Resistivity and Temperature Coefficients (at 20 C)

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1 Homework # 4 Resistivity and Temperature Coefficients (at 0 C) Substance Resistivity, Temperature ( m) Coefficient, (C ) - Conductors Silver.59 x Copper.6 x Aluminum.65 x Tungsten 5.6 x Iron 9.7 x Platinum 0.6 x Mercury 9 x Nichrome (alloy of Ni, Fe, Cr) 00 x Semiconductors Carbon (graphite) (3-60) x Germanium (-500) x Silicon Insulators Glass Hard Rubber American Wire Gauge AWG Diameter Diameter Cross Sectional Gauge (Inches) (mm) Area (mm ) Resistor Color Code Color Number Multiplier Tolerance Black 0 Brown 0 Red 0 Orange Yellow Green Blue Violet Gray 0 White Gold 0-5% Silver 0-0% No Color 0%

2 4. Voltage, Current, Resistance, and Ohm's Law Homework # 5 See Homework #4 in this chapter for the tables on "Resistivity and Temperature Coefficients (0 C)" and "American Wire Gauge". I 0. A battery charger charges a battery with a current of 3.5 A for 3.00 h. a.) How much charge passes through the battery? b.) How many electrons are transferred to the battery? 0. Nerve cells "communicate" with each other via varying the potential difference between the two sides of a neuron's (nerve cell) cell wall. What is the current if 00 Na + ions flow across a cell membrane in 4.5 s? A sodium ion has protons, neutrons, and 0 electrons so it has one more proton than electrons. 03. What is the resistance of a heater if it produces a current of 5.0 A when plugged into a household outlet that is wired for 0 V? 04. A.50-V flashlight battery (D cell) is placed in a flashlight whose bulb has a resistance of.35. How many electrons leave the battery if the flashlight is left on for 0.0 minutes? 05. What is the resistance of a 4-Gauge copper wire that is 4.75 m long? 06. What is the diameter of a 75.0-cm length of tungsten wire whose resistance is 0.350? 07. An electrical device draws.65 A at 0 V. In the summertime, demand for power in the community can cause the voltage to drop by 0.0%. If the voltage drops by this amount, how much current will this device draw? 0. A bird stands on an electric transmission line carrying 500 A. The line has.5 x 0-5 resistance per meter. If the bird's feet are 3.00 cm apart, how much voltage does it feel. 09. A 50.0-m long wire with a diameter of.60 mm has a resistance of 5.6. What is the resistance of a 90.0-m length of wire with a diameter of 4.0 mm made of the same material? 0. What diameter of tungsten wire must be made to have the same resistance as an equal length of.40-mm-diameter copper wire?. How much would the temperature of a copper wire, initially at 0.0 C, have to be raised to increase its resistance by 35%?. A 00-W light bulb has a resistance of.0 when cold and 40 when on (hot). If the average temperature coefficient of resistivity,, is (C ) -, approximate the temperature of the filament when the bulb is "on". I 3. Copper has approximately 0 9 free electrons per cubic meter. What is the approximate average velocity of electrons in a.00 mm radius wire carrying.00 A? ANSWERS: 0. a.) 35,00 C b.).9 x x 0 - A x mm A x 0-4 V mm. 5.5 C. 00 C x 0-5 m/s

3 4. Electric Power Homework # 6 I 0. What is the current through a 60.0-W light bulb wired (via a lamp to an outlet) to a 0-V power source (American household)? 0. The element of an electric oven that is designed to produce 3.00 kw of heat when wired to a 40-V source. What is the resistance of this element? 03. A 9.00-V transistor radio draws a maximum of 300 ma of current. What is the maximum power consumption of this radio? 04. If the starter motor in an automobile draws 50 A from the.0-v battery, how much power is being consumed? 05. What is the maximum voltage that can be applied across a 500- resistor rated at ½ W? 06. A woman vacuums the house for 45.0 minutes using a vacuum cleaner rated at drawing.0 A on 0-V line. a.) How many kwh does a vacuum cleaner use? b.) If the electric company charges \$0.094 per kwh, how much did this activity cost? 07. A physics student wishes to see how many 00-W light bulbs will be required to blow the 5.0-A fuse for the room in which his experiment is conducted. Assuming he has unlimited lamps, 0-V outlets, and 00-W light bulbs, what is the maximum number of bulbs that can be used without blowing the fuse? Assume the room is wired in series so the current drawn from each outlet arithmetically adds to the current drawn from the other outlets. 0. What is the total amount of energy stored in a.0-v, 40.0-A h car battery that is fully charged? 09. What is the efficiency of a 5.00-hp electric motor that draws. A from a 40-V line? 0. A power station delivers 50 kw of power to a town through power lines that have a net resistance of.5. a.) How much power is wasted as heat generated in the power lines if the power is delivered at 400 V? b.) How much power is wasted as heat generated in the power lines if the power is delivered at 4,000 V? I. The current in an electromagnet connected to a 40-V line is.5 A. At what rate must cooling water pass over the coils of the electromagnet if the water temperature is to rise by no more than.00 C?. A small immersion heater is designed to plug into the lighter accessory of a car and heat a cup of water for coffee. If the temperature of 0 ml of water increases from 6.00 C to 93.5 C in 7.50 minutes, how much current does it draw from the.0-v car battery? ANSWERS: A W W V 06. a.).0 kwh b.) \$0.06 (0.6 cents) bulbs x 0 6 J % 0. a.) 34 kw b.) kw kg/s (3 kg/h). 4.9 A

4 4.3 Alternating Current Homework # 7 I 0. An ac voltage supply with a peak voltage of 0 V is applied across a 40- resistor. a.) What is the value of the peak current in the resistor? b.) What is the value of the rms current in the resistor? 0. What is the peak current in a.0-k resistor connected to a 40-V ac power source? 03. Determine the resistance of the following 0-V rms light bulbs. a.) 40.0 W b.) 60.0 W c.) 75.0 W d.) 00 W 04. What is the peak current passing through a 00-W light bulb connected to a 0-V ac line? 05. If the peak value of alternating current passing through a 50-W electric device is 4.5 A, what is the rms voltage across it? 06. What is the maximum instantaneous value of the power dissipated by a 75.0-W light bulb? 07. A 5.0- heater coil is connected to a 40-V ac line. a.) What is the average power used by this coil? b.) What is the maximum value of the instantaneous power? c.) What is the minimum value of the instantaneous power? ANSWERS: 0. a.) A b.) 0.65 A A 03. a.) 360 b.) 40 c.) 9 d.) A V W 07. a.) 340 W b.) 760 W c.) 0 W

5 4.4 Resistors in Series and Parallel Homework # 0. Each cell of the circuit shown to the right has an emf of.50 V. a.) What is the net emf of the circuit? b.) What is the net resistance of the circuit? c.) What is the current through each cell of the battery? d.) Determine the current through each resistor. e.) What is the voltage, V, across resistor R? f.) What is the power generated by the battery V A? g.) What is the power generated by the battery V B? h.) What is the power generated by this combination of batteries? i.) What is the power consumption of resistor R 3 in this circuit? j.) At what rate is energy transformed by resistor R 4? k.) What is potential difference between points A and B? l.) What is the potential difference between points A and C? R.00 Problem 0 A R 3.0 R3 4.0 R4.0 VA VB B C R Each cell of the circuit shown to the right has an emf of.50 V. a.) What is the net emf of the circuit? b.) What is the net resistance of the circuit? c.) Determine the current through each resistor. d.) What is the voltage, V, across resistor R? e.) What is the power consumption of resistor R 3 in this circuit? 03. Assume all of the light bulbs in the circuit shown below are identical, each with a resistance of R. a.) What is the net resistance of the circuit? b.) Determine the current through each light bulb. c.) What is the voltage, V 4, across light bulb L 4? d.) What is the power consumption of light bulb L 3 in this circuit? Problem 0 R3.0 R4 3.0 R.0 VB R 6.00 Problem 03 VA L L L 3 L 4 L 5 ANSWERS: 0. a.) 6.00 V b.) 7.0 c.) 0. A 0. d.) I I 5 0. A, I A, I 3 0. A, I A e.).56 V f.).00 W g.) W 0. h.).33 W i.) 0.7 W j.) 0.0 W k.).56 V l.) 4. V 0. a.).0 V b.) c.) I 0.65 A, I 0.46 A, I 3 I A d.).30 V e.) 0.50 W 03. a.) R b.) I I R, I 3 R, I 4 I 5 R c.) V 4 d.) P 3 6 R 4

7 4.6 Kirchhoff's Rules Homework # 0 0. In the circuit shown to the right, V 0.0 V and V 0.0 V. Ignore any internal resistance in the power supplies. a.) What is the current through resistor R? b.) What is the current through resistor R? c.) What is the current through resistor R 3? d.) What is the current through resistor R 4? e.) What is the current through resistor R 5? f.) What is the current through resistor R 6? g.) What is the voltage across resistor R 4? h.) What is the power consumption of resistor R 6? i.) What is the power generated by battery V? j.) What is the potential difference between points A and C? k.) What is the potential difference between points B and C? R 4.0 R 5.0 A Problem 0 R3 3.0 R B R R6.0 V V C 0. In the circuit shown to the right, V 60.0 V, V 45.0 V and V V. Ignore any internal resistance in the power supplies. a.) What is the current through resistor R? b.) What is the current through resistor R? c.) What is the current through resistor R 3? d.) What is the current through resistor R 4? e.) What is the current through resistor R 5? f.) What is the current through resistor R 6? g.) What is the current through resistor R 7? h.) What is the current through resistor R? i.) What is the voltage across resistor R 3? j.) What is the power consumption of resistor R 6? k.) What is the power generated by battery V? l.) What is the potential difference between points A and B? R 5.0 R.0 A Problem 0 R4 6.0 R5.0 R V V3 R6 4.0 R7 0.0 V R.0 B ANSWERS: 0. a.).03 A b.).03 A c.).03 A d.) 0.43 A e.).46 A f.).46 A g.).0 V 0. h.) 3.4 W i.).3 W j.) 5 V k.) 9.0 V 0. a.) A b.) 0.3 A c.) A 0. d.) 0.3 A e.) 0.3 A f.) 0.3 A g.) A h.) A i.) 9.6 V j.).90 W 0. k.) 5.56 W l.) 5.6 V

8 4.7 Capacitors in Series and Parallel Homework # I 0. Six 7.0- F are to be used in a circuit. a.) What is their equivalent capacitance if they are connected in series? b.) What is their equivalent capacitance if they are connected in parallel? 0. A technician wants to change a circuit containing a 6400-pF capacitor to one with a capacitance of 50 pf. a.) How should an additional capacitor be added (in series or parallel) to achieve this goal? b.) What size capacitor should be added to the circuit to achieve this goal? 03. The capacitance of a portion of a circuit is to be reduced from F to F. a.) How should an additional capacitor be added (in series or parallel) to achieve this goal? b.) What size capacitor should be added to the circuit to achieve this goal? 04. A circuit is constructed as shown in the diagram to the right. Problem 04 a.) What is the equivalent capacitance of the circuit? b.) What is the total charge stored on the capacitors of this circuit? c.) What is the total energy stored on the capacitors of this circuit? C4.40 F d.) What is the charge, Q, stored on capacitor C? e.) What is the voltage, V, across capacitor C? f.) What is the energy stored, E, on capacitor C? g.) What is the charge, Q, stored on capacitor C? h.) What is the voltage, V, across capacitor C? C3.0 F i.) What is the energy stored, E, on capacitor C? j.) What is the charge, Q 3, stored on capacitor C 3? k.) What is the voltage, V 3, across capacitor C 3? l.) What is the energy stored, E 3, on capacitor C 3? C 4.0 F m.) What is the charge, Q 4, stored on capacitor C 4? n.) What is the voltage, V 4, across capacitor C 4? o.) What is the energy stored, E 4, on capacitor C 4? p.) What is the charge, Q 5, stored on capacitor C 5? V 5.0 V q.) What is the voltage, V 5, across capacitor C 5? r.) What is the energy stored, E 5, on capacitor C 5? Problem Three capacitors of capacitance 00 pf, 0.0 F, and 3400 pf are available to be used in a circuit in any arrangement desirable. a.) Describe arrangement and amount for maximum capacitance. b.) Describe arrangement and amount for minimum capacitance. C 5.0 F C F C 6.30 F C3.0 F C 4.40 F 06. A circuit is constructed as shown in the diagram to the right. a.) Determine the equivalent capacitance for the circuit. b.) What is the charge and voltage on each capacitor? V 40.0 V ANSWERS: 0. a.).0 F b.) 43. F 0. a.) parallel b.) 450 pf 03. a.) series b.) 0.35 F 04. a.).39 F b.).56 mc c.) 66.4 mj d.) 3 C e.) 4. V f.) 5.57 mj g.) 3 C h.) 36.7 V 04. i.) 4.4 mj j.).03 mc k.) 5.0 V l.) 44. mj m.) 95 C n.) 35. V o.) 5. mj p.) 95 C 04. q.) 50.0 V r.) 7.37 mj 05. a.) parallel (5,00 pf) b.) series ( pf) 06. a.) 6. F 06. b.) Q 73 C, V. V; Q 96.0 C, V. V; Q 3 77 C, V 3. V

9 4. Resistor-Capacitor (RC) Circuits Homework # 0. A fully-charged capacitor is wired, in series, to a switch (initially open), a galvanometer, and an.0-k resistor. The galvanometer is actually a computer, connected to the above circuit via sensors and an interface box, with software that measures current sensitive to the scale of a A. The switch is closed and the computer generates a graph of current discharging from the capacitor as a function of time as shown below. a.) What is the initial current out of the capacitor? b.) Graphically estimate the total charge initially stored on the capacitor. c.) What is the time constant for this circuit? d.) Write an equation that describes the current out of the capacitor as a function of time. e.) What is the current at 0.0 s? f.) What is the initial voltage across the capacitor? g.) Write an equation that describes the voltage across the capacitor as a function of time. h.) What is the voltage across the capacitor at 0.0 s? i.) What is the capacitance of this capacitor? j.) Calculate the total charge initially on the capacitor. k.) Write an equation that describes the charge on the capacitor as a function of time. l.) What is the charge on the capacitor at 0.0 s? m.) What is the initial energy stored on the capacitor? Current ( A) Discharging Current as a Function of Time 0. A 000- resistor is connected in parallel to the capacitor in the circuit below and to the right. The switch is closed and the circuit eventually reaches equilibrium. At equilbrium, determine. a.) the current in the 000- resistor b.) voltage across the 000- resistor c.) the charge on the capacitor Time (s) Problems 0 and 03 C 640 F 03. A circuit is constructed as shown to the right. Initially, the capacitor has no charge on it. The moment the switch is closed, a stopwatch is started. a.) What is the time constant for this circuit? b.) What is the initial current flow in this circuit? c.) Write an equation that describes the current out of the capacitor as a function of time. d.) What is the current flow after.40 s? e.) How long will it take for the current to drop to.00% of its original value? f.) What charge will have accumulated on the capacitor after.40 s? g.) What will be the voltage across the capacitor after 4.0 s? ANSWERS: 0. a.) 600 A b.) 9.50 mc c.) 6.0 s d.) I e - t g.) V. e - t V h.) 3.09 V i.) 9 F j.) 9.60 mc k.) mc R 000 V 9.00 V A e.) 4.04 A f.) 0. V Q. e - t l.).75 mc 0. m.) 0.05 J 0. a.) 3.00 ma b.) 3.00 V c.).9 mc I. e - t. 450mA d.) ma e.) 5.9 s f.) 4. mc g.).79 V 03. a.). s b.) 4.50 ma c.) Switch

10 4.9 DC Ammeters and Voltmeters Homework # 3 I 0. What is the resistance on a 0.0-V scale if the meter sensitivity is 5,000 /V? 0. An ammeter has a sensitivity of 0,000 /V and a full-scale deflection when 00 mv is across it. What minimum current passing through the galvanometer causes full-scale deflection? 03. A galvanometer has a full-scale deflection of 60 A when 0 mv are across it. a.) How could this galvanometer be used to make an ammeter with a full-scale deflection of.00 A? b.) How could this galvanometer be used to make an ammeter with a full-scale deflection of 0.0 A? c.) How could this galvanometer be used to make a voltmeter with a full-scale deflection of 5.00 V? d.) How could this galvanometer be used to make a voltmeter with a full-scale deflection of 5.0 V? 04. A galvanometer has a sensitivity of 40,000 /V and an internal resistance of 4.0. a.) How could this galvanometer be used to make an ammeter with a full-scale deflection of 0.0 ma? b.) How could this galvanometer be used to make an voltmeter with a full-scale deflection of 0.0 mv? 05. A milliammeter consists of a 0.50 resistor in parallel with a 40.0 galvanometer. It has a full-scale deflection of 50.0 ma. a.) How can this ammeter be used to construct a voltmeter with full-scale deflection of 0.0 V with out changing the structure of the ammeter (taking it apart)? b.) What will be the sensitivity of the voltmeter constructed in part a.) above? ANSWERS: k A 03. a.) (shunt resistor) b.) (shunt resistor) 03. c.) 3. k (series resistor) d.) 93.6 k (series resistor) 04. a.) (shunt resistor) b.) 376 (series resistor) 05. a.) 00 b.) 0 /V (terrible sensitivity)

12 Review Homework # In the circuit shown to the right, each cell of battery V A has an emf of.00 V and each cell of battery V B has an emf of.50 V. Problem 03 a.) What is the net emf of the circuit? b.) What is the net resistance of the circuit? c.) What is the current through each cell of the battery V A? d.) What is the current through each cell of the battery V B? e.) Determine the current through each resistor. f.) What is the voltage across resistor R? g.) What is the power generated by the battery V A? h.) What is the power generated by the battery V B? i.) What is the power generated by this combination of batteries? j.) What is the power consumption of resistor R 3 in this circuit? A R 0.0 k.) At what rate is energy transformed by resistor R 4? l.) What is potential difference between points A and B? R 0.0 R3 5.0 R4 5.0 R R R7 0.0 R 5.0 VA Problem 04 B VB 04. Ignore any internal resistance in the power supplies in the circuit shown to the right. a.) What is the current through resistor R? b.) What is the current through resistor R? c.) What is the current through resistor R 3? d.) What is the current through resistor R 4? e.) What is the current through resistor R 5? f.) What is the voltage across resistor R 4? g.) What is the power consumption of resistor R? h.) What is the power generated by battery V? i.) What is the potential difference between points A and B? V3 30V R 5.0 A V 5V R 40.0 R R3 0.0 R5 5.0 V 0V B ANSWERS: 03. a.) 5.00 V b.) 4.0 c.) 0.9 A d.) 0.9 A 03. e.) I I 0.9 A, I 3 I A, I A, I 6 I 7 I A f.).9 V g.) 0.95 W 03. h.) W i.) W j.) W k.) W l.) 5.6 V 04. a.) 0.45 A b.) 0.53 A 04. c.) 0.53 A d.) A e.) 0.45 A f.).4 V g.).3 W h.).30 W i.) 0.4 V

13 Review Homework # A capacitor is connected in series with a 500- resistor and a galvanometer. The capacitor is initially charged up to a potential of 4.50 Volts. The source of EMF is then removed and the capacitor is allowed to discharge. The current flowing out of the capacitor as a function of time is shown in the graph to the right. a.) What is the time constant for this circuit? b.) What is the capacitance of this capacitor? c.) How much charge is initially stored on the capacitor? d.) Write an equation that describes the charge on the capacitor as a function of time. e.) What is the charge on the capacitor at s? f.) Write an equation that describes the current out of the capacitor as a function of time. g.) What is the current at s? h.) Write an equation that describes the voltage across the capacitor as a function of time. i.) What is the voltage across the capacitor at s? j.) What is the initial energy stored on the capacitor? Current ( A) Discharging Current as a Function of Time Time (s) 06. Answer each of the following questions as clearly and concisely as possible. [It is intended that no answer to this portion should exceed /3 page in length!] a.) What is internal resistance of a battery, how can it be experimentally measured and how is the magnitude of this resistance determined by the internal characteristics of the battery? b.) Discuss the circuitry of an ammeter. Should an ammeter be connected in series or parallel when measuring the current of a resistance and why? c.) Discuss the circuitry of a voltmeter. Should an voltmeter be connected in series or parallel when measuring the voltage drop across a resistance and why? d.) What are the three characteristics which determine the resistance of a wire? How does each characteristic affect the resistance and why? e.) You have two light bulbs which are designed to be connected to 0 Volt household current, 00 Watts and 60 Watts. Which light bulb will have the higher resistance? Support your answer!!! f.) What is Kirchoff s loop rule and why does it work? g.) What is Kirchoff s junction rule and why does it work? ANSWERS: 05. a.) 64.0 s b.) F c.) 0.5 C d.) 05. f.) I 00 e 64 A g.) 3.47 A h.) V 45. e 64 Q 05 e - t 64. C e.). x 0-4 C V i.).69 mv j.) 0.59 J

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