TEST 104
Short Description
test 104...
Description
TEST 10 Problem 323: A 170 kV, 3-phase electric source deliers 200 !VA to a bala"ced load, #hich has a po#er $actor o$ %0& la''i"'( )hat is the curre"t* A( 2+7 A ( +02 A ( .02 A /( 7% A Problem 32.: A three-phase motor is rated +0 hp, ..0 olts a"d +& po#er $actor( )hat is its rated curre"t* A( 1(+ A ( +7(+ A ( ++ A /( +% A Problem 32+: A bala"ced 3-phase load dra#s 120 amperes li"e curre"t at 230 olts li"e to li"e, 0(. p$ la''i"' curre"t( Sole $or the real po#er( A( .0(+. (+. k) k) ( .2(3+ (3+ k) k) ( .1(.+ (.+ k) k) /( .3(1 .3(1+ + k) k) Problem 32: A 'e"erator supplies three-phase po#er to bala"ced load( The olta'e is 230 olts, the curre"t is 1 A a"d the po#er $actor is +&( )hat is the po#er* A( 3( k) ( 1( k) ( (1 k) /( 1(. k) k) Problem 327: A bala"ced 3-phase load dra#s 7+ amperes li"e curre"t at 230 V li"e li"e to li"e li"e a"d a"d 0(. 0(. la''i la''i"' "' po#er po#er $actor $actor(( Sole Sole $or the react reactie ie po#er bei"' dra#"( A( 1+( 1+(+3 +3 kVA kVA ( 1+(2 1+(2 kVA kVA ( 1+(3 1+(3+ + kVA kVA /( 1+(% 1+(%. . kVA kVA
Problem 32: The i"put po#er $actor to a three-phase, three-phase, poles, .0 olts, 0 4, +0-hp i"ductio" motor is 0(2 as 20 A is dra#" b5 the motor( 6i"d the po#er i"put to the motor( A( %,0 ) ( %,7+ ) ( %,%+ ) /( %,.7 ,.7 ) Problem 32%: A .0 olt, three-phase motor dra#s 20 A #ith a po#er $actor o$ 0(%1 la''i"'( alculate the k) i"put to the motor( A( 1+0( ( 1+(3 ( 1+2(. /( 10(3 Problem 330: /etermi"e the ratio o$ the li"e curre"t dra#" b5 three ide"tical impeda"ces co""ected i" #5e to the li"e curre"t dra#" b5 the same impeda"c impeda"ces es co""ect co""ected ed i" delta( delta( oth co""ect co""ectio" io"s s bei"' bei"' impres impressed sed #ith the same 3- φ olta'es( A( 1:2 ( 3:. ( 2:3 /( 1:3 Problem 331: A #5e co""ected load has a + ∠20 ohm impeda"ces per phase a"d is co""ected across a 120-V three-phase source( alculate the li"e curre"t( A( 2. A ( 13(+ A ( .1(+ A /( 1+(.+ (.+ A Problem 332: A balanced delta connected load having impedance per phase of 20∠ 20∠36.87º ohms is supplied from a balanced 3-phase, 20 ! source. "etermine the total real po#er.
A( ( ( /(
2. %12 701+ 7.0
) ) ) )
Problem 333: Three Three co"de"sers, co"de"sers, each hai"' a capacit5 o$ 7+ micro$arads micro$arads are co""ected i" star to a ..0 olts, 3-phase, +0 c5cles suppl5( alculate the capacita"ce o$ each o$ the three three co"de"sers so that #he" the5 are co""ected i" delta to the same suppl5 the li"e curre"ts remai" the same( A( 20 µ6 ( 2 µ6 ( 2+ µ6 /( 30 µ6 Problem 33.: Three Three impeda"ces, impeda"ces, -810, 810 a"d 10 ohms are #5e co""ected( co""ected( /etermi"e the impeda"ce o$ a" e9uiale"t delta( A( 12(+, 12(+, 812 812(+, (+, -12(+ -12(+ ohm ohms s ( 10, 10, 810, 810, -81 -810 0 ohms ohms ( 8(+, 8(+, -81 -812(+ 2(+,, ohms ohms /( +, 8+, -8+ ohms ohms Problem 33+: A s5stem co"sisti"' o$ three e9ual resistors co""ected i" star is $ed $rom a three-phase suppl5( 5 ho# much is the po#er reduced i$ o"e o$ the three resistors is disco""ected* A( 13 ( 3. ( 12 /( 23 Problem 33: A bala bala"c "ced ed thr three ee-p -pha hase se load load is #5e#5e-co co"" ""ec ecte ted d a"d a"d has has a" impeda"ce ;p < .-83 ohms per phase( 6i"d the li"e curre"t i$ this load is co""ected across a 220 V three-phase source( A( 2+(. A ( 22(3 A ( 20(+ A /( 2(7 A Problem 337: Three Three 10-ohm resista"ces resista"ces are co""ected delta o" a bala"ced three-phase source( =$ the e9uatio" o$ the phase V a" #t 30@ 30@ ( 12 si" >#t +(+ +(+@ @ /( 3 si" si" #t #t
Problem 33: Bie Bie" " a bala bala"c "ced ed 3-#i 3-#irre, thr three ee-p -pha hase se s5st s5stem em ser seri" i"' ' the the $ollo#i"' loads: Vab < 200∠0 ;ab < 10∠+3(13 Ω Vbc < 200∠2.0 ;bc < 10∠0 Ω Vca < 200∠120 ;ca < 10∠30 Ω /etermi"e li"e curre"t o" li"e b( A( 20(3. A ( 22(0. A ( 2.(3 A /( 21(+7 (+7 A Problem 33%: Bie" the $ollo#i"' li"e olta'es a"d t#o load impeda"ces: Vab < 117∠0 ;ac < + ? 812 ohms Vbc < 117∠2. ;bc < 13 ? 80 ohms Vca < 117∠0 Sole $or the li"e curre"t i" li"e c( A( 17(.1 A ( 17(%+ A ( 1(2 A /( 1(. (. A Problem 3.0: Three Three u"e9ual si"'le-phase loads so co""ected across the li"es o$ a bala"ced, 3-phase, 230 olts circuit( The Crst takes 10 A at 0(7 p$ la''i"' a"d is co""ected across li"es 1 D 2( The seco"d takes 1.2 A at 0(2 p$ la''i"' a"d =s co""ected across li"es 2 D 3( A"d the third takes 2(. k) at 0(77 p$ la'' la''i" i"' ' a"d a"d is co"" co""ec ecte ted d acr across oss li"e li"es s 3 D 1( 6i"d i"d the the thr three li"e li"e curre"ts( A( 2+.(. 2+.(.0 0 A, 211(3 211(3 A, 2+2 2+2 A ( 231(2 231(2 A, 21+(2 21+(20 0 A, 2 2 A ( 2+.(. 2+.(.0 0 A, 21+(2 21+(20 0 A, 2+2 2+2 A /( 231(2 231(2 A, A, 211(3 211(3 A, 2 2 A Problem 3.1: A 120-V per phase, three phase co""ected sourece deliers po#er to the $ollo#i"' delta- co""ected load: Phase 1 < .0∠0 Phas Phase e 2 < 20 20∠-0 Phase 3 < 1+∠.+ /etermi"e the li"e curre"ts( A( 12(.+ 12(.+ A, % A, 22(. 22(.+ +A ( 13(.% 13(.% A, % A, 22(. 22(.+ +A ( 13(.% 13(.% A, 10 10 A, 20(2 20(22 2A /( 12(.+ 12(.+ A, A, 10 A, A, 20(22 20(22 A
Problem 3.2: Bie": Vab < 2.0∠0 ;ab < ? 8 ohms Vbc < 2.0∠2.0 ;bc < + ? 8( ohms Vca < 2.0∠120 ;ca < 10 ? 80 ohms Sole $or the three li"e curre"ts = a, =b, a"d =c( A( =a < .+ A, =b < .3 A, =c < 20 A ( =a < . A, =b < .2 A, =c < 2. A ( =a < .+ A, =b < .2 A, =c < 20 A /( =a < . A, =b < .3 A, =c < 2. A Problem 3.3: A three-phase 230-V circuit seres t#o si"'le-phase loads, A a"d ( Foad A is a" i"ductio" motor rated hp, 230 V, 0(70 p$, 0(%0 eGcie"c5, #hich is co""ected across li"es a a"d b( Foad dra#s + k) at 1(0 p$ a"d is co""ected across li"es b a"d c( Assume a se9ue"ce ab-c, sole $or the li"e curre"t o" li"e b( A( .2(1% A ( 27(7. A ( .1(. A /( 3.(. A Problem 3..: A $our #ire 20-V three-phase s5stem is used to suppl5 po#er to a three-phase +-hp i"ductio" motor a"d a si"'le-phase k)-heater co""ected bet#ee" li"e c a"d the "eutral li"e( The operati"' eGcie"c5 a"d po#er $actor o$ the motor are 1 a"d 71 perce"t, respectiel5( alculate the curre"t i" li"e c( Assume a phase se9ue"ce o$ a-b-c( A( 71 A ( 7+ A ( . A /( % A Problem 3.+: A $actor5 is supplied b5 a three-phase, 3-#ire s5stem #ith the $ollo#i"' characteristics: Vab < 230∠0 V =a < 110∠-3(7 A Vbc < 230∠2.0 V =c < 12+∠+3(13 A 6i"d the curre"t = b( A( 1.+(3 A ( 13(3 A ( 1.( A /( 1(+ A
Problem 3.: Bie" a bala"ced 3-#ire, three-phase s5stem seri"' a" u"bala"ced #5e- delta co""ected load( /etermi"e the li"e curre"t i" li"e a( Vab < 210∠0 V ;a" < 10 Vbc < 210∠120 V;b" < 10 ? 810 Vca < 210∠2.0 V;c" < 10 A( 1+ A ( 12 A ( 1. A /( 1 A Problem 3.7: Three resistors 10, 1+ a"d 30 ohmic aluesare co""ected i" #5eco"C'uratio" to a bala"ced 20-olt three-phase suppl5( alculate the total po#er o$ the s5stem( A( 2.. ) ( 20 ) ( 300 ) /( 320 ) Problem 3.: Three impeda"ces each 10 ? 8+ ohms are co""ected i" delta o" a bala"ce three-phase source( =$ the e9uatio" o$ the phase olta'e is Va" < 120 si" #t( )hat is the e9uatio" o$ the curre"t throu'h the impeda"ce co""ected across phase A a"d * A( 20(02 si" >#t 22@ ( 1(+% si" >#t ? 3(..@ ( 1(21 si" >#t ? +(+@ /( 21(32 si" >#t (1+@ Problem 3.%: T#o parallel co""ected loads A a"d b are supplied b5 a ..0 V, 3phase, 0 4 'e"erator( Foad A dra#s a" po#er o$ 100 kVA at 0(0 p$ la''i"' a"d load dra#s a" appare"t po#er o$ 70 kVA at u"it5 p$( /etermi"e the $eeder curre"t( A( 20 A ( 212 A ( 21. A /( 202 a Problem 3+0: T#o diHere"t loads A a"d are co""ected across a bala"ced 230V, 3-φ li"es( Foad A is three-phase load that dra#s 10 kVA at 70&
la''i"' p$( Foad is a si"'le phase load co""ected across li"es a a"d b dra#i"' + kVA at u"it5 p$( /etermi"e the li"e curre"t i" li"e a( Assume a se9ue"ce phase o$ a-b-c( A( 37 A ( .2 A ( 31 A /( . a Problem 3+1: A three-phase motor takes 10 kVA at 0( p$ la''i"' $rom a source o$ 230 olts( =t is i" parallel #ith a bala"ced delta load hai"' 1 ohms resista"ce a"d 12 ohms capacitie reacta"ce i" series i" each phase( /etermi"e the total po#er $actor( A( 0(% la''i"' ( 0(% la''i"' ( 0(%17 la''i"' /( 0(%7 la''i"' Problem 3+2: A bala"ced delta load #hose impeda"ce is .+ ∠70 ohms per bra"ch, a three-phase motor that dra#s a total 10 kVA at 0(+ p$ la''i"' a"d #5e-co""ected load #hose impeda"ce is 10 ohms >resista"ce@ per bra"ch are supplied $rom a three-phase, three-#ire, 20 V, 0 4 $eeder( /etermi"e the oerall po#er $actor o$ the $eeder loads( A( 0(7+3 ( 0(70 ( 0(2 /( 0(72 Problem 3+3: A three-phase 230-V circuit seres t#o si"'le phase loads, A a"d ( Foad A is a" i"ductio" motor rated p, 230 V, 0(70 p$, 0(%0 eGcie"c5, #hich is co""ected across li"es a a"d b( Foad dra#s + k) at 1(0 p$ a"d is co""ected across li"es b a"d c( Assume a se9ue"ce ab-c, sole $or the total po#er $actor o$ the load( A( 0(%07 ( 0(70. ( 0(. /( 0( Problem 3+.: A ..0-V, three-phase 3-#ire, 0 4 $eeder supplies po#er to t#o 30-p i"ductio" motor( I"e motor is operati"' at $ull load, +& eGcie"c5 a"d has a po#er $actor 0$ %0&( The other motor is operati"' at o"e-hal$ o$ its rated horsepo#er, %& eGcie"c5 a"d has a po#er
$actor o$ 7&( )hat is the oerall po#er $actor o$ the s5stem o$ the motors* A( ( ( /(
0(2 la''i"' 0(2 la''i"' 0(3 la''i"' 0(01 la''i"'
Problem 3++: Three u"e9ual si"'le-phase loads so co""ected across the li"es o$ a bala"ced, 3-phase, 230 olts circuit( The Crst takes 10 A at 0(7 p$ la''i"' a"d is co""ected across li"es 1 D 2( The seco"d takes 1.2 A, at 0(2 p$ la''i"' a"d is co""ected across 2 D 3( A"d the third takes 2(. k) at 0(77 p$ la''i"'( /etermi"e total appare"t po#er( A( %. kVA ( 3 kVA ( 7 kVA /( 101 kVA Problem 3+: T#o bala"ced -co""ected loads A a"d are co""ected across a three-phase 3-#ire bala"ced s5stem( Foad A dra#s k) at 0& po#er $actor la''i"' #hile load dra#s 12 k) at 3(+& po#er $actor leadi"'( =$ the curre"t i" the three li"es are each e9ual to A, determi"e the curre"t dra#" b5 load A( A( .(.+ A ( 3(+ A ( .(1+ A /( 3(2 A Problem 3+7: The phase b li"e olta'e a"d the phase a li"e curre"t o$ a bala"ced three-phase s5stem are V < 220 si" >#t ? 210@ a"d = < 10 si" >#t 30@, respectiel5( )hat is the po#er o$ the s5stem( A( 1%0+ ) ( 3300 ) ( +71 ) /( 310 ) Problem 3+: The $ollo#i"' i"$ormatio" is 'ie" $or a delta-co""ected load o$ three "umericall5 e9ual impeda"ces that diHer i" po#er $actor: Fi"e olta'e < 120 olts, ; ab < 1+∠30J ;bc < 1+∠0J 4ca < 1+∠-30 phase se9ue"ce o$ olta'es a-b-c( Ksi"' the phase se9ue"ce as a 'uide, calculate the total po#er dra#" b5 the load( A( 2,2. )
( 2,.72 ) ( 2,+. ) /( 2,731 ) Problem 3+%: A three-phase motor takes 10 kVA at 0( p$ la''i"' $rom a source o$ 230 olts( =t is i" parallel #ith a bala"ced delta load hai"' 1 ohms resista"ce a"d 12 ohms capacitie reacta"ce i" series i" each phase( /etermi"e the total li"e curre"t( A( ( ( /(
30(0+ 3.(++ 32(0. 31(2.
A A A A
Problem 30: =" A circuits, C"d the total po#er i" k) i" a" u"bala"ced threephase circuit loaded as $ollo#s: Phase l < 120 V, 100 A, u"it5 p$( Phase ll < 100 V, 230 A, 0& p$ a"d phase lll < 110 V, + A, 77& p$( A( ( ( /(
37( k) 3+(3 k) 32( k) 3(2 k)
Problem 31: T#o si"'le-phase tra"s$ormers are co""ected i" V >ope" delta@ a"d seri"' a delta co""ected impeda"ce load, each impeda"ce is e9ual to 1 ∠3(7 ohms( =$ the tra"s$ormer olta'es impressed o" the impeda"ces are: Vab < 2.0∠0, Vab < 2.0∠2.0, Vab < 2.0∠120 olts Sole $or the total kVA dra#" b5 the load( A( ( ( /(
(23 (31 10( 11(3
Problem 32: Three impeda"ces, ;a" < 20 ?80, ;b" < 1 ? 812, ;c" < + 81+ ohms, are co""ected i" #5e across a 230 V >li"e to li"e@, 3-phase, . #ire source( The phase se9ue"ce is a-b-c, cou"terclock#ise( /etermi"e the curre"t passi"' thru the "eutral( A( 7(+. A ( %(12 A
( (1 A /( (02 A Problem 33: A #5e-co""ected tra"s$ormer #ith "eutral co""ectio" has bala"ced olta'es o$ 2+ olts bet#ee" li"e a"d "eutral( The tra"s$ormer is seri"' t#o si"'le-phase motors( !otor A >rated . hp, 0(%0 eGcie"c5, 0(0 po#er $actor la''i"'@ is co""ected across li"e a a"d "eutral( !otor >rated 3 hp, 0(+ eGcie"c5, 0(+ po#er $actor la''i"'@ is co""ected across li"e b a"d "eutral( Sole $or the "eutral curre"t, usi"' V a" as re$ere"ce ector( A( ( ( /(
20(.2 2+(37 22(.+ 23(1.
A A A A
Problem 3.: T#o si"'le-phase motors are co""ected bet#ee" the li"es a"d "eutral termi"als o$ a 3-phase, .-#ire, 230 V seco"dar5 side o$ a threephase tra"s$ormer( Foad A is co""ected across li"e a a"d "eutral #hile is across li"e b a"d "eutral( The curre"ts = a a"d =b are .0 A, 0(707 p$ la''i"', a"d 2+ A, u"it5 p$, respectiel5( /etermi"e "eutral curre"t = "( A( ( ( /(
+.(2+ +0(3. +1( +2(37
A A A A
Problem 3+: T#o si"'le-phase motors are co""ected to a three-phase, .-#ire #5e $eeder hai"' 220 V bet#ee" phase a"d the "eutral( I"e motor rated + p, 0( p$ la''i"' a"d %0& eH is co""ected across A a"d "eutral( The seco"d motor is co""ected across phase a"d "eutral, a"d 3 p, 0(707 p$ la''i"' a"d %0& eH( Sole $or the curre"t throu'h the "eutral( A( ( ( /(
20(+ 2%(+. 21(7 23(.3
A A A A
Problem 3: A 230-V, three-phase, .-#ire bala"ced s5stem supplies po#er to 'roup o$ lamp loads( =$ the li"e curre"ts are respectiel5 0 A, A a"d
.0 A respectiel5, sole $or the curre"t i" the "eutral #ire( Assume the po#er $actor o$ the lamps to be u"it5( A( .0 A ( 1. A ( A /( 3 A Problem 37: The loads o$ #5e-co""ected tra"s$ormer areF: =a < 10 cis>-30@ =b < 12 cis 21+ =c < 1+ cis 2 )hat is the "eutral curre"t* A( ( ( /(
1(0. cis 72( 2(21 cis >-30@ 0(%2 cis 2(+ 3(11 cis 72( TEST 11
Problem 3: A $actor5 is supplied b5 a three- phase, 3-#ire s5stem #ith the $ollo#i"' characteristics: Vab < 230∠0 V =a < 110∠-3(7 A Vbc < 230∠2.0 V=c < 12+∠+3(13 A /etermi"e the po#er co"sumed b5 the load( A( .(27 k) ( .(.7 k) ( .0(23 k) /( .+(12 k) Problem 3%: A 3-phase, 3-#ire $eeder has the $ollo#i"' li"e curre"ts a"d li"e olta'es: Vab < 220∠0 V =aa < 30 830 A Vbc < 220∠2.0 V=cc < 2% ? 83%( A /etermi"e the reactie po#er supplied b5 a $eeder( A( 7(7+ kVA ( 7(3. kVA ( (32 kVA /( (.+ kVA Problem 370: Bie" a bala"ced three-phase s5stem #ith the $ollo#i"' loads:
Vab < 230∠0 V ;ab < 0 Vbc < 230∠120 V ;bc = 30 ? 8+0 Vca < 230∠2.0 V ;ca < -80 /etermi"e the readi"' o$ the t#o #attmeters properl5 co""ected usi"' li"e c as the commo" poi"t( A( ..0(% ), %07(+ ) ( 3%.(1 ), %+1(2 ) ( ..0(% ), %+1(2 ) /( 3%.(1 ), %07(+ ) Problem 371: Bie" a bala"ced 3-#ire, three-phase s5stem seri"' the $ollo#i"' loads: Vab < 220∠0 V ;ab < 11∠0 Ω Vbc < 220∠2.0 V;bc < 11∠.+ Ω Vca < 220∠120 V;ca < 11∠30 Ω /etermi"e the readi"' o$ the t#o #attmeters #ith li"e b as commo"( A( %21(+ ), .20 ) ( %21(+ ), ..00 ) ( 3.2(+ ), .+0 ) /( 3.2(+ ), ..00 ) Problem 372: The $ollo#i"' li"e olta'es a"d li"e curre"ts #ere measured to 3phase, 3-#ire $eeder seri"' a commercial buildi"': Vab < 2,.00∠0 V =a < +∠330 A Vbc < 2,.00∠2.0 V =c < 100∠100 A Sole $or the real po#er i" k) dra#" b5 the commercial buildi"'( A( .0.(2 ( .0.(+ ( .1%(3 /( .21(+ Problem 373: A 3-phase, 3-#ire load dra#s the $ollo#i"' li"e curre"ts: =a < 0∠330 A =b < 7(.∠21. A =c < 7+∠0 A =$ the olta'es impressed o" the load are bala"ced 3-phase, hai"' a ma'"itude o$ .1.0 olts li"e to li"e, sole $or the total po#er i" k)( A( ++(1+ ( +0(+ ( +3(+. /( +20(1 Problem 37.: Bie" the $ollo#i"' olta'es a"d load impeda"ces:
Vab < 220∠0 V ;ab < 10∠3(7 Ω Vbc < 220∠2.0 V;bc < 10∠0 Ω Vca < 220∠120 V;ca < 10∠.+ Ω /etermi"e the readi"' o$ k) meter co""ected #ith its curre"t coil co""ected i" li"e b #hile the pote"tial coil co""ected across li"es b a"d c( A( +(12 k) ( .(2 k) ( .(0 k) /( +(.+ k) Problem 37+: Bie" the $ollo#i"' load impeda"ces i" delta a"d the empressed olta'es as $ollo#s: Vab < 220∠0 V ;ab < ? 8 Vbc < 220∠2.0 V;bc < ( 8+ Vca < 220∠120 V;bc < 10 ? 80 )hat #ill be the readi"' o$ the t#o #attmeters co""ected to measure total po#er( Kse li"e a as the commo" pote"tial poi"t( A( 3(% k), %(031 k) ( 2(+. k), (3+7 k) ( 3(12+ k), (77 k) /( .(0++ k), %(. k) Problem 37: The 3-phase po#er suppl5 to a $actor5 has the $ollo#i"' measureme"ts: Vab < 2.0∠0 V =a < 120∠330 A Vbc < 2.0∠2.0 V=b < 1+7∠21. A Vca < 2.0∠120 V=c < 1+0∠0 A Sole $or the total po#er dra#"( A( 0(2 k) ( +(+ k) ( +( k) /( 2(. k)
Problem 377: Bie" Vab < 220∠0 V Vbc < 220∠-120 V 2.0 V /etermi"e the readi"' o$ the #attmeter sho#"(
A( ( ( /(
Vca < 220∠-
.0+(+ ) .(32 ) ..2( ) .7(+. )
Problem 37: A bala"ce 3-phase load dra#s 120 amperes li"e curre"t at 230 olts li"e to li"e, 0(. p$ la''i"' curre"t( Sole $or the readi"'s o$ the t#o #attmeters used to measure the 3-phase po#er( A( 2+(+.3 k), 1+(07 k) ( 2(1++ k), 12(3+ k) ( 2.(3+ k), 1(17+ k) /( 27(+3 k), 12(%+7 k) Problem 37%: A "umber o$ i"ca"desce"t lamps are co""ected i" delta across the li"es o$ a bala"ced 230-V, 3-phase, 3-#ire s5stem( A si"'le-phase #attmeter is co""ected i" the circuit( The curre"t coil o$ the meter is co""ected i" li"e 1 #hile the pote"tial coil is co""ected across li"es 1 a"d 3( This #attmeter re'isters (. k)( =$ the pote"tial termi"al o$ the meter, #hich #as co""ected i" li"e 3, is tra"s$erred to li"e 2, the #attmeter reads 7(+ k)( =$ each lamp is rated 100 ), ho# ma"5 lamps are co""ected across li"es 1 a"d 2( Assume lamp p$ to be u"it5(
A( ( ( /(
.2 .+ .3 ..
Problem 30: !EAFI used to #attmeters to measure the bala"ced 3-phase d5"atro" eleator motor drie( The curre"t coils o$ the #attmeters are co""ected to the curre"t tra"s$ormers, #hich are i" li"es 1 a"d 2 respectiel5( The pote"tial coils are co""ected to the pote"tial tra"s$ormers, #hich are across li"es 1, 2 D 3 a"d li"es 3 D 1, respectiel5( The li"e pote"tials are 230 V a"d the li"e curre"t are each 1+0 A( The #attmeters each i"dicate 1%( k)( Assume load is #5e-co""ected( )hat is the total po#er supplied* A( .%(17+ k) ( .(23 k) ( .+(.1 k) /( .7(3+0 k) Problem 31: A .0 olt, three-phase motor dra#s 20 A #ith a po#er $actor o$ 0(%1 la''i"'( alculate the i"dicatio"s o$ ) 1 a"d )2 $or the 'ie" co"ditio"( A( 7+(.0 k), 7+(.0 k) ( %1(23 k), +%(+ L) ( %(+ k), 1(2+ k) /( %+(2. k), ++(+7 k) Problem 32: T#o #attmeters are used to measure the po#er deliered to a bala"ced delta co""ected load( )attmeter 1 reads 1000 ) a"d #attmeter 2 reads +00 ) a$ter the curre"t coil termi"als are reersed( =$ li"e to li"e olta'e is 20 V, sole $or the li"e curre"t dra#" b5 the load( A( 323 A ( 7(+7 A ( (0 A /( 7(3. A Problem 33: The po#er dra#" b5 three-phase bala"ced load is measured usi"' t#o #attmeters properl5 co""ected( At #hat po#er $actor #ill the readi"' o$ o"e o$ the #attmeters be 4ero* A( 0( ( 1(0 ( 0(+
/( 0(707
Problem 3.: T#o #attmeters co""ected to a three-phase ..0 V s9uirrel ca'e i"ductio" motor i"dicate a total o$ 12 k)( =$ the operati"' po#er $actor o$ the motor is 0(., determi"e the i"diidual readi"' o$ the #attmeters( A( 10(. k), 10 k) ( %(2. k), 2(7 k) ( 13(%. k), -1(%. k) /( Mo"e o$ these Problem 3+: A 3-phase i"ductio" motor is co""ected across a 220-V threephase source( A #attmeters reads 00 ) #he" its curre"t coil is co""ected i" li"e 1 a"d its pote"tial coil across li"e 1 a"d 2( =$ the pote"tial coil o$ the #attmeter is tra"s$erred to li"es 2 a"d 3, the readi"' o$ the #attmeter is the same( alculate the po#er $actor o$ the motor( A( 0(7 ( 0(2% ( 0( /( 0(707 Problem 3: T#o #attmeters used to measure the total po#er dra#" b5 a three-phase circuit a"d are co""ected properl5( The Crst #attmeter reads .00 #atts #hile the other reads .00 #atts a$ter reersi"' its curre"t coil( Sole $or the load po#er $actor( A( 0(+. ( 0(+32 ( 0(. /( 0(.3% Problem 37: T#o-#attmeter method is used to test a 2+ P, 230 olt, 100 rpm, 0 c5cle, 3-phase i"ductio" motor( )he" the li"e olta'es are 230 olts, o"e #attmeter reads ?13,.00 #atts a"d the other ?7,.00 #atts( /etermi"e motor po#er $actor( A( 0(%1 ( 0( ( 0(%. /( 0(07 Problem 3:
A #ou"d rotor motor, 7(+ P, 230 olts, 3-phase takes a li"e curre"t o$ 1(. amperes, #he" operati"' at rated output at a" eGcie"c5 o$ &( alculate the i"dicatio" o" the #attmeters #he" this is i"serted to measure po#er b5 the T-method( A( 3(17% k) ( .(.01 k) ( 3(31 k) /( .(0.2 k) Problem 3%: A #attmeter #ith its curre"t coil i" li"e 2 a"d pote"tial coil across li"es 2 a"d 3 is co""ected to a bala"ced 3-phase s5stem( The o"l5 load supplied is a si"'le phase o"e co""ected to li"es 1 a"d 2( This load is k"o#" to be i"ductie( =$ the #attmeter reads 4ero #atts, determi"e the po#er $actor o$ the si"'le-phase load( A( ( ( /(
0(707 0( 0(00 0(%00
Problem 3%0: Three u"e9ual si"'le-phase motor loads are co""ected across the li"es o$ a bala"ced 230 V, 0 4, three-phase s5stem( !otor N1 is co""ected across li"es 1 D 2 a"d dra#s 10 A at 0& p$( !otor N2 is co""ected across li"es 2 D 3 a"d takes 1.2 A (& p$( A"d motors N3 is co""ected across li"es 3 D 1 takes 1. A at 7+& p$( Ksi"' t#o #attmeters properl5 co""ected #ith the commo" pote"tial poi"t i" li"e 2, #hat are the readi"'s o$ these i"strume"ts* A( 2(.2 k), 13( k) ( +0(71 k), +2(37 k) ( .(21 k), 27(7 k) /( .(2+ k), 2%(3 k) Problem 3%1: A bala"ced 3-phase load dra#s 7+ amperes li"e curre"t at 230 olts li"e to li"e, a"d 0(. la''i"' po#er $actor( =$ the t#o#attmeter method is used, sole $or the readi"'s o$ the #attmeters( A( ( ( /(
1+(32 k), 10(02 k) 17( k), 7(. k) 1(.2 k), (%2 k) 17(2. k), (10 k)
Problem 3%2: Three e9ual impeda"ces, each hai"' a resista"ce o$ ohms a"d a" i"ductie reacta"ce o$ 7 ohms are co""ected i" delta to li"es a, b, a"d c o$ a 2.0 V, 3-phase, 3-#ire li"e, phase se9ue"ce: a-b-c( )hat is the readi"' o$ a si"'le-phase #attmeter co""ected #ith its curre"t coil i" li"e a a"d pote"tial coil across li"es b a"d c* A( (10 ) ( (32. ) ( , +1 ) /( ,00. ) Problem 3%3: A bala"ced three-phase load dra#s 20 k) at 0(..7-p$ la''i"' $rom a 230- V, 0 4 three-phase tra"smissio" li"e( 6i"d the readi"'s o$ the t#o #attmeters properl5 co""ected to measure po#er( A( 1(.+ k), 1(++ k) ( 1.(2+ k), +(7+ k) ( 21(++ k), -1(++ k) /( 2+(7+ k), -+(7+ k) Problem 3%.: /etermi"e the operati"' po#er $actor o$ a three-phase bala"ced load i$ the readi"'s o$ the t#o #attmeters properl5 co""ected to measure po#er is 3:1( A( 0(7 ( 0(++ ( 0(7+ /( 0(1 Problem 3%+: A 3-phase $eeder carries t#o la''i"' bala"ced loads( The po#er obsered b5 each is measured b5 t#o #attmeters method, 'ii"' the $ollo#i"' readi"'s: 6irst load: )1< 10 k) )2 < % k) Seco"d load: )1 < %0 k) )2 < . k) )hat is the combi"ed kVA load o" the $eeder* A( .3.( ( .2(3+ ( +0.(2. /( .20(12 Problem 3%: A si"'le- #attmeter is used to determi"e the po#er take" b5 a three-phase s9uirrel ca'e i"ductio" motor( The curre"t coil is placed i" li"e 1 #hile the pote"tial coil is shi$ted $rom li"es 1 a"d 2, the" $rom li"es 1 a"d 3 respectiel5( =$ the #attmeter re'isters +70 a"d
330#atts respectiel5, #hat is the li"e curre"t dra#" b5 the motor( Fi"e to li"e olta'e is 230 V( A( 2+(17 A ( 23(. A ( 3.(1 A /( 3(3 A Problem 3%7: Matio"al Po#er orporatio" used to #attmeters to measure to measure 3-phase po#er o$ a bala"ced - co""ected la''i"' po#er $actor motors loads( Each #attmeter i"dicate 1+(. k)( The li"e to li"e olta'es are 230 olts #ith V 12 leadi"' V23 a"d the li"e curre"ts are each 120 A( alculate the total po#er supplied( A( 37( .. k) ( 30(72 k) ( 3%(7 k) /( 3.( k) Problem 3%: A 3-phase, 00 V bala"ced s5stem supplies e"er'5 to a" u"bala"ced delta co""ected load( The three li"e curre"ts l a lb a"d lc are 1.1(. A, 100 A a"d 100A respectiel5( A #attmeter #ith its curre"t coil i" li"e a a"d pote"tial coil across a a"d b i"dicates .(. k)( Sole $or the total po#er dra#" b5 the load( Assume a se9ue"ce o$ a-b-c( A( 102(.+ k) ( 100(37 k) ( 107(2+ k) /( 110(12 k) Problem 3%%: Three e9ual "o"-i"ductie resista"ces are co""ected i" star across a bala"ced .00 V, 0 4 s5stem( A si"'le-phase #attmeter is co""ected o" the s5stem #ith its curre"t coil i" li"e 1 a"d pote"tial coil i" li"es 1 a"d 3( The #attmeter re'isters %00 )( =$ li"e 2 is accide"tall5 ope" circuited, #hat #ill be the #attmeter readi"' u"der this co"ditio"* A( %00 ) ( 1200 ) ( 00 ) /( 300 )
Problem .00:
A bala"ced three-phase load hai"' a resista"ce o$ 10 ohms a"d a reacta"ce o$ 10 ohms are co""ected i" star across the li"es o$ a bala"ced 230 V three-phase suppl5( 6i"d the readi"' o" each t#o #attmeters properl5 co""ected to measure the po#er dra#"( A( 20++ ), +% ) ( 20+ ), ++% ) ( 21+ ), .7% ) /( 210+ ), +3% ) Problem .01: A" u"bala"ced delta-co""ected load is co""ected across the li"es o$ a .-#ire bala"ced three-phase suppl5 #ith "eutral co""ectio"( T#o #attmeters )1 )2 are co""ected i" li"es 1 a"d 3 #ith the commo" pote"tial co""ectio" i" the li"es 1 a"d 3 are 20 a"d 2+ A, respectiel5( =$ the commo" pote"tial co""ectio" is tra"s$erred to li"e 2, #hat #ill be the readi"' o$ the t#o #attmeters* The s5stem olta'e per phase is 20 V( Assume a phase se9ue"ce o$ 1-2-3 #ith V 1" as re$ere"ce( A( )1 < .013 #atts, )2 < .+0 #atts ( )1 < .0.3 #atts, )2 < .+30 #atts ( )1 < .03 #atts, )2 < .+10 #atts /( )1 < .073 #atts, )2 < .+00 #atts Problem .02: T#o #attmeters are used to measure the total po#er dra#" b5 a bala"ced delta co""ected properl5( =$ the #attmeters reads 1200 ) a"d 00 ) respectiel5, a"d the li"e to li"e olta'e is 20 V, sole $or the impeda"ce per phase o$ the load( A( +(31 ? 823(7 ohms ( +7(%. ? 820(07 ohms ( +0(31 ? 8 31(72ohms /( +2(.7 ? 823(2 ohms Problem .03: T#o #attmeters used to measure the total po#er dra#" b5 a three-phase circuit a"d are co""ected properl5( I"e o$ the #attmeter read 10 k) #he" the po#er $actor o$ the load is u"it5( )hat does each #attmeter read #he" the po#er $actor $alls to 0( la''i"', assume the total three-phase po#er remai"s the same( A( 12(.+ k), 7(++ k) ( 13(33 k), (7 k) ( 1+(2+ k), .(7+ k) /( 10(7 k), %(33 k) Problem .0.:
A $actor5 is supplied b5 a three-phase, 3-#ire s5stem #ith the $ollo#i"' characteristics( /etermi"e the aera'e po#er $actor o$ the load( Vab < 230∠0V =a < 110∠ - 3(7 A Vbc < 230∠2.0 V =c 20 ohms@ F< i"ducta"ce >1 he"r5@ t< time i" seco"ds i< curre"t i" amperes =$ i20 ohms@ F < i"ducta"ce >1 he"r5@ t < time i" seco"ds i < curre"t i" amperes
=$ i < 0 #he" t < 0, C"d i a$ter a lo"' time( A( 10 A ( 11(2 A ( 0 /( i"C"ite Problem .0: A (0 coil #hose resista"ce is 12 ohms is co""ected i" series #ith a 2. ohms resistor a"d to a 1.. batter5 a"d a s#itch( The s#itch is closed at t < 0( /etermi"e the time co"sta"t o$ the circuit( A( 0(3 sec ( 0(.+ sec ( 0( sec /( 0(+0 sec Problem .0%: The curre"t i" a coil deca5s as $ollo#s: #he" t < 0(002 sec, the curre"t is 10 mAJ #he" t < 0(00 s, the curre"t drops to . mA( The time co"sta"t o$ the coil is ( A( .(+0 ms ( 3(2 ms ( .(3 ms /( 2(1+ ms Problem .10: A time o$ 10 milliseco"ds is re9uired $or the curre"t o" a series F dc circuit to reach %0& o$ its C"al stead5 alue( Assume at t < 0, i>0@ < 0( )hat is the time co"sta"t i" seco"ds $or the circuit* A( .(2+ ms ( 3( ms ( .(3 ms /( .(3. ms Problem .11: A coil has a resista"ce o$ 10 ohms a"d a time co"sta"t o$ 1 seco"d( =$ the coil is co""ected across a stead5 pote"tial o$ 2. V, ho# much us the curre"t a$ter 2 ms* A( .(07 mA ( .(7% mA ( .(%1 mA /( .(3. mA
Problem .12:
The shu"t #i"di"' o$ a machi"e has a resista"ce o$ 0 ohms a"d a" i"ducta"ce o$ . is sudde"l5 s#itched o" to a 220-V suppl5( 6i"d the time take" $or the curre"t to rise to hal$ its stead5 state alue( A( 0(0+ sec ( 0(03. sec ( 0(02+1 sec /( 0(0172 sec Problem .13: A dc olta'e E is applied across a" F circuit at t < 0( At #hat time a$ter, is the olta'e across the resistor e9ual to that across the i"ductor* A( 0(%3 T ( 0(73 T ( 0(707 T /( 0(77% T Problem .1.: A +00-ohm rela5 coil has a" i"ducta"ce o$ 10 m( This rela5 re9uires a curre"t o$ .0 mA i" order to tri''er( o# lo"' a$ter the s#itch is closed #ill the rela5 tri''er i$ a 2. V / source is applied across its termi"als( Assume at t < 0, i < 0( A( 23(+. µsec ( 30(3 µsec ( 3+(3 µsec /( 37(22 µsec Problem .1+: A (0 coil #hose resista"ce is 12 ohms is co""ected i" series #ith a 2. ohms resistor a"d to a 1.. V batter5 a"d a s#itch( The s#itch is at t < 0( /etermi"e the curre"t at t < 0(1 sec( A( 1(+3 A ( 1(7+0 A ( 1(0+ A /( 1(2. A Problem .1: A coil hai"' a resista"ce o$ 10 Ω a"d i"ducta"ce o$ 10 is co""ected i" series #ith a 1+ Ω resistor( A 200-V / source is co""ected to the circuit at t < 0( /etermi"e the olta'e across the coil at t < 0(0+ sec( A( 1%0( V ( 1(+1 V ( 17(2 V /( 1+(%0 V
Problem .17: A series F circuit is co""ected across a dc source throu'h a s#itch( Three >3@ milliseco"ds a$ter the s#itch is closed, the olta'e across the i"ducta"ce is 20 V a"d drops to + V a$ter 20 ms( =$ < 100 ohms, C"d F( Assume t < 0, l < 0( A( 1(30 ( 1(22 ( 1(+% /( 1(2+ Problem .1: A 1Ω resistor is co""ected i" series #ith a 2-m i"ductor( =$ a 12V dc source is sudde"l5 co""ected across its termi"als, ho# lo"' #ill it take, such that the olta'e across the resistor #ill be t#ice as that o$ the co"ductor( A( 2(+ ms ( 1(7 ms ( 2(2 ms /( 1(% ms Problem .1%: A resista"ce o$ 100 k Ω is co""ected i" series #ith a 100 µ6 capacitor( =$ the combi"atio" is sudde"l5 co""ected across a 12+ V / source, determi"e the curre"t o"e seco"d a$ter the s#itch is closed( A( 1(13 mA ( 1(2+ mA ( 1(0+ mA /( 1(12 mA Problem .20: A" u"char'ed co"de"ser i" series #ith a 120-olt oltmeter o$ 10,000 ohms resista"ce is sudde"l5 co""ected to a 100 V batter5( I"e seco"d later, the oltmeter reads 0 olt( /etermi"e the capacita"ce o$ the co"de"ser( A( 17(+. µ6 ( 1%0(2 µ6 ( 1%+(7 µ6 /( 1%2(23 µ6 Problem .21: A 120 µ6 capacitor has a" i"itial char'ed o$ 00 µ6( =t is dischar'ed throu'h a .0 Ω resistor( o# lo"' #ill it take i" order $or the capacitor to dischar'e to 1+0 µ6* A( (+ ms ( (2 ms
( .( ms /( +(+ ms Problem .22: A +0 µ6 capacitor is co""ected across a .00 V dc source( =t is the" dischar'ed throu'h a oltmeter #hose resista"ce is 100-k Ω( o# lo"' #ill it take $or the capacitor to dischar'e 1( Q o$ stored e"er'5* A( 2(3 s ( 1(% s ( 2(0 s /( 1( s Problem .23: A 20 ohm resista"ce a"d a 0(001 $arad capacita"ce are i" series( A direct curre"t olta'e E o$ 100 olts is applied across the series circuit at t < 0 a"d the i"itial curre"t =>0@ < + A( The applicable diHere"tial e9uatio" is: >didt@? i< 0 Sole the diHere"tial e9uatio" a"d determi"e the resulti"' curre"t =>t@ at t < 0(01 seco"d( A( 3(3. A ( 3(7 A ( 2(7 A /( 3(03 A Problem .2.: A series circuit co"sist o$ < 2 !Ω a"d a" u"char'ed capacitor t@( A( +(+1 A ( (0 A ( (7 A /( 7(3. A Problem .3%:
A 10-ohm resista"ce a"d 0(001 $arad capacita"ce are i" series( A" A olta'e e < 100 si"377t is applied across the series circuit( The applicable diHere"tial e9uatio" is: >didt@ ? >1c@i < dedt Sole $or the particular solutio" >#ithout the complime"tar5 solutio"@ a"d determi"e the amplitude o$ the resulti"' si"usoidal curre"t i>t@( A( %(7 A ( 10(3 A ( (7% A /( 11(70 A Problem ..0: A series F circuit has < 10 ohms a"d F < 1 he"r5( The circuit is co""ected across a olta'e source e>t@ < 10 e -10t throu'h a s#itch that is i"itiall5 ope"( The s#itch is closed at t < 0( /etermi"e the curre"t a$ter 0(01 seco"d( Assume i"itial curre"t to be 4ero( A( ( A ( %0(+ A ( %(3 A /( %2(2 A Problem ..1: The diHere"tial e9uatio" o$ a series circuit #ith / applied olta'e is: i ? 1 idt < E =$ < +0 ohms, < 0(0001 $arad, E < 100 olts a"d i>0@ < 2(0 amperes, determi"e the Faplace tra"s$orm epressio" $or l>s@( A( l>s@ < 2s ? 200 ( l>s@ < 2s>s ? 2@ ( l>s@ < 2s ? +0 /( l>s@ < 2s ? 2 Problem ..2: A series circuit has < 1k Ω a"d < µ6 #ith a" i"itial char'e o$ 2000 µ( The combi"atio" is co""ected across a 100V dc source a"d the s#itch is closed at t < 0( =$ the capacitor is co""ected i" the circuit such that it #ill be dischar'i"', determi"e the Faplace tra"s$orm epressio" o$ the curre"t dra#"( A( i>s@ < 0(12s ? 10 ( i>s@ < 0(12s ? 12 ( i>s@ < 0(10s ? 10 /( i>s@ < 0(10s ? 12
Problem ..3:
/etermi"e the i"erse Faplace tra"s$orm o$ = >s@ < 200s2 ? +0s ? 102+( A( =>t@ < 2 e-2+tsi"100t ( =>t@ < 2t e-2+tsi"100t ( =>t@ < 2 e-2+tcos100t /( =>t@ < 2t e-2+tcos100t TEST 13 Problem ...: A / ammeter has a" i"ter"al resista"ce o$ 0(1 ohm( A shu"t o$ 1(010 10-3 is co""ected to the ammeter( )hat is the multiplier o$ the set up* A( 0 ( 100 ( +0 /( 10 Problem ..+: A 1& dOArso"al meter moeme"t has coil a"d s#ampi"' resista"ce addi"' to 200 ohms( The $ull-scale olta'e is +0 mV( /etermi"e the shu"t resista"ce re9uired 1 A $ull-scale curre"t meter* A( +2(02 mΩ ( .%(22 mΩ ( +0(01 mΩ /( .(7. mΩ Problem ..: A 'ala"ometer #ith a 20-ohm coil resista"ce has a $ull-scale deWectio" curre"t o$ 10 mA( =$ a 0(02 ohm is placed across the meter to i"crease its capacit5, #hat is the approimate "e# $ull scale curre"t o$ the meter* A( 10(10 A ( 11(01 A ( 10(11 A /( 10(01 A Problem ..7: A moi"' iro" meter 'ies $ull-scale deWectio" #ith 1oo V applied across the coil( The coil has 20,000 tur"s a"d a resista"ce o$ 2(+ k Ω( =$ this i"strume"t is to be used as a" ammeter #ith a $ull-scale deWectio" o$ 10 A, ho# ma"5 tur"s are "eeded* A( 0 ( 100 ( +0
/( 70 Problem ..: A moi"' iro" ammeter is #ou"d #ith +0 tur"s a"d 'ies $ullscale deWectio" #ith . A( =$ it is desired to ete"d the $ull-scale readi"' to 10 A, ho# ma"5 tur"s are "eeded o" the same bobbi"* A( .0 ( 20 ( 10 /( 30 Problem ..%: A 'ala"ometer has a coil resista"ce o$ +0 ohms a"d a curre"t se"sitiit5 o$ 0(001 µA per mm( o# much is the olta'e across its termi"als #he" the deWectio" is 1+ cm at $ull-scale* A( 7(+0 µV ( 10(0 µV ( (2+ µV /( %(0+ µV Problem .+0: A 0-10 mA 'ala"ometer #ith a coil resista"ce o$ 20 ohms is co"erted to 0-+0 oltmeter b5 usi"' A( +0 ohms shu"t resistor ( .%0 ohms series resistor ( +000 ohms series resistor /( +020 ohms series resistor Problem .+1: A certai" +0 µA metermoeme"t has a resista"ce o$ %0 ohms( )hat alue o$ series multiplier is "eeded to make the i"strume"t to read + V >maimum@( A( 102 kΩ ( %%(%1 kΩ ( 110 kΩ /( % kΩ Problem .+2: A oltmeter #ith a" i"ter"al resista"ce o$ +000 ohms is calibrated to read 10 olts at $ull-scale( o# much series resista"ce is "eeded i" order to measure 1+0 olts at $ull-scale* A( 70 kΩ ( 7+ kΩ ( 72 kΩ /( 7 kΩ
Problem .+3: A 1000 ohms per olt, 2 & meter moeme"t has coil resista"ce o$ 200 ohms( /etermi"e the eter"al resista"ce "ecessar5 to proide a $ull-scale readi"' o$ + V( A( .(+ kΩ ( +(2 kΩ ( +(0 kΩ /( .( kΩ Problem .+.: A" ammeter rated + A, hai"' a resista"ce o$ 0(+ Ω, is to be co"erted i"to a 200-V oltmeter b5 co""ecti"' a resistor i" series #ith the ammeter( alculate the alue o$ the resista"ce( A( 37(. Ω ( 3.( Ω ( 3%(+ Ω /( 3+(+ Ω Problem .++: A direct curre"t #attmeter #ith a pote"tial coil co""ected across the load side o$ the i"strume"ts reads 2+0 )( =$ the olta'e across the load is rated at 230 V, #hat is the actual po#er dra#" b5 the load( The resista"ce o$ the pote"tial coil is k"o#" to be 1 k Ω( A( 1%.(2 ) ( 1%7(1 ) ( 1%3(+ ) /( 1%( ) Problem .+: The stator o$ a ..0-V, +0 hp shu"t motor is tested at 7+ $or its i"sulatio" resista"ce bet#ee" termi"als co""ected to'ether a"d the 'rou"d $rame( )he" a +0,000-ohm oltmeter is co""ected i" series #ith a 00-V / source a"d the i"sulatio" resista"ce, the meter i"dicates 12+ V( alculate the i"sulatio" resista"ce( A( 170 kΩ ( 1%0 kΩ ( 10 kΩ /( 200 kΩ Problem .+7: =t is desired to measure the resista"ce o$ the i"sulatio" bet#ee" the motor #i"di"' a"d the motor $rame( A 300-V, +0,000 ohm
oltmeter is used i" maki"' the measureme"ts( The oltmeter #he" co""ected across the source reads 230 V a"d #he" co""ected i" series #ith the i"sulatio", it reads + V( 6i"d the i"sulatio" resista"ce( A( 2(.2 !Ω ( 2(2+ !Ω ( 2(% !Ω /( 2(3+ !Ω Problem .+: )he" a 1+0 k Ω oltmeter is co""ected across a co"sta"t source, it re'isters 230 V( )he" o"e termi"al is co""ected to the core o$ a cable #hile the rubber i"sulatio" o$ the cable is co""ected to the other termi"al o$ the li"e, the meter re'isters 1+ V( /etermi"e the i"sulatio" resista"ce o$ the cable( A( 21+0 kΩ ( 2000 kΩ ( 2202 kΩ /( 2.0 kΩ Problem .+%: A" u"k"o#" olta'e is to be measured b5 mea"s o$ a 2+0 Vscale oltmeter hai"' a" i"ter"al resista"ce i$ 10,000 ohms( 6or sa$et5 purposes a 1000 ohms resistor is co""ected i" series #ith o"e o$ the oltmeter termi"als( =$ the meter reads 200 olts, determi"e the u"k"o#" olta'e( A( 2+0 V ( 220 V ( 230 V /( 300 V Problem .0: T#o ide"tical 1000 ohm per olt /c oltmeter are co""ected i" series to measure a" u"k"o#" suppl5 olta'e( The Crst oltmeter is co""ected to its 200 V scale #hile the seco"d oltmeter is co""ected to its 2+0 V scale( )hat is the olta'e o$ the suppl5 i$ the Crst oltmeter reads 100 V( A( 22+ V ( 220 V ( 230 V /( 2.2 V Problem .1: A 20 kΩ per olt oltmeter i"dicated a readi"' o$ 2+0 V o" its 300 V scale #he" used to measure a" u"k"o#" olta'e( =$ a +0 L Ω
resistor #as co""ected i" series #ith the i"strume"t duri"' the test, determi"e the alue o$ the u"k"o#" olta'e( A( 23 V ( 2.+ V ( 2. V /( 22+ V Problem .2: A 300-V oltmeter dra#s 2-mA curre"t $or $ull-scale deWectio"( This oltmeter is used to measure the olta'e across a +0 k Ω resistor i" series #ith a 2+ kΩ resistor( The combi"atio" o$ the resistor is bei"' co""ected across 1+0-V source( )hat is the oltmeter readi"'* A( % V ( 102 V ( %0 V /( V Problem .3: The !eralco test o$ a 10-A #attmeter hai"' a co"sta"t o$ 0(., the disk makes .0 reolutio"s i" +3( seco"ds( The aera'e olts a" amperes duri"' this period o$ test are 11 olts "ad %(. A( )hat is the perce"t accurac5 o$ the meter at this load* A( %7(.+& ( %(+& ( %(07& /( %(..& Problem ..: =" a test o$ 10-ampere #attmeter hai"' a co"sta"t o$ 0(.0, the disk makes .0 reolutio"s i" ++ seco"ds( The aera'e olts a"d amperes duri"' this period are 11 olts a"d 10 amps( /etermi"e the perce"t accurac5 o$ this meter at this load( A( %2(3.& ( %1(03& ( 3(.& /( %0(2& Problem .+: A 'ie" ampere-hour meter is u"der test b5 co""ecti"' it across a 230-V / source( 6or a duratio" o$ 10 mi"utes, a co"sta"t curre"t o$ 20 A Wo#s( This meter re'isters +70(+ a"d +2(3 k)-hr be$ore a"d a$ter the test respectiel5( alculate the perce"ta'e accurac5 o$ the meter( A( %2(31& ( %0(02& ( %1(..&
/( %(20& Problem .: A 1+ A, 120-V #atthour meter has a disk co"sta"t o$ 2( )he" tested o" a u"it5 po#er $actor load, 2. disk reolutio"s are cou"ted i" a period o$ 2 mi"utes( o# ma"5 disk reolutio"s #ould be cou"ted per mi"ute i$ the po#er $actor #here cha"'ed to 0(+ la''i"'( Assume the same li"e curre"t a"d olta'e i" both co"ditio"s( A( ( 10 ( /( 12 Problem .7: A si"'le-phase three-#ire, 0 4, 220 V, #atthour-meter has a disc co"sta"t 1(2( /etermi"e the e"er'5 recorded b5 the meter a$ter 1,000 reotutio"s o$ the disc( A( 21( k)-hr ( 20(+ k)-hr ( 2+(. k)-hr /( 27( k)-hr Problem .: A 11+-V, 10 A, three-phase #att-hour meter, hai"' a basi meter co"sta"t o$ k < 23 is co""ected to a three-phase, three-#ire circuit throu'h a 100:+ ampere T a"d 2300:11+ olt PT( A time check sho#s that the meter disk is maki"' 1+ reolutio"s i" +0 seco"ds( )hat is actual k) o$ the load* A( 720 k) ( 2 k) ( +2. k) /( 30 k) Problem .%: A po#er pla"t customer dra#s po#er at 220 olts $rom tra"s$ormers o" a pole( urre"t tra"s$ormers #ith ratio 200+ are used to meter the electrical usa'e( )hat is the multiplier o$ the k)-hr a"d dema"d meters* A( .0 ( 200 ( 100 /( 0 Problem .70:
A curre"t tra"s$ormer #ith a tur"s ratio o$ 100:+ a"d a pote"tial tra"s$ormer #ith a tur"s ratio o$ 10:1 are co""ected to the curre"t a"d olta'e coils o$ a si"'le-phase #attmeter measuri"' po#er deliered to a load( =$ the #attmeter readi"' is 2.0 k), #hat is the actual po#er measured deliered to the load* A( +0,000 #atts ( .2,000 #atts ( .,000 #atts /( .+,000 #atts Problem .71: At a 11+ kV substatio", the PT ratio is 1000 a"d the T is 1200+( The pote"tial 'oi"' i"to the #attmeter is 11+ olts( )hat is the !) i"dicated #he" the #attmeter reads 00 #atts* A( 1%2 !) ( 1+(0 !) ( 1%(2 !) /( 1+0 !) Problem .72: A 1+ A, 120-V #att-hour meter has a disk co"sta"t o$ 2( )he" tested o" a 0( po#er $actor load, 2. disk reolutio"s are cou"ted i" a period o$ 3 mi"utes( alculate the curre"t dra#" b5 the load( A( 10 A ( A ( A /( 12 A Problem .73: =" a 'ie" test, it #as $ou"d out that #ith a curre"t .0 A, the disc o$ a 'ie" ampere-hour meter made 10 reolutio"s i" . mi"utes( =$ the meter co"sta"t o$ the i"strume"t is +0 coulombs per reolutio", determi"e the multipl5i"' $actor to be used i" order to 'ie the correct e"er'5 co"sumptio" o$ the load( A( 0(33 ( 0(707 ( 0(%22 /( 0(
Problem .7.: A" u"k"o#" resistor as sho#" is to be measured b5 mea"s o$ a )heatsto"e brid'e, #he" the ratio arms are arra"'ed 1 < 10 ohms a"d 2 < 1200 ohms, bala"ce is obtai"ed #he" rheostat arm is e9ual to 12+ ohms, #hat is the alue o$ the u"k"o#" resistor*
A( 10(.7 Ω ( 11(2. Ω ( 13(22 Ω /( 1.(0+ Ω Problem .7+: A" u"k"o#" resista"ce as sho#" is measured b5 a slide #ire brid'e >a simple $orm o$ )heatsto"e brid'e0 A is a u"i$orm #ire 100 cm lo"' a"d / is a slidi"' co"tact( ala"ced is obtai"ed #he" A/ e9uals 32(+ cm( 6i"d the alue o$ the u"k"o#" resista"ce (
A( ( ( /(
.+(32 .(1. +0(0. .3(..
Ω Ω Ω Ω
Problem .7: A t#o-co"ductor u"der'oes cable 200 $t lo"' to i"terco""ect a home base statio" to a"other statio"( I"e co"ductor is 'rou"ded at some poi"t( A !urra5 loop test #as co"ducted at the home base #ith a 100-cm slide #ire brid'e( =$ a bala"ce o" the brid'e #as obtai"ed at 7 cm, at #hat dista"ce is the $ault $rom the home base*
A( ( ( /(
127 $t 1.1+ $t 13.. $t 1302 $t Test 1.
Problem .77: A $our-pole, / 'e"erator #ith lap #i"di"' . slots a"d . eleme"ts per slot( o# ma"5 coils does it hae* A( . ( 3. ( 1%2 /( % Problem .7: =$ the armature o$ a" ei'ht-pole machi"e #ere #ou"d #ith a simple #ae #i"di"', ho# ma"5 parallel paths #ould there be* A( 1 paths ( paths ( 2 paths /( . paths Problem .7%: The armature o$ a $our-pole shu"t 'e"erator is lap #ou"d a"d 'e"erates 21 olts #he" ru""i"' at 00 rpm( The armature has 1.. slots, #ith si co"ductors per slot( =$ this armature is re#ou"d, #ae co""ected, C"d the em$ 'e"erated at the same speed a"d Wu per pole( A( .12 V ( .27 V ( .+ V
/( .32 V Problem .0: A t#o-pole / 'e"erator has a" armature co"tai"i"' a total o$ .0 co"ductors co""ected i" t#o parallel paths( The Wu per pole is (. 10 li"es a"d the speed o$ the prime moer is 30 rpm( The resista"ce o$ each co"ductor is 0(01 ohm a"d the curre"t carr5i"' capacit5 o$ each co"ductor is 10 A( alculate the termi"al olta'e o$ the 'e"erator( A( 127( V ( 12+(2 V ( 130( V /( 12(. V Problem .1: A $our-pole / 'e"erator has a" armature #i"di"' co"tai"i"' a total o$ . co"ductors co""ected i" t#o parallel paths( =$ the Wu per pole is 0(321 10 ma#ells a"d the speed o$ rotatio" o$ the armature is 1,00 rpm( alculate the ampacit5 re9uired i" each armature co"ductor i$ the po#er deeloped b5 the armature is + k)( A( .0 A ( 30 A ( 20 A /( 2+ A Problem .2: A .-pole / 'e"erator #ith duple lap #i"di"' has . slots a"d $our eleme"ts per slot( The Wu per pole is 2(+ 10 ma#ells a"d it ru"s at 1+00 rpm( )hat is the output olta'e* A( 0 V ( 30 V ( 22+ V /( 120 V Problem .3: The armature o$ a .-pole, 12 slots shu"t 'e"erator is lap #ou"d #ith $our co"ductors per slot( The Wu per pole is +0 m)b( The armature a"d shu"t Celd resista"ces are 0(0. ohm a"d +0 ohms respectiel5( /etermi"e the speed o$ the machi"e #he" suppl5i"' .00 A at a termi"al olta'e o$ 2+0 V( A( 1+ rpm ( 22 rpm ( 3. rpm /( 2. rpm Problem ..:
A $our-pole shu"t co""ected 'e"erator has a lap co""ected armature #ith 72 co"ductors( The Wu pole is 2+ m)b( =$ the 'e"erator supplies t#o hu"dred C$t5 110 V, 7+ ) i"ca"desce"t lamp( The Celd a"d armature resista"ce are 110 ohms a"d 0(02+ ohm respectiel5( /etermi"e the speed i" rpm o$ the 'e"erator( A( 3. ( 3 ( 377 /( 3%3 Problem .+: A speed-i"dicati"' deice co"sists o$ a 2 pole perma"e"t ma'"et / 'e"erator #ith a 2000-ohms / oltmeter co""ected across its termi"als( The 'e"erator has a" armature #ith 1200 co"ductors hai"' t#o parallel paths a"d a total resista"ce o$ 1000 ohms bet#ee" brushes( The air 'ap Wu is .0,000 li"es per pole( =$ the oltmeter reads 10 V, at #hat speed #ill this readi"' i"dicates* A( 1+3. rpm ( 1+2 rpm ( 1+12 rpm /( 1+2 rpm Problem .: A shu"t 'e"erator supplies a load o$ +,+00 ) at 110 V throu'h a pair o$ $eeder co"ductors hai"' a resista"ce o$ 0(02 ohm each( The armature, shu"t Celd resista"ces are 0(1+ ohm a"d +0 ohms respectiel5( 6i"d the em$ 'e"erated( A( 11% V ( 11 V ( 121 V /( 120 V Problem .7: The "o"-load olta'e o$ a +0-k), 220 olts, shu"t 'e"erator i" the 6EK laborator5 is 232 olts a"d rated load olta'e is 220 olts( The armature resista"ce i"cludi"' brushes, is 0(02 ohm a"d the resista"ce o$ the shu"t Celd resista"ce is +2 ohms( )hat is the i"duced electroma'"etic $orce at rated load* A( 221(3 V ( 22(02 V ( 22.(+ V /( 227(0+ V
Problem .: The Celd curre"t o$ a 10 k), 2+0 olts / shu"t 'e"erator is A #he" ru""i"' $ull load at rated termi"al olta'e( =$ the combi"ed armature a"d brush resista"ce is 0(02 ohm, sole $or the electrical eGcie"c5 o$ the 'e"erator( A( %2(13& ( %.(0+ & ( %3(73 & /( %1(7 & Problem .%: The Celd circuit o$ a 200,000 #atts, 230-V shu"t 'e"erator is A #he" ru""i"' $ull load at rated termi"al olta'e( =$ the combi"ed brush a"d armature resista"ce is 0(03 ohm, sole $or the electrical eGcie"c5 o$ the 'e"erator( A( +(3. & ( %(1. & ( (%1 & /( 7(2 & Problem .%0: The Celd curre"t o$ a 100 L), 2+0-olt shu"t 'e"erator is + amperes #he" delieri"' po#er at rated termi"al olta'e a"d rated load curre"t( The combi"ed armature a"d brush resista"ce is 0(01 ohm( /etermi"e the eGcie"c5 o$ the 'e"erator( A( %7(2 & ( %.(3 & ( %(2 & /( %.(7 & Problem .%1: The armature o$ a shu"t 'e"erator has 0(0+ ohm( The termi"al olta'e is 100 olts #hile the curre"t is .0 amperes( )hat is it eGcie"c5* A( %+(1+ & ( %7(+ & ( %7(30 & /( %(+2 & Problem .%2: A shu"t 'e"erator is co""ected to a load that dra#s 2( k)( a < 0(0.Ω( =$ the po#er deeloped i" the armature is 10(3& o$ the po#er deliered to the load( /etermi"e the termi"al olta'e o$ the 'e"erator( A( 23 V ( 2.0 V
( 23. V /( 23 V Problem .%3: A 1+ k), 230 V, shu"t 'e"erator #as ru" li'ht as a motor to determi"e its stra5 po#er losses at rated load( The applied olta'e across the armature, computed $or test #as 2+. V a"d the armature curre"t dra#" is 2A( The armature a"d shu"t Celd resista"ce are 0(2+ a"d 100 Ω, respectiel5( alculate the 'e"erator eGcie"c5 at hal$ load( Assume stra5 po#er losses to be co"sta"t(X A( 1(3. & ( .(3 & ( 3(77 & /( 7(0 & Problem .%.: A shu"t 'e"erator supplies 100 A at 200 V( The armature a"d shu"t resista"ces are 0(02+ Ω a"d 100 Ω, respectiel5( =$ the copper losses are e9ual to the iro" losses at this load, C"d the brake horsepo#er o$ the e"'i"e drii"' the 'e"erator( A( ( ( /(
2(.3 2(+ 30(12 32(2.
hp hp hp hp
Problem .%+: A 20 k), 200 V shu"t 'e"erator is operated at rated load( =$ the drii"' e"'i"e is deelopi"' 30 bhp, determi"e the iro" a"d $rictio" losses( Armature resista"ce is 0(0+ ohm a"d shu"t Celd resista"ce is +0 ohms( A( 13.0 ) ( 103% ) ( %+. ) /( 103. ) Problem .%: A 220 V shu"t 'e"erator has a" armature resista"ce o$ 0(02 Ω a"d a shu"t resista"ce o$ .. Ω( At rated load, the drii"' e"'i"e deelops 2(2+ hp( =$ the iro" a"d $rictio" losses amou"t to 100 ), ho# much is the curre"t deliered to the load at rated co"ditio"* A( 1% A ( 200 A ( 1%+ A /( 1%2 A
Problem .%7: A / 'e"erator has "o-load output olta'e o$ 120 olts( =ts armature circuit resista"ce is 0(%+ ohm a"d its Celd coils are separatel5 e"er'i4ed( =$ the load is rated 2 k) at 11+ V( Me'lecti"' the eHect o$ armature reactio", #hat po#er could be deliered to the load* A( 1,+1 ) ( 2,10 ) ( 1,70 ) /( 2,000 ) Problem .%: The armature o$ a -pole separatel5 ecited dc 'e"erator is lap #ou"d #ith +3. co"ductors( This machi"e deliers po#er to the load at 2+0 V #hile bei"' drie" at 1000 rpm( At this load, the armature circuit dissipates .0 )( =$ the Wu per pole o$ this 'e"erator is 30-m)b, determi"e the k) rati"' o$ the load sered( Assume a total brush co"tact drop o$ 2 V( A( 10(7 k) ( 11(2. k) ( 12(+ k) /( 1+(.. k) Problem .%%: A separatel5 ecited 'e"erator #he" ru""i"' at 1200 rpm supplies 200 A at 12+ V to a circuit o$ co"sta"t resista"ce( Armature circuit resista"ce is 0(01 ohm( /etermi"e the termi"al olta'e #he" the speed is dropped to 1000 rpm* Assume that the Celd curre"t is u"altered( A( 10. V ( 12+ V ( 11 V /( 11. V Problem +00: A dc series 'e"erator is suppl5i"' a curre"t o$ + A to a series li'hti"' s5stem throu'h a $eeder o$ total resista"ce, 1(0 ohm( The termi"al olta'e is 2+00 V( The armature a"d series Celd resista"ces are respectiel5 1 a"d 1+ ohms respectiel5( A 30-ohm dierter resista"ce is shu"ted across the series Celd( /etermi"e the po#er deeloped i" the armature o$ the 'e"erator( A( 132(2+ k) ( 137(+0 k) ( 123(2% k) /( 13(0 k)
Problem +01: A 30 k) series 'e"erator has a" eGcie"c5 o$ perce"t #he" operati"' at rated load( =$ the stra5 po#er loss is 1+& o$ the $ull load losses, calculate the maimum eGcie"c5 o$ the 'e"erator( Assume that the stra5 po#er loss is co"sta"t a"d the other losses ar5 as the s9uare o$ the load( A( %0(.3 & ( %2(0. & ( %1(12 & /( %(%2 & Problem +02: The h5steresis a"d edd5 curre"t losses o$ a / machi"e ru""i"' at 1000rpm are 2+0 #atts a"d 100 #atts, respectiel5( =$ the Wu remai"s co"sta"t, at #hat speed #ill the total iro" loss be haled* A( +00 rpm ( ++0 rpm ( +70 rpm /( 30 rpm Problem +03: The edd5 curre"t loss i" a / machi"e is 00 #atts #he" the total Wu is 2,000,000 ma#ells per pole a"d the machi"e is ru""i"' at 1000 rpm( /etermi"e the loss #he" the ecitatio" o$ the machi"e is ad8usted to produce 2,+00,000 ma#ells per pole a"d the speed is i"creased to 1200 rpm( A( %00 #atts ( 102+ #atts ( 120 #atts /( 13+0 #atts Problem +0.: =" a / 'e"erator, the iro" losses at 1,000 rpm are 10 k) at a 'ie" Celd curre"t( At a speed o$ 7+0 rpm a"d at the same Celd curre"t, the total iro" losses become k)( Assume the h5steresis loss is directl5 proportio"al to the speed a"d the edd5 curre"t loss is proportio"al to the s9uare o$ the speed( /etermi"e the iro" losses at +00 rpm( A( . k) ( + k) ( 3 k) /( 2 k)
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