Essential University Physics, 3e (Wolfson) Chapter 28 Alternating-Current Circuits
2 8. 1 Co nc e pt ua lQue s t i o ns 1) An ac source of period T and and maximum voltage V is is connected to a single unknown ideal element that is either a resistor, and inductor, or a capacitor. At time t = = 0 the voltage vo ltage is zero. At time t = = T / / the current in the unknown element is e!ual to zero, and at time t = = T /" /" the current is I = = # I I max where I max max, where I max is the current amplitude. $hat is the unknown element% A) a resistor &) an inductor ') a capacitor () an inductor or a capacitor Answer ' *ar 1
") A resistor is connected to an ideal ac power suppl+. a) -he phase angle etween the current and voltage is A) 0 &) /" /" rad radia ians ns.. ') #/" #/" rad radia ians ns.. () rad radiians. ans. ) / / radi radian ans. s. ) -he current in the resistor A) leads the voltage voltage across across the resistor resistor + 203. &) lags the the voltage voltage across across the resist resistor or + 203. ') is in phase phase with with the voltag voltagee across across the resist resistor. or. () the voltage voltage across across the resist resistor or + 43. 43. ) lags the voltag voltagee across across the the resistor resistor + 43. 43. c) 5ow does the average power po wer dissipated in the resistor change as the fre!uenc+ in the ac power suppl+ decreases% A) 6t decre decreas ases es.. &) 6t incr increa ease ses. s. ') 6t does does not not chang change. e. () 6t increases increases or decrease decreasess depending depending on the sign of the phase phase angle. Answer a) A ) ' c) ' *ar 1
) $hen an LRC an LRC series series circuit is at resonance, which one of the following statements aout that circuit is accurate% -here ma+ e more than one correct choice.) A) -he impedance has its maximum value. &) -he reactance of the inductor is zero. ') -he reactance of the capacitor is zero. () -he reactance due to the inductor and capacitor has its maximum value. ) -he current amplitude is a maximum. Answer *ar 1 1 'op+right 7 "018 9earson ducation, 6nc.
) 6n a series LRC circuit, the fre!uenc+ at which the circuit is at resonance is f 0. 6f +ou doule the resistance, the inductance, the capacitance, and the voltage amplitude of the ac source, what is the new resonance fre!uenc+% A) f 0 &) " f 0 ') f 0 () f 0/" ) f 0/ Answer ( *ar 1
4) $hich one of the phasor diagrams shown elow est represents a series LRC circuit driven at resonance%
A) 1 &) " ') () ) 4 Answer ' *ar 1
8) $hen an LRC series circuit is driven at resonance, which of the following statements aout the circuit are correct% -here ma+ e more than one correct choice.) A) -he impedance of the circuit is zero. &) -he impedance of the circuit has its maximum value. ') -he impedance of the circuit has its minimum value. () -he inductive reactance and the capacitive reactance are oth zero. ) -he inductive reactance and the capacitive reactance are exactl+ e!ual to each other. Answer ', *ar 1
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2 8 . 2 Pr o bl e ms 1) a) 6n an ac circuit, if the peak value of the voltage is 100 *, what is the rms value of the voltage% A) 11 * &) 100 * ') "10 * () :1 * ) 1"0 * ) 6n an ac circuit, if the rms value of the current is 100 mA, what is the peak value of the current% A) 11 mA &) 100 mA ') "10 mA () :1 mA ) 1"0 mA Answer a) () A *ar 1
") An alternating current is supplied to an electronic component with a warning that the voltage across it should never exceed $hat is the highest rms voltage that can e supplied to this component while sta+ing elow the voltage limit in the warning% A) 8 * &) 1" * ') 1 * () 8 * Answer A *ar 11
) -he inductor in a radio receiver carries a current of amplitude "00 mA when a voltage of amplitude ".0 * is across it at a fre!uenc+ of 1 00 k5z. $hat is the value of the inductance% A) 1. ;5 &) 1.8 ;5 ') 2."0 ;5 () ." ;5 ) 1.2: ;5 Answer & *ar 1
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) -he 80#5z ac source of the series circuit shown in the figure has a voltage amplitude of 1"0 *. -he capacitive reactance is :20 <, the inductive reactance is ":0 <, and the resistance is 400<.
a) $hat is the capacitance of the capacitor% ) $hat is the inductance of the inductor% Answer a) . ; ) :"0 m5 *ar 1
4) 6f the voltage amplitude across an >.40#n capacitor is e!ual to 1".0 * when the current amplitude through it is . mA, the fre!uenc+ is closest to A) ".8 ?5z &) 4."0 ?5z ') ".8 k5z () 4."0 k5z ) ".8 5z Answer & *ar 1
8) An ac series circuit consists of a voltage source, an >>0#< resistor, and an inductance L. -here is no capacitance in the circuit.) -he current amplitude is 0.80 A, and the phase angle etween the source voltage and the current has a magnitude of 13 a) (oes the source voltage lag or lead the current% ) $hat is the voltage amplitude of the source% Answer a) -he source voltage leads the current. ) :00 volts *ar 1
:) An LRC series circuit has R = 14.0 <, L = "4.0 m5, and C = 0.0 @. -he circuit is connected to a 1"0#* rms) ac source with fre!uenc+ "00 5z. a) $hat is the impedance of the circuit% ) $hat is the rms current in the circuit% c) $hat is the rms voltage across the resistor% d) $hat is the rms voltage across the inductor% e) $hat is the rms voltage across the capacitor% Answer a) 14.> < ) :.81 A c) 11 * d) "2 * e) "0" * *ar 1
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>) An ac circuit is shown in the figure. -he rms current in the circuit is measured to e 1.> A. $hat is the capacitance of the capacitor%
A) " @ &) " @ ') "1 @ () 12 @ ) 1> @ Answer A *ar 1
2) -he 80#5z ac source of a series circuit has a voltage amplitude of 1"0 *. -he resistance, capacitive reactance, and inductive reactance are as shown in the figure. $hat is the rms current in the circuit%
A) 0.02: A &) 0.11 A ') 0.1" A () 0.1 A ) 0.1: A Answer A *ar 1
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10) A series ac circuit consists of an inductor having a reactance of >0 < and an inductance of 120 m5, a 0#< resistor, a capacitor whose reactance is 100 <, and an ac source. -he rms current in the circuit is measured to e "." A. $hat is the rms voltage of the source% A) 2> * &) 28 * ') 2 * () 21 * ) >> * Answer A *ar 1
11) A 1"0#* rms voltage at 1000 5z is applied to an inductor, a ".00#@ capacitor and a 100#< resistor, all in series. 6f the rms value of the current in this circuit is 0.8>0 A, what is the inductance of the inductor% A) ." m5 &) 4.> m5 ') 11. m5 () 1:.2 m5 ) "".> m5 Answer & *ar 1
1") A series LRC circuit has a sinusoidal voltage supplied to it at with a peak voltage of a resistance, a capacitor, and a inductance. $hat is the peak current for this circuit% A) .4 @A &) ". @A ') ." @A () 8.8 @A Answer A *ar 40
1) A series circuit consists of a 40#5z ac source, a 40#< resistor, a 0.40#5 inductor, and a 80#@ capacitor. -he rms current in the circuit is measured to e .1 A. $hat is the voltage amplitude of the source% A) 410 * &) ":0 * ') ""0 * () 1>0 * ) 180 * Answer A *ar 1
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1) A series circuit consists of ac source, a 20#< resistor, a 0.>0#5 inductor, and an >0#@ capacitor. -he fre!uenc+ of the source is adBusted so that the capacitive reactance is e!ual to twice the inductive reactance. $hat is the fre!uenc+ of the source% A) 1 5z &) 1 5z ') 18 5z () 1: 5z ) 12 5z Answer A *ar 1
14) An LRC series circuit consists of an >4.0#< resistor, a 1.0#@ capacitor, a 1.4 0#m5 inductor, and a variale fre!uenc+ ac source of voltage amplitude 1."4 *. At what angular fre!uenc+ will the inductive reactance e .00 times as large as the capacitive reactance% A) 1.> C 10 rad/s &) 8.20 C 10 rad/s ') .4 C 10 rad/s () "."0 C 10 rad/s ) 1.10 C 10 rad/s Answer A *ar 1
18) A series ac circuit consists of a voltage source of fre!uenc+ 80 5z and source voltage amplitude 4 volts, a resistor, a capacitor, and an inductor of inductance L. a) $hat must e the value of L for the phase angle to e zero% ) $hen L has the value calculated in part a), what is the current amplitude in the circuit% Answer a) . 5 ) 0.2" A *ar 40
1:) A series LRC circuit consists of an ac voltage source of amplitude :4.0 * and variale fre!uenc+, a 1".4#; capacitor, a 4.00#m5 inductor, and a 4.0#< resistor. a) -o what angular fre!uenc+ should the ac source e set so that the current amplitude has its largest value% ) Dnder the conditions of part a), what is the maximum current amplitude% c) Euppose that the voltage source is set to twice the angular fre!uenc+ needed in part a). $hat will e the current amplitude in this case% Answer a) .00 C 10 rad/s ) ".1 A c) 1.8 A *ar 1
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1>) An ac circuit is shown in the figure. -he rms current in the circuit is 1. A. $hat is the peak magnetic energ+ in the inductance%
A) 0." F &) 0.18 F ') 0.> F () 0.8 F ) 0.>0 F Answer A *ar 1
12) A 1"0#* rms voltage at 80.0 5z is applied across an inductor, a capacitor, and a resistor in series. 6f the peak current in this circuit is 0.>> A, what is the impedance of this circuit% A) "00 < &) 11 < ') "0. < () 1"0 < ) 100 < Answer A *ar 1
"0) A "4.0#m5 inductor, a ".00#@ capacitor, and a certain resistor are connected in series across an ac voltage source at 1000 5z. 6f the impedance of this circuit is "00 <, what is the resistance of the resistor% A) 100 < &) 1> < ') "00 < () 44" < ) 4:2 < Answer & *ar 1
"1) A series circuit has a resistance of .0 <, a reactance due to the capacitance) of "1.0 <, and a reactance due to the inductance) of 1:.0 <. ind the impedance of the circuit. A) 4.: < &) ": < ') >.0 < () " < Answer A *ar 1 > 'op+right 7 "018 9earson ducation, 6nc.
"") -he phase angle of an LRC series circuit with an inductive reactance of "00 < and a capacitive reactance of 100 < is 0.03. $hat is the value of the resistor in this circuit% A) 100 < &) 112 < ') 148 < () "00 < ) "84 < Answer & *ar 1
") -he phase angle of an LRC series circuit with an inductive reactance of "00 <, a resistor of "00 < and a certain capacitor at 1000 5z is 0.03. $hat is the value of the capacitance in this circuit% A) 1.24 ; &) ".24 ; ') .24 ; () .24 ; ) 4.24 ; Answer ( *ar 1
") -he phase angle of an LRC series circuit with a capacitive reactance of 0 <, a resistor of 100 < and a certain inductor at 1000 5z is 0.03. $hat is the value of the inductance in this circuit% A) 11.> m5 &) 1" m5 ') "1" m5 () 81.2 m5 ) 12.: m5 Answer *ar 1
"4) An LRC series circuit has voltage supplied to it at a fre!uenc+ of 1.0 k5z with a phase difference etween the current and the voltage of magnitude 0."0 rad. 6f the circuit has a capacitance of 4.0 @ and an inductance of 0.040 5 find the resistance of the circuit. A) "0 k< &) 0.22 k< ') 2.0 k< () 0." k< Answer A *ar 1
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"8) A series LRC ac circuit has a resistance of .0 k<, a capacitance of .0 @, and an inductance of ".0 5. 6f the fre!uenc+ of the alternating current is ".0/ k 5z, what is the phase angle etween the voltage and the current% A) 1.4 rad &) #1.8 rad ') " rad () .1 rad Answer A *ar 1
":) An LRC ac series circuit has R = 14 <, L = "4 m5, and C = 0 @. -he circuit is connected to a 1"0#* rms) ac source with fre!uenc+ "00 5z. a) $hat is the average power dissipated + the circuit% ) $hat is the power factor for the circuit% Answer a) >:0 $ ) 0.24 *ar 1
">) An LRC ac series circuit with R = 14 <, L = "4 m5, and C = 0 @, is attached to a 100#* rms) ac power suppl+. -he fre!uenc+ of the power suppl+ is adBusted so that the circuit is in resonance. a) $hat is the rms current in the circuit% ) $hat is the power dissipated + the circuit% Answer a) 8.: A ) 8:0 $ *ar 1
"2) $hat is the average power dissipated + a "4#< resistor in an LRC series ac circuit for which the power factor is e!ual to 0."4 and the maximum voltage of the ac source is >.0 *% A) 0.00 $ &) 0." $ ') 0.18 $ () 0.8" $ ) 0.0>0 $ Answer *ar 1
0) A series LRC ac circuit has a peak voltage of and a peak current of current lags the voltage + what is the average power of the circuit% A) 21 $ &) 1>" $ ') :> $ () 148 $ Answer A *ar 40
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6f the
1) An LRC ac circuit has a reactance due to its capacitance) of 1: k<, a reactance due to its inductance) of 2.0 k<, and a resistance of "> k<. $hat is the power factor of the circuit% A) 0.28 &) 0."> ') 1.0 () 0.> Answer A *ar 1
") or an RLC ac circuit, the rms current is 10 A. 6f the impedance is 1" k< when the voltage leads the current + 23, find the average power of the circuit. A) 20 k$ &) : k$ ') 2 k$ () 120 k$ Answer A *ar 1
) A series LRC ac circuit has a peak current of 1.0 A with a fre!uenc+ of 4 k5z. 6f the resistance of the circuit is 41 k<, the capacitance of the circuit is 12 @, and the inductance of the circuit is "4 @5, determine the average power of the circuit. A) "8 k$ &) :: k$ ') :.: k$ () .1 k$ Answer A *ar 1
) A series circuit consists of a 40#5z ac source, a 0#< resistor, a 0.0#5 inductor, and a 80#@ capacitor. -he rms current in the circuit is measured to e 1.8 A. $hat is the power factor of the circuit% A) 0.:0 &) 0.88 ') 0.8 () 0.42 ) 0.48 Answer A *ar 1
4) An ac series circuit consists of a voltage source of fre!uenc+ 80 5z and voltage amplitude V , a resistor, and a capacitor of capacitance $hat must e the source voltage amplitude V for the average electrical power consumed in the resistor to e 2>2 $% -here is no inductance in the circuit. Answer 100 * *ar 40
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8) or an LRC series circuit containing a resistance of a capacitance of inductance of what fre!uenc+ is needed to minimize the impedance% A) 0.0" k5z &) 0.1 k5z ') 10 k5z () 1.: k5z Answer A
and an
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:) A series LRC circuit consists of a 100#< resistor, a 0.100#@ capacitor and a ".00#m5 inductor connected across a 1"0#* rms ac voltage source operating at
. At what fre!uenc+
will this circuit e in resonance% A) :0.: k5z &) 1:.2 k5z ') "".4 k5z () 4. k5z ) 11. k5z Answer *ar 1
>) An ac source having a maximum voltage output of 0 * is connected in series with a 40#< resistor, a 0.80#5 inductor, and a "0#; capacitor. $hat is the maximum charge on the capacitor when the fre!uenc+ of the source is adBusted so that the circuit is in resonance% A) 1.0 m' &) 0.00 m' ') ".1 m' () ." m' ) >. m' Answer ' *ar 1
2) A series LRC circuit consists of a 4.00#p capacitor, a :."4#m5 inductor, a :4.0#< resistor, and a 40.0#* ac power source of variale fre!uenc+. At what fre!uenc+ will the impedance of this circuit e e!ual to :4.0 <% Answer >8 k5z *ar 1
0) A series LRC circuit consists of a 1".0#m5 inductor, a 14.0#; capacitor, a resistor, and a 110#* rms) ac voltage source. 6f the impedance of this circuit is 4.0 < at resonance, what is its impedance at a fre!uenc+ twice the resonance fre!uenc+% Answer 81.> < *ar 1
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1) -he primar+ coil of a transformer has 100 turns and its secondar+ coil has 00 turns. 6f the ac voltage applied to the primar+ coil is 1"0 *, what voltage is present in its secondar+ coil% A) 100 * &) 0 * ') :0 * () >0 * ) 00 * Answer ( *ar 1
") A transformer changes the 10,000 * power line to 1"0 *. 6f the primar+ coil contains :40 turns, how man+ turns are on the secondar+% A) &) 8 ') 2 () 8,000 ) "1,000 Answer ' *ar 1
) 6n a transformer, how man+ turns are necessar+ in a 110#* primar+ if the "#* secondar+ has 100 turns% A) 4> &) "0 ') 110 () "" ) Answer A *ar 1
) $hen a current of ".0 A flows in the 100#turn primar+ of an ideal transformer, this causes 1 A to flow in the secondar+. 5ow man+ turns are in the secondar+% A) :00 &) 48 ') 11 () 1 ) Answer ( *ar 1
4) An ideal transformer consists of a 400#turn primar+ coil and a "000#turn secondar+ coil. 6f the current in the secondar+ is .0 A, what is the current in the primar+% A) 0.:4 A &) 1. A ') 1" A () " A ) > A Answer ' *ar 1 1 'op+right 7 "018 9earson ducation, 6nc.
