Essential University Physics, 3e (Wolfson) 3e (Wolfson) Chapter 24 Electrict Current
2 4. 1 Co nc e pt ua lQue s t i o ns 1) The figure shows a steady electric current passing through a wire with a narrow region. What happens to the drift velocity of the moving charges as they go from region A to region B and then to region C ?
A) The drift velocity decreases from A to B and increases from B to C. B) The drift velocity increases all the time. time. C) The drift velocity remains constant. D) The drift velocity decreases all the time. ) The drift velocity increases from A to B and decreases from B to C. Answer! "ar! 1
#) When electric current is flowing in a metal$ the electrons are moving A) at nearly the speed of light. B) at the speed of light. C) at the speed of sound in the metal. D) at the speed of sound in air. ) at none of the a%ove speeds. Answer! "ar! 1
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+) The figure shows two connected wires that are made of the same material. The current entering the wire on the left is #.' A and in that wire the electron drift speed is vd. What is the electron drift speed in the wire on the right side?
A) ,vd B) #vd C) vd D) vd-# ) vd-, Answer! "ar! 1
,) A narrow copper wire of length L and radius b is attached to a wide copper wire of length L and radius #b$ forming one long wire of length # L. This long wire is attached to a %attery$ and a current is flowing through it. *f the electric field in the narrow wire is E $ the electric field in the wide wire is A) E . B) # E . C) , E . D) E -#. ) E -,. Answer! "ar! 1
) A cylindrical wire has a resistance R and resistivity ρ. *f its length and diameter are B/T0 cut in half$ a) what will %e its resistance? A) , R B) # R C) R D) R-# ) R/ , %) what will %e its resistivity? A) , ρ B) # ρ C) ρ D) ρ-# E) ρ-, Answer! a) B %) C "ar! 1
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() 2ou are given a copper %ar of dimensions + cm 3 cm 3 4 cm and as5ed to attach leads to it in order to ma5e a resistor. a) *f you want to achieve the 67A886T possi%le resistance$ you should attach the leads to the opposite faces that measure A) + cm 3 cm. B) + cm 3 4 cm. C) cm 3 4 cm. D) Any pair of faces produces the same resistance. %) *f you want to achieve the 8A9:6T possi%le resistance$ you should attach the leads to the opposite faces that measure A) + cm 3 cm. B) + cm 3 4 cm. C) cm 3 4 cm. D) Any pair of faces produces the same resistance. Answer! a) C %) A "ar! 1
;) A wire of resistivity ρ must %e replaced in a circuit %y a wire of the same material %ut , times as long. *f$ however$ the resistance of the new wire is to % e the same as the resistance of the original wire$ the diameter of the new wire must %e A) the same as the diameter of the original wire. B) 1-# the diameter of the original wire. C) 1-, the diameter of the original wire. D) # times the diameter of the original wire. ) , times the diameter of the original wire. Answer! D "ar! 1
4) As current flows through a uniform wire$ the wire gets hotter %ecause the electrons stop moving and therefore transform their lost 5inetic energy into thermal energy in the wire. A) True B)
=) When a potential difference of 1' " is placed across a certain solid c ylindrical resistor$ the current through it is # A. *f the diameter of this resistor is now tripled$ the current will %e A) #-= A. B) #-+ A. C) # A. D) + A. ) 14 A. Answer! "ar! 1
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1') Two ca%les of the same length are made of the same material$ e>cept that one ca%le has twice the diameter of the other ca%le. When the same potential difference is maintained across %oth ca%les$ which of the following statements are true? There may %e more than one correct choice.) A) The same current flows through %oth ca%les. B) Both ca%les carry the same current density. C) The electrons have the same drift velocity in %oth ca%les. D) The current in the thin ca%le is twice as great as the current in the thic5 ca%le. ) The current in the thin ca%le is four times as great as the current in the thic5 ca%le. Answer! B$ C "ar! 1
2 4 . 2 Pr o bl e ms 1) An electric device delivers a current of .' A to a device. 0ow many electrons flow through this device in 1' s? e 1.(' 3 1'@1= C) A) '.#' B) #' C) #.' D) +.1 > ) +1 > Answer! D "ar!
#) *n a certain electroplating process gold is deposited %y using a current of 1,.' A for 1= minutes. A gold ion$ Au$ has a mass of appro>imately +.+ 3 1'@## g. 0ow many grams of gold are deposited %y this process? A) ++ g B) 1( g C) ## g D) #4 g ) =; g Answer! A "ar! '
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+) The figure shows a #.'@cm diameter roller that turns at =' rpm. A ,.'@cm wide plastic film is %eing wrapped onto the roller$ and this plastic carries an e>cess electric charge having a uniform surface charge density of .' nC-cm#. What is the current of the moving film?
A) 1=' nA B) #+ A C) +' nA D) 11 A Answer! A "ar! '
,) The current supplied %y a %attery as a function of time is What is the total num%er of electrons transported from the positive electrode to the negative electrode from the time the %attery is first used until it is essentially dead? e 1.(' 3 1'@1= C) A) 1.# 3 B) ,., 3 C) .+ 3 D) +.+ 3 Answer! A "ar! '
) A gold wire that is 1.4 mm in diameter and 1 cm long carries a current of #(' mA. 0ow many electrons per second pass a given cross section of the wire? e 1.(' 3 1'@1= C) A) 1.( 3 1'14 B) 1.( 3 1'1; C) 1. 3 1'#+ D) +.; 3 1'1 ) (.+ 3 1'1 Answer! A "ar! '
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() *n an electroplating process$ copper ionic charge #e$ atomic weight (+.( g-mol) is deposited using a current of 1'.' A. What mass of copper is deposited in 1'.' minutes? Avogadros num%er is (.'## 3 1'#+ molecules-mol and e 1.(' 3 1'@1= C. A) +.=( g B) #.# g C) '.== g D) #.+ g ) 1.=4 g Answer! "ar! 1
;) The current in a wire varies with time according to the euation I t ) (.'' A ,.4' A-s)t $ where t is in seconds. 0ow many coulom%s of charge pass a cross section of the wire in the time period %etween t '.'' s and Answer! +=.( C "ar! '
4) *f a current of #., A is flowing in a cylindrical wire of diameter #.' mm$ what is the average current density in this wire? A) ;.( 3 1' A-m# B) .# 3 1'@( A-m# C) 1.= 3 1' A-m# D) +.( 3 1' A-m# ) #1 3 1'@( A-m# Answer! A "ar! 1
=) A proton %eam that carries a total current of 1.+ mA has 1'.' mm diameter. The current density in the proton %eam increases linearly with distance from the center. This is e>pressed mathematically as J r ) J ' r/R)$ where R is the radius of the %eam and J ' is the current density at the edge. Determine the value of J '. A) # AB) (.# AC) 1# AD) 1; AAnswer! A "ar! '
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1') A certain fuse E%lowsE if the current in it e>ceeds 1.' A$ at which instant the fuse melts with a current density of What is the diameter of the wire in the fuse? A) '., mm B) '.(+ mm C) '.(4 mm D) '.=1 mm Answer! A "ar! '
11) *f the current density in a wire or radius R is given %y J kr $ ' F r F R$ what is the current in the wire? A) #GkR+-+ B) +GkR+-# C) kR+-+ D) kR# ) kR#-# Answer! A "ar! 1
1#) A silver wire has a cross sectional area A #.' mm#. A total of =., 3 1'14 electrons pass through the wire in +.' s. The conduction electron density in silver is .4 3 1'#4 electrons-m+ and e 1.(' 3 1'@1= C. What is the drift velocity of these electrons? A) #.; 3 1'@ m-s B) =.1 3 1'@ m-s C) .# 3 1'@ m-s D) 1.1 3 1'@ m-s ) ;., 3 1'@ m-s Answer! A "ar! 1
1+) The diameter of a 1#@gauge copper wire is '.'41 in. The ma>imum safe current it can carry in order to prevent fire danger in %uilding construction) is #' A. At this current$ what is the drift velocity of the electrons? The num%er of electron carriers in 1.' cm+ of copper is 4. 3 1'## and e 1.(' 3 1'@1= C. A) '.',, mm-s B) '.,, mm-s C) '.,, cm-s D) '.,, m-s ) ,., cm-s Answer! B "ar! 1
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1,) A wire has a cross@sectional area of '.1' mm#. *f there are ,.' 3 1'#4 atoms per cu%ic meter in this wire$ and if each atom contri%utes # free electrons$ what is the drift velocity of the electrons when the current in the wire is (.' A? e 1.(' 3 1'@1= C) A) '.'',; m-s B) '.''=# m-s C) '.=, m-s D) '.'1= m-s Answer! A "ar! 1
1) Building codes usually limit the current carried %y a Ho. 1, copper wire to 1 A. 7any household circuits are wired with this siIe wire. What is the drift velocity of the electrons in this case? The diameter of this wire is 1.( mm. Assume one conduction electron per atom in copper. The atomic weight of copper is (+.+ g-mol and its density is 4='' 5g-m+. Avogadros num%er is (.'## 3 1'#+ molecules-mol and e 1.(' 3 1'@1= C. A) .1 × 1'@, m-s B) ,.( × 1'@, m-s C) 1.( × 1'@+ m-s D) ,.,, × 1'@# m-s ) ,.4= × 1'@ m-s Answer! A "ar! 1
1() The resistivity of gold is
at room temperature. A gold wire that is '.= mm
in diameter and 1, cm long carries a current of =,' mA. What is the electric field in the wire? A) '.'+( "-m B) '.''=' "-m C) '.'#4 "-m D) '.',( "-m ) '.'=' "-m Answer! A "ar! '
1;) A silver wire with resistivity carries a current density of is the magnitude of the electric field inside the wire? A) '.'(, "-m B) #. "-m C) '.',' "-m D) '.1' "-m Answer! A "ar! ;
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What
14) A tu%e of mercury with resistivity =.4, 3 1'@; J K m has an electric field inside the column of mercury of magnitude #+ H-C that is directed along the length of the tu%e. 0ow much current is flowing through this tu%e if its diameter is 1.' mm? A) 14 A B) 14' A C) #= A D) #4' A Answer! A "ar! 1
1=) What length of a certain metal wire of diameter '.1 mm is needed for the wire to have a resistance of 1 J? The resistivity of this metal is 1.(4 3 1' @4 J K m. A) 1( mm B) 1( cm C) 1.( m D) 1( m ) 1(' m Answer! D "ar! 1
#') A #.' mm diameter wire of length #' m has a resistance of '.# J. What is the resistivity of the wire? A) .' 3 1'@; J K m B) +.= 3 1'@4 J K m C) ,.' 3 1'@; J K m D) 1( 3 1'@4 J K m ) '.# J K m Answer! B "ar! 1
#1) What must %e the diameter of a cylindrical 1#'@m long metal wire if its resistance is to %e (.' J? The resistivity of this metal is 1.(4 3 1'@4 J K m. A) '.'( mm B) '.( mm C) '.( cm D) '.+# mm ) '.'+# mm Answer! B "ar! 1
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##) Hichrome wire$ often used for heating elements$ has resistivity of 1.' 3 1'@( J K m at room temperature. What length of Ho. +' wire of diameter '.#' mm) is needed to wind a resistor that has ' ohms at room temperature? A) +.(( m B) #., m C) '.(1 m D) (., m ) ##., m Answer! B "ar! 1
#+) Calculate the current through a 1'.'@m long ## gauge having radius '.+#1 mm) nichrome wire if it is connected to a 1#.'@" %attery. The resistivity of nichrome is 1'' 3 1'@4 J K m. A) 1;. A B) +'.= A C) (1.4 A D) +44 mA ) ;;( mA Answer! D "ar! 1
#,) 0ow much current will %e flowing through a ,'.' m length of cylindrical metal wire with radius '.' mm if it is connected to a source supplying 1(.' "? The resistivity of this metal is 1.(4 3 1'@4 J K m. A) 1#'' A B) =. 3 1'4 A C) (4 nA D) ;1' A Answer! A "ar! 1
#) When a voltage difference is applied to a piece of metal wire$ a current flows through it. *f 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 o f %oth wires are the same$ and the voltage difference remains unchanged. The resistivity of the original metal is 1.(4 3 1'@4 J K m$ and the resistivity of silver is 1.= 3 1'@4 J K m.) A) #1 mA B) 1= mA C) 11 mA D) .+ mA Answer! A "ar! =
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#() A cylindrical wire of radius #.' mm carries a current of #. A. The potential difference %etween points on the wire that are ,( m apart is +.; ". a) What is the electric field in the wire? %) What is the resistivity of the material of which the wire is made? Answer! a) '.'4' "-m %) ,.' 3 1'@; J K m "ar! '
#;) The power rating of a ,''@J resistor is '.4'' W. a) What is the ma>imum voltage that can %e applied across this resistor without damaging it? %) What is the ma>imum current this resistor can draw without damaging it? Answer! a) 1;.= " %) ,,.; mA "ar! 1
#4) A 11'@" hair dryer is rated at 1#'' W. What current will it draw when operating from a 11'@ " electrical outlet? A) =' mA B) 1.' A C) .' A D) 11 A ) 1, A Answer! D "ar! 1
#=) A light %ul% is connected to a 11'@" source. What is the resistance of this %ul% if it is a 1''@ W %ul%? A) 1'' J B) 4.' mJ C) (.' mJ D) 1#' J ) #,' J Answer! D "ar! 1
+') A certain electric furnace consumes #, 5W when it is connected to a #,'@" line. What is the resistance of the furnace? A) 1.' 5J B) 1' J C) #., J D) '.,# J ) 1'' J Answer! C "ar! 1
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+1) A 1''@W heater is connected to a 1#'@" line. 0ow much heat energy does it produce in #.' hours? A) 1. 5L B) +.' 5L C) '.14 7L D) 11 7L ) 14 7L Answer! D "ar! 1
+#) The resistivity of gold is #.,, 3 1'@4 J K m at room temperature. A gold wire that is 1.4 mm in diameter and 11 cm long carries a current of 1;' mA. 0ow much power is dissipated in the wire? A) '.'+' mW B) '.'';( mW C) '.'1+ mW D) '.'1= mW ) '.'# mW Answer! A "ar! 1
++) A ,''@W computer including the monitor) is turned on for 4.' hours per day. *f electricity costs 1'M per 5Wh$ how much does it cost to run the computer annually for a typical +(@day year? A) N1#' B) N1#'' C) N1 D) N1; ) N1' Answer! A "ar! 1
+,) The voltage and power ratings of a particular light %ul%$ which are its normal operating values$ are 11' " and (' W. Assume the resistance of the filament of the %ul% is constant and is independent of operating conditions. *f the light %ul% is operated with a current that is 'O of the current rating of the %ul%$ what is the actual power drawn %y the %ul%? A) 1' W B) 1 W C) #' W D) # W ) +' W Answer! B "ar! 1
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+) The voltage and power ratings of a particular light %ul%$ which are its normal operating values$ are 11' " and (' W. Assume the resistance of the filament of the %ul% is constant and is independent of operating conditions. *f the light %ul% is operated at a reduced voltage and the power drawn %y the %ul% is +( W$ what is the operating voltage of the %ul%? A) (( " B) ;# " C) ;4 " D) 4 " ) =' " Answer! D "ar! 1
+() The heater element of a particular 1#'@" toaster is a 4.=@m length of nichrome wire$ whose diameter is '.4( mm. The resistivity of nichrome at the operating temperature of the toaster is 1.+ 3 1'@( J K m. *f the toaster is operated at a voltage of 1#' "$ how much power does it draw? A) ;#' W B) ;'' W C) ;' W D) ;;' W ) 4'' W Answer! A "ar! '
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