Ejercicios - WordPress.com · 83 In Fig.27-75, the ideal batteries have emfs %1 : I2.0 V and 8z: 4.00 V and the resistances are each 4.00 ,0. What Tank unrt I 4o,,r. I FlG. 27-70

Chapter 27 I Circuits

battery t has emfnal resistance rr : Zrlhas emf 8z: I2.0 !/

V and internal resistance 12: 0.012 f). ZrlThe batteries are connected in series with - o

an external resistance R. (u) What Rvalue makes the terminal-to-terminal po-tential difference of one of the batterieszero? (b) Which battery is that? ssMcooll A solar cell generates a potential difference of 0.10 Vwhen a 500 ,f) resistor is connected across it, and a potential dif-ference of 0.15 V when a 1000 ,f) resistor is substituted. What arethe (a) internal resistance and (b) emf of the solar cell? (c) Thearea of the cell is 5.0 cm2, and the rate per unit area at which itreceives energy from light is 2.0 mWcm2. What is the efficiencyof the cell for converting light energy to thermal energy in the1000 C) external resistor?

nRlsec. 27-7 Multiloop Circuits.23 In Fig. 27-38, Rr : Rz:4.00 f) and Rr : 2.50 0. Find theequivalent resistance betweenpoints D and E. (Hint: Imaginethat a battery is connected across those points.).24 When resistors 1 and 2 are connected in series, theequivalent resistance is 16.0 0. When they are connected inparallel, the equivalent resistance is 3.0 O. What are (a) thesmaller resistance and (b) the larger resistance of these tworesistors?.25 Four 18.0 C) resistors are connected in parallel across a25.0 V ideal battery. What is the current through the battery?.26 Figure 27 -39 shows five5.00 C) resistors. Find the equiva-lent resistance between points(u) F and H and (b) F and G.(Hint: For each pair of points,imagine that a battery is con-nected across the pair.).27 In Fig. 27-40, Rr : 100 C),Rz: 50 C), and the ideal batterieshave emfs 8t :6.0 V %z:5.0 Vand ffiz:4.0 V. Find (u) the cur-rent in resistor 1, (b) the current inresistor 2,and (c) the potential dif-ference between points a and b..28 In Fig. 27 -g,what is the po- a

tential difference Va - V,between points d and c if. V, -4.0 V %z: 1.0 V, Rr : Rz:10 f), and R: : 5.0 O, and thebattery is ideal?.29 Nine copper wires of length / and diameter d areconnected in parallel to form a single composite conductor ofresistance R. What must be the diamet er D of a single copperwire of length / if it is to have the same resistance? ssMoo30 The resistances in Figs.27-4Ia and b are all 6.0 C), andthe batteries are ideal IzV batteries. (a) When switch S inFig. 27 -4Ia is closed, what is the change in the electric poten-tralVl across resistor L, or does Vlremain the same? (b) When

switch S in Fig. 27 -47b is closed, what is the change in v l acrossresistor 1, or does Vl remain the same?

(") (b)

FlG. 27-41 Problem 30.

.o31 In Fig. 27-42, the current in resistance 6 is io:1.40 Aand the resistances are Rr : Rz: Rt : 2.00 f,), R+ : 16.0 C),Rs : 8.00 C), and Ro : 4.00 O. What is the emf of the idealbattery? e


FtG. 27-37Problem 21.

Flc. 27-38 ProblemZ3.

FlG. 27-39 Problem26.

FlG. 27-4A Problem2T.

..32 In Fig. 27-43, the idealbatteries have emfs Zt : 10.0V and %z:0.500%1, &nd the re-sistances are each 4.00 0. Whatis the current in (a) resistan ce 2and (b) resistance 3?

oo33 In Fig. 27-44., the idealbatteries have emfs Et :5.0 Vand Ez : 12 V, the resistancesare eachz.O C), and the potentialis defined to be zero at thegrounded point of the circuit.What are potentials (a) V1 and(b) V2 at the indicated points?ssMoo34 Figure 27-45 shows asection of a circuit. The resis-tances are R1 : 2.0 C), Rz : 4.0f), and R: : 6.0 C), and theindicated current is i : 6.0 A.The electric potential differ-ence between points A and Bthat connect the section to therest of the circuit is Va - Va :78 V. (u) Is the device repre-sented by "Box" absorbing orproviding energy to the circuit,and (b) at what rate?..35 In Fig. 27-46, Rr : 2.00f,), R, : 5.00 C), and the batteryis ideal. What value of R3 maxi-mizes the dissipation rate inresistan ce 3?

..36 Both batteries in Fig.27-47a are ideal. Emf Zt ofbattery t has a fixed value, butemf %2 of. battery 2 can be varied

FlG. 27-43 Problems 32.43, and 98.


--+?,

FlG. 27-45 Problem34.

FlG. 27-46 Problems35,99,106, and I07.


your potential is greater than 100 V you could ruin the com-ponent. (b) How long must you wait until your potentialreaches the safe level of 100 V?

If you wear a conducting wrist strap that is connected toground, your potential does not increase as much when youstand up; you also discharge more rapidly because the resis-tance through the grounding connection is much less thanthrough your body and shoes. (c) Suppose that when youstand up, your potential is 1400 V and the chair-to-you capaci-tance is 10 pF, What resistance in that wrist-strap groundingconnection will allow you to discharge to 100 V in 0.30 s,

which is less time than you would need to reach for, say,yourcomputer? #72 An automobile gasolinegauge is shown schematically inFig. 27-69. The indicator (on thedashboard) has a resistance of10 C). The tank unit is a float con-nected to a variable resistorwhose resistance varies linearlywith the volume of gasoline. Theresistance is 140 f) when thetank is empty and 20 O whenthe tank is full. Find the currentin the circuit when the tank is (a)full.Tieat the battery as ideal.

across the cable, and a currentof 50 A. Which part is defec-tive? ssM

78 Figure 27-70 shows a por-tion of a circuit through whichthere is a current I : 6.00 A.The resistances are R r : Rz :2.00R1 : 2.00R + : 4.00 g1. Whatis the current it throughresistor 1?

79 In Fig. 27-77, Rt: 20.0 O,Rz : 10.0 ,f), and the ideal bat-tery has emf,'8 : 720V.What isthe current at point a if we close(u) only switch S,, (b) onlyswitches Sr and 52, ?nd (c) allthree switches?

80 In Fig. 27 -72., the idealbatteries have emfs Zt:20.0V 8z: 10.0 V' 8t:5.00 Vand Et: 5.00 V and the resis-tances are each 2.00 O. Whatare the (u) size and (b) direc-tion (left or right) of current i

1

and the (.) size and (d) direc-tion of curr ent i2? (This can beanswered with only mental cal-culation.) (") At what rate isenergy being transferred inbattery 4' and (f) is the energybeing supplied or absorbed bythe battery?81 In Fig. 27-73,, R : 10 f).What is the equivalent resis-tance between points A and B?(Hint: This circuit section mightlook simpler if you first assumethat points A and B areconnected to a battery.)82 In Fig. 27-74, the ideal bat-tery has emf.'8 :30.0 Y and theresistances are Rr : Rz : 14 f,),R3 : R+ : Rs : 6.0 C), Re : 2.0f), and Rt : 1.5 O. What are cur-rents (a) ir, (b) io, (c) i

', (d) i3, and

(e) r'? FlG. 27-73 Problem 81.

t4


83 In Fig.27-75, the ideal batteries have emfs %1 : I2.0 Vand 8z: 4.00 V and the resistances are each 4.00 ,0. What

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FlG. 27-69 ProblemT2.

empty, (b) half-full, and (c)

73 A controller on an electronic arcade game consists ofa variable resistor connected across the plates of a 0.220 p.Fcapacitor. The capacitor is charged to 5.00 Y then dischargedthrough the resistor. The time for the potential differenceacross the plates to decrease to 0.800 V is measured by a clockinside the game. If the range of discharge times that canbe handled effectively is from 10.0 ps to 6.00 ms, what shouldbe the (a) lower value and (b) higher value of the resistancerange of the resistor? ssM

74 (a) In Fig. 27-4a, show that the rate at which energy isdissipated in R as thermal energy is a maximum when R - r.(b) Show that this maximum power is P - '8214r.

75 Wires A and B, having equal lengths of 40.0 m andequal diameters of 2.60 ffiffi, are connected in series. A po-tential difference of 60.0 V is applied between the ends ofthe composite wire. The resistances are RA - 0.I27 O andRn:0.729 f). For wire.4, what are (a) magnitude / of thecurrent density and (b) potential difference V? (c) Of whattype material is wire A made (see Table 26-7)? For wire B.,what are (d) / and (e) V? (f) Of what type material is Bmade? ssM

76 Figure 27-63 shows an ideal battery of emf Z - lzY,a resistor of resistance R : 4.0 O, and an uncharged capacitorof capacitance C - 4.0 pcF.After switch S is closed, what is thecurrent through the resistor when the charge on the capacitoris 8.0 pC?

77 The starting motor of a car is turning too slowly, andthe mechanic has to decide whether to replace the motor,the cable, or the battery.The car's manual says that the 12Vbattery should have no more than 0.020 0 internal resis-tance, the motor no more than 0.200 C) resistance, and thecable no more than 0.040 f,) resistance. The mechanic turnson the motor and measures 1I.4V across the battery,3.0 V

k1

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lRr

+I

R,r'

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f^,1 l^,1


your potential is greater than 100 V you could ruin the com-ponent. (b) How long must you wait until your potentialreaches the safe level of 100 V?

If you wear a conducting wrist strap that is connected toground, your potential does not increase as much when youstand up; you also discharge more rapidly because the resis-tance through the grounding connection is much less thanthrough your body and shoes. (c) Suppose that when youstand up, your potential is 1400 V and the chair-to-you capaci-tance is 10 pF, What resistance in that wrist-strap groundingconnection will allow you to discharge to 100 V in 0.30 s,

which is less time than you would need to reach for, say,yourcomputer? #72 An automobile gasolinegauge is shown schematically inFig. 27-69. The indicator (on thedashboard) has a resistance of10 C). The tank unit is a float con-nected to a variable resistorwhose resistance varies linearlywith the volume of gasoline. Theresistance is 140 f) when thetank is empty and 20 O whenthe tank is full. Find the currentin the circuit when the tank is (a)full.Tieat the battery as ideal.

across the cable, and a currentof 50 A. Which part is defec-tive? ssM

78 Figure 27-70 shows a por-tion of a circuit through whichthere is a current I : 6.00 A.The resistances are R r : Rz :2.00R1 : 2.00R + : 4.00 g1. Whatis the current it throughresistor 1?

79 In Fig. 27-77, Rt: 20.0 O,Rz : 10.0 ,f), and the ideal bat-tery has emf,'8 : 720V.What isthe current at point a if we close(u) only switch S,, (b) onlyswitches Sr and 52, ?nd (c) allthree switches?

80 In Fig. 27 -72., the idealbatteries have emfs Zt:20.0V 8z: 10.0 V' 8t:5.00 Vand Et: 5.00 V and the resis-tances are each 2.00 O. Whatare the (u) size and (b) direc-tion (left or right) of current i

1

and the (.) size and (d) direc-tion of curr ent i2? (This can beanswered with only mental cal-culation.) (") At what rate isenergy being transferred inbattery 4' and (f) is the energybeing supplied or absorbed bythe battery?81 In Fig. 27-73,, R : 10 f).What is the equivalent resis-tance between points A and B?(Hint: This circuit section mightlook simpler if you first assumethat points A and B areconnected to a battery.)82 In Fig. 27-74, the ideal bat-tery has emf.'8 :30.0 Y and theresistances are Rr : Rz : 14 f,),R3 : R+ : Rs : 6.0 C), Re : 2.0f), and Rt : 1.5 O. What are cur-rents (a) ir, (b) io, (c) i

', (d) i3, and

(e) r'? FlG. 27-73 Problem 81.

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83 In Fig.27-75, the ideal batteries have emfs %1 : I2.0 Vand 8z: 4.00 V and the resistances are each 4.00 ,0. What

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RrR2ryFlG. 27-71 Problem 79.


4.0R

FlG. 27-69 ProblemT2.

empty, (b) half-full, and (c)

73 A controller on an electronic arcade game consists ofa variable resistor connected across the plates of a 0.220 p.Fcapacitor. The capacitor is charged to 5.00 Y then dischargedthrough the resistor. The time for the potential differenceacross the plates to decrease to 0.800 V is measured by a clockinside the game. If the range of discharge times that canbe handled effectively is from 10.0 ps to 6.00 ms, what shouldbe the (a) lower value and (b) higher value of the resistancerange of the resistor? ssM

74 (a) In Fig. 27-4a, show that the rate at which energy isdissipated in R as thermal energy is a maximum when R - r.(b) Show that this maximum power is P - '8214r.

75 Wires A and B, having equal lengths of 40.0 m andequal diameters of 2.60 ffiffi, are connected in series. A po-tential difference of 60.0 V is applied between the ends ofthe composite wire. The resistances are RA - 0.I27 O andRn:0.729 f). For wire.4, what are (a) magnitude / of thecurrent density and (b) potential difference V? (c) Of whattype material is wire A made (see Table 26-7)? For wire B.,what are (d) / and (e) V? (f) Of what type material is Bmade? ssM

76 Figure 27-63 shows an ideal battery of emf Z - lzY,a resistor of resistance R : 4.0 O, and an uncharged capacitorof capacitance C - 4.0 pcF.After switch S is closed, what is thecurrent through the resistor when the charge on the capacitoris 8.0 pC?

77 The starting motor of a car is turning too slowly, andthe mechanic has to decide whether to replace the motor,the cable, or the battery.The car's manual says that the 12Vbattery should have no more than 0.020 0 internal resis-tance, the motor no more than 0.200 C) resistance, and thecable no more than 0.040 f,) resistance. The mechanic turnson the motor and measures 1I.4V across the battery,3.0 V

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lRr

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R,r'

R7

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f^,1 l^,1

.60 In an RC series circuit, Z - I2.0 V R : I.40 MC), andC - 1.80 p.F. (u) Calculate the time constant. (b) Find themaximum charge that will appear on the capacitor duringcharging. (c) How long does it take for the charge to build upto 16.0 pC?.61 Switch S in Fig. 27 -63 is closedat time / : 0' to begin charging an ini-tially uncharged capacitor of capaci-tance C - 15.0 pF through a resistorof resistance R - 20.0 C). At what timeis the potential across the capacitorequal to that across the resistor?..62 A capacitor with an initial potential difference of100 V is discharged through a resistor when a switch betweenthem is closed at / : 0. At t : 10.0 s, the potential differenceacross the capacitor is 1.00 V. (a) What is the time constant ofthe circuit? (b) What is the potential difference across thecapacitor at t : 77.0 s?

..63 The potential difference between the plates of a leaky(meaning that charge leaks from one plate to the other) 2.0pF capacitor drops to one-fourth its initial value in2.0 s. Whatis the equivalent resistance between the capacitor plates?.o64 A 1.0 pF capacitor with an initial stored energyof 0.50 J is discharged through a 1.0 MO resistor. (u)What is the initial charge on the capacitor? (b) What is thecurrent through the resistor when the discharge starts? Findan expression that gives, as a function of time r, (c) the poten-tial difference V 6 across the capacitor, (d) the potential differ-ence V p across the resistor, and (e) the rate at which thermalenergy is produced in the resistor.fo65 In the circuit of Fig. 27-64., Z - l.zkv, C - 6.5 p.F,Rr : Rz: R: : 0.73 MC). With C completely uncharged,switch S is suddenly closed (at r - 0). At t:0, what are (a)current i1 in resistor 1, (b) cur-rent i2 in resistor 2, and (c) cur-rent h in resistor 3? At t : @

(that is, after many time con-

FrG. 27-66Problems 67 and 97 .:5

FlG. 27-63Problems 61 and76.

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+stants), what are (d) ir, (e) ir,and (f) t3? What is the potentialdifference V) across resistor 2at (g) /:0 and (h) t-q? (i)Sketch V2 versus / betweenthese two extreme times. ssm www..66 Figure 27-65 shows thecircuit of a flashing lamp, likethose attached to barrels athighway construction sites. Thefluorescent lamp L (of negligi-ble capacitance) is connectedin parallel across the capacitorC of an RC circuit. There is acurrent through the lamp onlywhen the potential difference across it reaches the breakdownvoltage Vy; then the capacitor discharges completely throughthe lamp and the lamp flashes briefly. For a lamp with break-down voltage Vr:72.0 V,wired to a 95.0 V ideal battery anda 0.150 p,F capacitor, what resistance R is needed for twoflashes per second?..67 In Fig. 27-66, Rr : 10.0 kC), Rz: 15.0 kC), C - 0.400 p.F,

Problems

and the ideal battery has emf V -20.0 V. First, the switch is closed along time so that the steady state isreached. Then the switch is openedat time / : 0. What is the current inresistor 2 at t : 4.00 ms? €*o r rS$ Figure 27 -67 displaystwo circuits with a chargedcapacitor that is to be dischargedthrough a resistor when a switchis closed. In Fig. 27-67a, Rr :20.0 'C) and Cr :5.00 p,F. In Fig.27-67b, Rz: 10.0 O and Cz:8.00 pF. The ratio of the initialcharges on the two capacitors iseozleu : 1.50. At tim e t - 0, bothswitches are closed. At what time r do the two capacitors havethe same charge?ooo$Q A 3.00 MO resistor and a 1.00 p,F capacitor are con-nected in series with an ideal battery of emf 8 - 4.00 V. At 1.00s after the connection is made, what is the rate at which (a) thecharge of the capacitor is increasing, (b) energy is being storedin the capacitor, (c) thermal energy is appearing in the resistor,and (d) energy is being delivered by the battery?

Additional Problems7A What are the (a) size and (b) direction (up or down) ofcurrent i in Fig.27-68,, where all resistances are 4.0 C) and allbatteries are ideal and have an emf of 10 V? (Hin r: This can beanswered using only mental calculation.)


71 Suppose that, while you are sitting in a chair, charge sep-aration between your clothing and the chair puts you at a po-tential of 200 V with the capacitance between you and thechair at 150 pF. When you stand up, the increased separationbetween your body and the chair decreases the capacitance to10 pF. (a) What then is the potential of your body? That po-tential is reduced over time, as the charge on you drainsthrough your body and shoes (you are a capacitor dischargingthrough a resistance). Assume that the resistance along thatroute is 300 GO. If you touch an electrical component while

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Ejercicios - WordPress.com · 83 In Fig.27-75, the ideal batteries have emfs %1 : I2.0 V and 8z: 4.00 V and the resistances are each 4.00 ,0. What Tank unrt I 4o,,r. I FlG. 27-70