Problems for Chapter 20

20.7 Resistors in Parallel20. 1 Electric Current

1. How many electrons are associatedwith a current of 5.00 A?

2. A wire carries a current of 7.50 Afor a period of 30.0 min. How muchcharge flows through a cross sectionof the wire? How many electronsdoes this represent?

3. Suppose that the region between twooppositely charged parallel plates isoccupied by both singly chargedpositive ions and by electrons. If 5 X106 electrons flow from the negativeplate to the positive plate in 4.00 s,while 6 X 106 ions flow from thepositive plate to the negative plate inthe same time, find the value of thenet current flowing from the positiveplate to the negative plate.

20.2 Ohm's Law

4. A 500-n resistor is connected to a12.0-V battery. Find the currentthrough the resistor.

5. What value of resistance is necessaryto get a current of 2.50 A when it isconnected to a 120-V source?

6. If a current of 8.75 rnA passesthrough a resistor of 550 n, find thevoltage drop across the resistor.

20.3 Resistivity

7. Find the resistance of a 100-m spoolof #22 B&S gauge copper wire(diameter 6.44 X 10-4 m).

8. The connecting wires in an electricalexperiment are 1.00 m long and aremade of copper. Their diameter is6.44 X 10-4 m. What is theresistance of the connecting wires? Isit reasonable to neglect their effect inanalyzing a circuit?

9. Does doubling both the length andthe diameter of a wire have anyeffect on its resistance?

10. What length of #22 B&S gaugecopper wire is needed to make aresistance of 500 n?

11. Find the resistance of an aluminumbar 1.00 m long, 2.00 cm wide, and1.00 cm high from (a) end to end and(b) from the 1.00-cm side to theother 1.00-cm side.

12. A wire 2.00 m long and 1.00 mm indiameter has resistance of 0.500 n. Asecond wire 4.00 m long and 2.00mm in diameter has twice theresistivity of the first wire. Find theresistance of the second wire.

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20.4 The Variation of Resistancewith Temperature

13. If the resistance of a resistor is 20.00nat 20.00 °C, find its resistance at200.00 °C. The temperaturecoefficient of resistance a for copperis 3.93 X 1O-3;oC.

14. If the resistance of a copper wire is500 n at 20°C, find its resistance at100°C.

15. A copper wire has a resistance of20.00 n at room temperature. Thewire is placed in an oven and theresistance is then measured as 30.0n. Find the temperature of the oven.

16. The resistance of a copper wirechanges from 200 n to 210 n. Whatwas the change in temperature of thewire?

17. A copper resistor has a resistance of500 n at a temperature of 20.0 0c.What is the resistance if thetemperature doubles?

20.5 Conservation of Energy andthe Electric Circuit-PowerExpended in a Circuit

18. An electric toaster is rated at 1200W. If it is connected to a 120-V line,what current does it draw? What isthe resistance of the toaster? Howmuch energy is used if the toaster is"on" for 1.00 min?

19. A stereo amplifier is rated at 60.0 W.If it is connected to a 120-V line,how much current does it draw? Ifthe stereo is "on" for 5 hr, how muchenergy is used?

20. A 60.0-W light bulb is connected toa 120-V outlet. What is the currentthrough the bulb? How manyelectrons flow through the bulb persecond? "

21. A power line carries 1000 A and hasa resistance of 20.0 n. How muchenergy is lost per second in terms ofJoule heat?

22. How much power is consumed instarting a car if 200 A is drawn froma 12.0-V battery?

20.6 Resistors in Series23. Find the equivalent resistance of

three resistors of 100, 200, and 300 nwhen connected in series.

24. Find the equivalent resistance of fourresistors of 250, 400, 186, and 375 nwhen connected in series.

25. Find the equivalent resistance ofthree resistors of 100, 200, and 300 nwhen connected in parallel.

26. Find the equivalent resistance of fourresistors of 250, 400, 186, and 375 nwhen connected in parallel.

20.8 Combinations of Resistorsin Series and Parallel

27. Find the equivalent resistance of thecircuit in the diagram.

28. Find the equivalent resistance of thecircuit in the diagram if R\ = 30.0n, Rz = 40.0 n, R3 = 50.0 n, R4 =70.0 n, Rs = 300 n, R6 = 200 n,and R, = 100 n.

t29. In the diagram find (a) theequivalent resistance of the circuit,(b) the current flowing from thebattery, (c) the voltage drop acrossRt, (d) the voltage drop across Rzand R3, (e) the current through eachresistor, (f) the power supplied to thecircuit, and (g) the power dissipatedin each resistor. The emf of thebattery is 12.0 V.

R2 = 300 n';zA5~~JI I~I __

&=12.0V

Electricity and Magnetism

30. Find the current through eachresistor in the diagram.

Cry.:;..3.~.n J~~'j,~J,.~~

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&~6V R,~90n

t31. In the diagram, find (a) theequivalent resistance of the resistorsin parallel, (b) the equivalentresistance of the circuit, (c) thecurrent from the battery, (d) thevoltage drop across R\, (e) thevoltage drop across R2' R3, and R4'([) the current through each resistor,and (g) the power dissipated in eachresistor.

32. Find the voltage drop across R3 inthe diagram.

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R1 = 100n

R2 = 200 fl R3 = 300

33. Find (a) the equivalent resistance ofthe circuit shown in the diagram ifR\ = 50.0 fl, R2 = 80.0 fl, R3 =150 fl, R4 = 30.011, Rs = 200 fl,and R6 = 300 fl and (b) the currentthrough each resistor.

R4\, \, I I

' 'j..

Chapter 20 Electric Currents and DC Circuits

t34. In the diagram find (a) theequivalent resistance, (b) the currentfrom the battery, (c) the currentthrough each resistor, (d) the voltagedrop across each resistor, (e) thepower supplied to the circuit, and([) the power dissipated in eachresistor.

I '/\'/\/'.10n I

~' ,.J ~ .,,<_ ;?3fl (>S!l 20,'

Ul~\ .:?} 113 ,>

.-"\i~\~/VJ--/v~~.J(l, cr' (2. fuJ

20.9 The Electromotive Forceand the Internal Resistanceof a Battery

35. A 6.00- V battery is connected to a100-fl resistor. A voltmeter placedacross the resistor measures 5.60 V.Find the internal resistance of thebattery.

36. A 12-V battery has an internalresistance of 5.5 11.Find the voltageapplied to a circuit of 50 11.

37. Six 1.50- V batteries are connected inseries, with the positive terminal ofone battery connected to the negativeterminal of the next. What is the emfof the combination? If the internalresistance of each battery is 2.00 fl,find the terminal voltage when thereis a current of 200 rnA in the circuit.

38. Six 1.50- V batteries are connected inseries to a resistance of 50.0 fl. Findthe current in the circuit(a) neglecting the internal resistanceof the battery and (b) taking the 2.00 flresistance of each battery intoaccount.

39. Three 12-V batteries are connectedin series to a 35-11 resistor. If theinternal resistance of each battery is10 11,20 fl, and 30 11,respectively,find the voltage drop across the 35-flresistor.

40. When a battery is connected to anexternal resistance of 10.0 11,thecurrent through the externalresistance is 0.100 A. When the samebattery is connected to an externalresistance of 5 fl, the current is 0.150 A.Find the emf of the battery and theinternal resistance of the battery.

20.10 Making an Ammeterand Voltmeter froma Galvanometer

41. A galvanometer has an internalresistance of 3.00 11and gives full-scale deflection for a current of 10.0rnA. What shunt resistance isnecessary to convert this to anammeter that can read a maximumcurrent of 5.00 A?

42. A galvanometer has an internalresistance of 3.00 11and gives full-scale deflection for a current of 10.0rnA. What series resistor is necessaryto convert this to a voltmeter that canread a maximum voltage of 150 V?

20 ..11 The Wheatstone Bridge43. The voltmeter reads 12.0 V and the

ammeter reads a current of 5.45 X10-2 A in the circuit shown. Theammeter has a resistance of 20.0 11and the voltmeter has a resistance of5000 fl. Taking the resistance of theammeter and voltmeter into account,find the value of the resistor R.

I&= 12V

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44. Find the value of R2 in the diagramif the bridge is balanced.

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45. Find the equivalent resistance of theWheatstone bridge in problem 44when the bridge is balanced. Find thecurrent through each resistor.

20.12 Kirchhoff's Rulest46. In the accompanying diagram

(a) find the current through eachresistor and (b) plot the potential asyou traverse each loop.

t47. Two batteries, with emf's andinternal resistances shown, areconnected in parallel. UsingKirchhoff's rules, find the currentthrough R and the voltage dropacross R.

i I~.--------(1 = 3 n

I I~AA.----- V V v,-----..JI(2 = 2 n

R=30n

t48. Find the current through eachresistor in the diagram.

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t49. Using Kirchhoff's rules, find thecurrent through each resistor in thediagram.

R2 = 120A A

R &,~3 = 200

50. Three 12.0- V batteries with differentinternal resistances are connected inparallel as shown in the diagram. Ifr\ = 10.0 n, r2 = 20.0 n, and r3 =30.0 11,find the voltage drop acrossAB.

Additional Problemst51. Find the potential difference across

AB in the accompanying diagram ifR\ = 10.0 n, R2 = 20.0 n, R3 =

30.0 n, and the current through R3 is0.300 A.

A i

B i

52. Find the voltage drop across R2 if R\= 20.0 n, R2 = 30.0 11,R3 = 50.0n, and the emf is 6.00 V in thediagram.

Fr-----53. Find the current through each of the

seven resistors, and the potential dropacross each resistor in the circuit inthe diagram.

&= 60V

t54. Find the equivalent resistance of thecircuit shown in the diagram if R\ =10.0 n, R2 = 20.0 n, R3 = 30.0 n,R4 = 40.0 n, Rs = 50.0 n, R6 =60.0 11,and R, = 70.0 n.

Electricity and Magnetism

t55. If R. = 10.011, R2 = 20.0 n, R3 =30.0 n, and R4 = 40.0 11in thecircuit shown, find (a) the equivalentresistance of the circuit and, if jg. =12.0 V, (b) the current through eachresistor.

71

56. (a) What is the resistance of 100resistors of 10.0 n each if they are allin series? (b) What is the resistanceof 100 resistors of 10.0 11each if theyare all in parallel?

tS7. A 200-W immersion heater is placedin a beaker of water containing 0.500liters at room temperature. How longwill it take for the water to boil?

tS8. An electrically insulated coil of wireis immersed in 100.0 g of water in acalorimeter cup at room temperature.The wire is connected to a 120- Vsource and a current of 2.00 A isobserved in the wire. Find thetemperature of the water after 60.0 s.

Chapter 20 Electric Currents and DC Circuits

t59. A voltage divider is shown in thediagram. The resistor R is a variableslide wire 'resistor. Show that bysliding the arrow contact in the figurealong the slide wire any fraction ofthe original applied voltage can beobtained. In particular show that thevoltage out of the divider is given by

loutVout = -I. Vi.

m

where Ii. is the original length of thewire resistor and lout is the shorterlength of the wire resistor that theoutput connector is attached to.

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Vin t >Rin 1Routt «

Va

t60. The Wheatstone bridge shown in thediagram is not balanced. UsingKirchhoff's rules find the currentthrough each resistor if R. = 10.0 n,R2 = 20.0 n, R3 = 30.0 n, R4 =40.0 n, Rg = 50.0 n, and jg. = 6.00 V.Find the equivalent resistance ofthe circuit.

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ut t61. In problem 60, find the potentialdifferences across points (a) AC,(b) AD. (c) CD, (d) CB, and (e) DB.

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