: A Wire is wound on a square frame, 30 cm by 30 cm, to form a coil of 7 turns. The frame is mounted on a horizontal shaft through its center (perpendicular to the plane of the diagram), as shown in the figure. The coil is in clockwise rotation, with a period of 0.060 s. A uniform, horizontal, magnetic field of magnitude 0.40 T is present. At a given instant, the plane of the coil forms a 60° angle with the horizontal, as shown. At that instant, what is the magnitude of the emf induced in the coil? A) 13 V B) 23 V C) 2.1 V D) 3.6 V E) 26 V Answer: A A series LR circuit consists of a 2.0-H inductor with negligible internal resistance, a 100-ohm resistor, an open switch, and a 9.0-V ideal power source. After the switch is closed, what is the maximum power delivered by the power supply? A) 0.40 W B) 81 W C) 0.090 W D) 8.1 W E) 0.81 W Answer: E A 45-mH ideal inductor is connected in series with a 60-Ω resistor through an ideal 15-V DC power supply and an open switch. If the switch is closed at time t = 0 s, what is the current 7.0 ms later? A) 250 mA B) 650 mA C) 550 mA D) 280 mA E) 850 mA Answer: A What is the self-inductance of a solenoid 30.0 cm long having 100 turns of wire and a cross-sectional area of 1.00 × 10-4 m2? (μ0 = 4π × 10-7 T · m/A) A) 4.19 nH B) 4.19 pH C) 4.19 μH D) 4.19 mH E) 4.19 H Answer: C How much energy is stored in a room 3.0 m by 4.0 m by 2.4 m due to the earthʹs magnetic field with a strength of 5.0 × 10-5 T? (μ0 = 4π × 10-7 T · m/A) A) 570 mJ. B) 29 mJ. C) 10 mJ. D) 100 mJ. E) 570 mJ. Answer: B An inductor has a current I(t) = (0.500 A) cos[(275 s-1)t] flowing through it. If the maximum emf across the inductor is equal to 0.500 V, what is the self-inductance of the inductor? A) 4.37 mH B) 3.64 mH C) 2.75 mH D) 0.73 mH E) 1.43 mH Answer: B An insulated wire of diameter 1.0 mm and negligible resistance is wrapped tightly around a cylindrical core of radius 5.0 cm and length 30 cm to build a solenoid. What is the energy stored in this solenoid when a current I = 0.20 A flows through it? (μ0 = 4π × 10-7 T · m/A) A) 1.2 × 10-4 J B) 9.6 × 10-4 J C) 4.8 × 10-4 J D) 2.4 × 10-4 J E) 5.9 × 10-5 J Answer: E What is the energy density in the magnetic field 25 cm from a long straight wire carrying a current of 12 A? (μ0 = 4π × 10-7 T · m/A) A) 7.3 × 10-5 J/m3 B) 3.7 × 10-5 J/m3 C) 3.6 × 10-4 J/m3 D) 1.2 × 10-4 J/m3 E) The density cannot be determined without knowing the volume. Answer: B A solenoid of length 0.700 m having a circular cross-section of radius 5.00 cm stores 6.00 μJ of energy when a 0.400-A current runs through it. What is the winding density of the solenoid? ( μ0 = 4π × 10-7 T · m/A) A) 865 turns/m B) 472 turns/m C) 1080 turns/m D) 104 turns/m E) 327 turns/m Answer: D At a certain instant the current flowing through a 5.0-H inductor is 3.0 A. If the energy in the inductor at this instant is increasing at a rate of 3.0 J/s, how fast is the current changing? A) 0.20 A/s B) 0.40 A/s C) 0.10 A/s D) 0.80 A/s Answer: A For a long ideal solenoid having a circular cross-section, the magnetic field strength within the solenoid is given by the equation B(t) = 5.0t T, where t is time in seconds. If the induced electric field outside the solenoid is 1.1 V/m at a distance of 2.0 m from the axis of the solenoid, find the radius of the solenoid. A) 0.30 m B) 77 m C) 0.94 m D) 9.0 m Answer: C A loop of radius r = 3.0 cm is placed parallel to the xy-plane in a uniform magnetic field B = 0.75 T k ^ . The resistance of the loop is 18 Ω. Starting at t = 0, the magnitude of the field decreases uniformly to zero in 0.15 seconds. What is the magnitude of the electric current produced in the loop during that time? A) 0.79 mA B) 3.9 mA C) 1.7 mA D) 2.1 mA E) 0.20 mA Answer: A A 2.0-m long conducting wire is formed into a square and placed in the horizontal xy-plane. A uniform magnetic field is oriented 30.0° above the horizontal with a strength of 9.0 T. What is the magnetic flux through the square? A) 1.1 T · m2 B) 1.9 T · m2 C) 2.3 T · m2 D) 18 T · m2 Answer: A A circular coil of radius 5.0 cm and resistance 0.20 Ω is placed in a uniform magnetic field perpendicular to the plane of the coil. The magnitude of the field changes with time according to B = 0.50e-20t T. What is the magnitude of the current induced in the coil at the time t = 2.0 s? A) 1.3 mA B) 9.2 mA C) 7.5 mA D) 4.2 mA E) 2.6 mA Answer: E A ten-loop coil having an area of 0.23 m2 and a very large resistance is in a 0.047-T uniform magnetic field oriented so that the maximum flux goes through the coil. The coil is then rotated so that the flux through it goes to zero in 0.34 s. What is the magnitude of the average emf induced in the coil during the 0.34 s? A) 0.0032 V B) 0.00 V C) 0.032 V D) 0.32 V E) 1.0 V Answer: D A uniform magnetic field is applied perpendicular to the plane of a 60-turn circular coil with a radius of 6.0 cm and a resistance of 0.60 Ω. If the magnetic field increases uniformly from 0.20 T to 1.8 T in 0.20 s, what is the magnitude of the emf induced in the coil? A) 7.2 V B) 5.4 V C) 9.2 V D) 12 V E) 16 V Answer: B A 50-cm wire placed in an east-west direction is moved horizontally to the north with a speed of 2.0 m/s. The horizontal component of the earthʹs magnetic field at that location is 25 μT toward the north and the vertical component is 50μT downward. What is the emf induced between the ends of the wire? A) 10 μV B) 20 μV C) 30 μV D) 40 μV E) 50 μV Answer: E A coil of 160 turns and area 0.20 m2 is placed with its axis parallel to a magnetic field of initial magnitude 0.40 T. The magnetic field changes uniformly from 0.40 T in the +x direction to 0.40 T in the -x direction in 2.0 s. If the resistance of the coil is 16 Ω, at what rate is power generated in the coil? A) 5.0 W B) 10 W C) 15 W D) 20 W E) 25 W Answer: B A conducting bar slides without friction on two parallel horizontal rails that are 50 cm apart and connected by a wire at one end. The resistance of the bar and the rails is constant and equal to 0.10 Ω. A uniform magnetic field is perpendicular to the plane of the rails. A 0.080 -N force parallel to the rails is required to keep the bar moving at a constant speed of 0.50 m/s. What is the magnitude of the magnetic field? A) 0.10 T B) 0.25 T C) 0.36 T D) 0.54 T E) 0.93 T Answer: B A closed loop conductor that forms a circle with a radius of 2.0 m is located in a uniform but changing magnetic field. If the maximum emf induced in the loop is 5.0 V, what is the maximum rate at which the magnetic field strength is changing if the magnetic field is oriented perpendicular to the plane in which the loop lies? A) 0.40 T/s B) 2.5 T/s C) 0.080 T/s D) 5.0 T/s Answer: A As shown in the figure, a wire and a 10-Ω resistor are used to form a circuit in the shape of a square, 20 cm by 20 cm. A uniform but nonsteady magnetic field is directed into the plane of the circuit. The magnitude of the magnetic field is decreased from 1.50 T to 0.50 T in a time interval of 63 ms. The average induced current and its direction through the resistor, in this time interval, are closest to A) 63 mA, from b to a. B) 38 mA, from b to a. C) 63 mA, from a to b. D) 38 mA, from a to b. E) 95 mA, from a to b. Answer: A Chapter 32 AC Circuits An ac circuit is shown in the figure. The rms current in the circuit is measured to be 1.8 A. What is the capacitance of the capacitor? A) 23 μF B) 24 μF C) 21 μF D) 19 μF E) 18 μF Answer: A The 60-Hz ac source of a series circuit has a voltage amplitude of 120 V. The resistance, capacitive reactance, and inductive reactance are as shown in the figure. What is the rms current in the circuit? A) 0.097 A B) 0.11 A C) 0.12 A D) 0.14 A E) 0.17 A Answer: A (a) In an ac circuit, if the peak value of the voltage is 100 V, what is the rms value of the voltage? A) 141 V B) 100 V C) 210 V D) 71 V E) 120 V (b) In an ac circuit, if the rms value of the current is 100 mA, what is the peak value of the current? A) 141 mA B) 100 mA C) 210 mA D) 71 mA E) 120 mA Answer: (a) D (b) A The phase angle of an LRC series circuit with an inductive reactance of 200 Ω and a capacitive reactance of 100 Ω is 40.0°. What is the value of the resistor in this circuit? A) 100 Ω B) 119 Ω C) 156 Ω D) 200 Ω E) 265 Ω Answer: B An alternating current is supplied to an electronic component with a warning that the voltage across it should never exceed 12 V. What is the highest rms voltage that can be supplied to this component while staying below the voltage limit in the warning? A) 6 sqrt 2 V B) 12 sqrt2 V C) 144 V D) 6 V Answer: A The inductor in a radio receiver carries a current of amplitude 200 mA when a voltage of amplitude 2.40 V is across it at a frequency of 1400 kHz. What is the value of the inductance? A) 1.43 μH B) 1.36 μH C) 9.20 μH D) 4.42 μH E) 1.97 μH Answer: B A series ac circuit consists of an inductor having a reactance of 80 Ω and an inductance of 190 mH, a 40-Ω resistor, a capacitor whose reactance is 100 Ω, and an ac source. The rms current in the circuit is measured to be 2.2 A. What is the rms voltage of the source? A) 98 V B) 96 V C) 93 V D) 91 V E) 88 V Answer: A An ideal transformer consists of a 500-turn primary coil and a 2000-turn secondary coil. If the current in the secondary is 3.0 A, what is the current in the primary? A) 0.75 A B) 1.3 A C) 12 A D) 24 A E) 48 A Answer: C If the voltage amplitude across an 8.50-nF capacitor is equal to 12.0 V when the current amplitude through it is 3.33 mA, the frequency is closest to: A) 32.6 MHz B) 5.20 MHz C) 32.6 kHz D) 5.20 kHz E) 32.6 Hz Answer: B A 120-V rms voltage at 1000 Hz is applied to an inductor, a 2.00-μF capacitor and a 100-Ω resistor, all in series. If the rms value of the current in this circuit is 0.680 A, what is the inductance of the inductor? A) 34.2 mH B) 35.8 mH C) 11.4 mH D) 17.9 mH E) 22.8 mH Answer: B The phase angle of an LRC series circuit with an inductive reactance of 200 Ω, a resistor of 200 Ω and a certain capacitor at 1000 Hz is 40.0°. What is the value of the capacitance in this circuit? A) 1.95 μF B) 2.95 μF C) 3.95 μF D) 4.95 μF E) 5.95 μF Answer: D When a current of 2.0 A flows in the 100-turn primary of an ideal transformer, this causes 14 A to flow in the secondary. How many turns are in the secondary? A) 700 B) 356 C) 114 D) 14 E) 4 Answer: D A series LRC circuit has a sinusoidal voltage supplied to it at 197 kHz with a peak voltage of 270 V, a 41-kΩ resistance, a 14-μF capacitor, and a 63-H inductance. What is the peak current for this circuit? A) 3.5 μA B) 2.3 μA C) 4.2 μA D) 6.6 μA Answer: A A series circuit consists of a 50-Hz ac source, a 50-Ω resistor, a 0.50-H inductor, and a 60-μF capacitor. The rms current in the circuit is measured to be 3.1 A. What is the voltage amplitude of the source? A) 510 V B) 270 V C) 220 V D) 180 V E) 160 V Answer: A The phase angle of an LRC series circuit with a capacitive reactance of 40 Ω, a resistor of 100 Ω and a certain inductor at 1000 Hz is 40.0°. What is the value of the inductance in this circuit? A) 11.8 mH B) 124 mH C) 212 mH D) 61.9 mH E) 19.7 mH Answer: E A series circuit consists of ac source, a 90-Ω resistor, a 0.80-H inductor, and an 80-μF capacitor. The frequency of the source is adjusted so that the capacitive reactance is equal to twice the inductive reactance. What is the frequency of the source? A) 14 Hz B) 13 Hz C) 16 Hz D) 17 Hz E) 19 Hz Answer: A An LRC series circuit has voltage supplied to it at a frequency of 13.0 kHz with a phase difference between the current and the voltage of magnitude 0.20 rad. If the circuit has a capacitance of 5.0 μF and an inductance of 0.050 H find the resistance of the circuit. A) 20 kΩ B) 0.99 kΩ C) 9.0 kΩ D) 0.32 kΩ Answer: A An LRC series circuit consists of an 85.0-Ω resistor, a 14.0-μF capacitor, a 1.50-mH inductor, and a variable frequency ac source of voltage amplitude 13.25 V. At what angular frequency will the inductive reactance be 4.00 times as large as the capacitive reactance? A) 1.38 × 104 rad/s B) 6.90 × 103 rad/s C) 3.45 × 104 rad/s D) 2.20 × 104 rad/s E) 1.10 × 104 rad/s Answer: A In a transformer, how many turns are necessary in a 110-V primary if the 24-V secondary has 100 turns? A) 458 B) 240 C) 110 D) 22 E) 4 Answer: A An ac circuit is shown in the figure. The rms current in the circuit is 1.3 A. What is the peak magnetic energy in the inductance? A) 0.32 J B) 0.16 J C) 0.48 J D) 0.64 J E) 0.80 J Answer: A A series LRC ac circuit has a resistance of 4.0 kΩ, a capacitance of 33.0 μF, and an inductance of 23.0 H. If the frequency of the alternating current is 2.0/π kHz, what is the phase angle between the voltage and the current? A) 1.5 rad B) -1.6 rad C) 23 rad D) 3.1 rad Answer: A A 120-V rms voltage at 60.0 Hz is applied across an inductor, a capacitor, and a resistor in series. If the peak current in this circuit is 0.8484 A, what is the impedance of this circuit? A) 200 Ω B) 141 Ω C) 20.4 Ω D) 120 Ω E) 100 Ω Answer: A A transformer changes the 10,000 V power line to 120 V. If the primary coil contains 750 turns, how many turns are on the secondary? A) 3 B) 6 C) 9 D) 63,000 E) 21,000 Answer: C A 25.0-mH inductor, a 2.00-μF capacitor, and a certain resistor are connected in series across an ac voltage source at 1000 Hz. If the impedance of this circuit is 200 Ω, what is the resistance of the resistor? A) 100 Ω B) 184 Ω C) 200 Ω D) 552 Ω E) 579 Ω Answer: B What is the average power dissipated by a 25-Ω resistor in an LRC series ac circuit for which the power factor is equal to 0.25 and the maximum voltage of the ac source is 8.0 V? A) 0.040 W B) 0.32 W C) 0.16 W D) 0.62 W E) 0.080 W Answer: E A series circuit has a resistance of 4.0 Ω, a reactance (due to the capacitance) of 21.0 Ω, and a reactance (due to the inductance) of 17.0 Ω. Find the impedance of the circuit. A) 5.7 Ω B) 27 Ω C) 8.0 Ω D) 42 Ω Answer: A The primary coil of a transformer has 100 turns and its secondary coil has 400 turns. If the ac voltage applied to the primary coil is 120 V, what voltage is present in its secondary coil? A) 100 V B) 30 V C) 70 V D) 480 V E) 400 V Answer: D A series LRC ac circuit has a peak voltage of 111 V and a peak current of 2.00 A. If the current lags the voltage by 35.0°, what is the average power of the circuit? A) 91 W B) 182 W C) 78 W D) 156 W Answer: A An ac source having a maximum voltage output of 30 V is connected in series with a 50 -Ω resistor, a 0.60-H inductor, and a 20-μF capacitor. What is the maximum charge on the capacitor when the frequency of the source is adjusted so that the circuit is in resonance? A) 1.0 mC B) 0.00 mC C) 2.1 mC D) 4.2 mC E) 8.4 mC Answer: C A series LRC circuit consists of a 100-Ω resistor, a 0.100-μF capacitor and a 2.00-mH inductor connected across a 120-V rms ac voltage source operating at 1000/π. At what frequency will thiscircuit be in resonance? A) 70.7 kHz B) 17.9 kHz C) 22.5 kHz D) 35.3 kHz E) 11.3 kHz Answer: E An LRC ac circuit has a reactance (due to its capacitance) of 17 kΩ, a reactance (due to its inductance) of 9.0 kΩ, and a resistance of 28 kΩ. What is the power factor of the circuit? A) 0.96 B) 0.28 C) 1.04 D) 0.48 Answer: A For an LRC series circuit containing a resistance of 11.0 kΩ, a capacitance of 2.0 μF, and an inductance of 24.0 H, what frequency is needed to minimize the impedance? A) 0.023 kHz B) 0.14 kHz C) 10 kHz D) 1.7 kHz Answer: A For an RLC ac circuit, the rms current is 10 A. If the impedance is 12 kΩ when the voltage leads the current by 39°, find the average power of the circuit. A) 930 kW B) 47 kW C) 93 kW D) 190 kW Answer: A A series LRC ac circuit has a peak current of 1.0 A with a frequency of 54 kHz. If the resistance of the circuit is 51 kΩ, the capacitance of the circuit is 19 μF, and the inductance of the circuit is 25 μH, determine the average power of the circuit. A) 26 kW B) 77 kW C) 7.7 kW D) 4.1 kW Answer: A A series circuit consists of a 50-Hz ac source, a 40-Ω resistor, a 0.30-H inductor, and a 60-μF capacitor. The rms current in the circuit is measured to be 1.6 A. What is the power factor of the circuit? A) 0.70 B) 0.66 C) 0.63 D) 0.59 E) 0.56 Answer: A You can also click the terms or definitions to blur or reveal them R