1. Thirty-six dry cells are are connected connected in in four four parallel parallel groups of nine nine cells in series per per group. group. If the voltage and current rang of each cell is 1,45 volts and 4 amp respecvely, respecvely, (a calculate the voltage, current and po!er rang of the enre com"inaon. (" #ecalculate the pro"lem for nine parallel groups of four cells in series per group. #$r%d& (a 'oltage, 'oltage, urrent and )o!er )o!er #ang (" 'oltage, urrent and )o!er #ang *ol%n& (a '+ (1.45'( '+ 1.5' I+ (40(4 I+10
(" '+ (1.45'(4 '+ 5./' I+ (40( I+ 0
)+ ' I + (1.5' (10 )+ 2/./ 3as
)+ (5./'(0 )+ 2/./ 3as
2. alculate the average average voltage generated in a moving conductor if it cuts 2.5 x 1 max!ells in (a (a 14 seconds and (" 1/ seconds. #$r%d& 6av *ol%n& 6av+ 7 t x 1/ (a 6av + 2.5 x 1 (14 x 1/ 1/
+ 1 'olt
(" 6av 6av + 2.5 x 1 (1/1/ (1/1/ + 2 'olts . 0 six-pole 8-generator has an armature !inding !ith 54 conductors conductors connected in six parallel paths. alculate the generated voltage in this machine if each pole produces 1.5 x 1 max!ells and the armature speed is 1/ rpm. #$r%d& 6g
*ol%n& 6g + () 7 # 9 0 x 1-/ 6g + (((1.5 x 1(1/(54 ( x 1-/ + 24.4/' : 25 ' 4. The armature !inding of the generator of )ro". is modi;ed so that it has t!o parallel paths instead of six. 0t !hat speed should the machine "e driven if is to develop the same voltage as "efore the change, assuming all other condions to remain unchanged< #$r%d& # + 0rmature speed *ol%n& 6g + () 7 # 9 0 x 1-/ #+ ((25((2 x 1/ ((1.5 x 1(5 #+ 1.25 rpm
5. alculate the voltage generated "y a four-pole 8 machine given the follo!ing parculars& num"er of slots in armature + 55= num"er of conductors per slot + 4= >ux per pole + + 2.2 x 1 max!ells= speed +12 rpm= num"er of parallel paths in armature+2. #$r%d& 6g *ol%n& 6g + () 7 # 9 0 x 1-/ 6g + (4(2.2 x 1(12(55 x 1-/ ((2 + 2'
. If the armature !inding in pro".5 had four parallel paths, !hat should have "een the generated voltage< #$r%d&
6g *ol%n& 6g + () 7 # 9 0 x 1-/ 6g + (4(2.2 x 1(12(55 x 1-/ ((4 6g + 115'
?. 0 four-pole machine generates 25 volts !hen operated at 1,5 rpm. If the >ux per pole is 1./5 x 1 max!ells, the num"er of armature slots is 45, and the armature !inding has t!o parallel paths, calculate (@ the total num"er of armature conductors= (" the num"er of conductors in each slot. #e$%d& @. no. of amurture conductors ". no. condutors in each slots *ol%n& 6g + ()A#B @ x 1/ Cet D + no.of conductors B + slots (v (a B + ((25 ( (2 (4 (1./ x 1 (1,5 (1-/ B + 2?.2? (" D + 2?.2? 45 D + conductors /. Eo! many total conductors and conductors per slot !ould "e necessary in the armature of )ro". ? if the !inding had four parallel paths< Fiven& @+4 # + 15 rpm ) +4 G + 1./5 x 1 6g + 25v #e$d& B and no. of conductors or slot *oln& 6g + ()A#B @ x 1-/ (a 25 +( ((4 (1./5 x 1 (15 B (4 x 1-/ , + 1.11 x 11 B x 1-/ 24 B + 54.54 slots (" no. of conductors + 54.54 45 + 12.1 . The speed of the generators of )ro". ? is decreased to 1,5 rpm. (@ 3hat !ill "e the generated voltage if the >ux per pole is maintained at the same value, i.e., 1./5 x 1 max!ells< (" To !hat value of >ux per pole should the excitaon "e adHusted if the generated voltage is to remain the same, i.e., 25 volts< *ol%n& @. 6g + )A#B x 1-/ @ + (4 (1./5x1(15(2? x 1-/ (2 + 224.?/v ". 25 + 4 (G(15(2? x 1-/ (2
G + 2.5 x 1 max!ell 1. 3hat is the fre$uency of the alternang voltage generated in the armature conductors of (@ a sixpole -rpm machine< (". an eigth-pole ?5-rpm machine< (c. a 1-pole 5-rpm machine< Fiven& @. ) + poles ". ) + / poles c. ) + 1 # + rpm # + ?5 rpm # + 5 rpm #ead& +< #ead& +< #ead& +< *oln& *oln& *oln& +)# 12 +)#12 +)#12 + ( 12 + /(?5 12 + 1(5 12 + 45hJ + 5hJ + 41.? hJ 11. Eo! many poles are therenin a generator in !hich the armature fre$uency is cps !hen operang at a speed of rpm< Five& #ead& )+< + cps #+ rpm *oln& +)# 12 + )( 12 )+ poles 12. 0t !hat speed is an armature rotang in a 12-pole machine if the fre$uency in the armature conductors is 5 cps< Fiven& #ead& #+< )+ 12 poles + 5 cps *oln& + )# 12 #+ f(1/ ) + 5(12 12 #+ 5 rpm 1. alculate the force exerted "y each conductor, inch long on the armature of the dc motor !hen it carries the current of amp and lies in a ;eld the density of !hich 52, lines per s$uare inch. #e$Kd& )+< *oln& + ()x#12 )+ (x12 )+ poles
14. 3hat tor$ue !ill the conductor of pro"lem 1 develop if it lies on an armature the diameter of !hich is inch<
Fiven& 8+in
#e$Kd& T+<
+2.4/5 l"s *oln& T+ xr r+82 r+in2+4.5in r+4.5in x (1L12in + .?5L T+ (.?5L x (2.4/5l"s T+.L-l". 15. The armature of a dc motor has 1 slots !ith 1 conductors in each slots. Anly / percent of the conductors lie directly under the pole faces, !here the >ux density is uniform at 4, lines per s$uare inch. If the armature-core diameter is ?.25 inch, its length 4.25 inch and the current in each conductor is 25 amp, calculate & (a the force exerted "y the armature tending to produce rotaon= (" the tor$ue in pound-feet. Fiven& *lots+1 M/N onductors+1 M/N O+ 4liness$uare inches 8+?.5in C+4.25in I+25amp #e$Kd& a (l" " T (l"-L *oln& a + (O x I x C11.x1 + (1x1x./x4x25x4.25 11.x1 + 14l"s. " T+ x r T+ (14l"s x (?.25in2 x (1L12in T+ 44.1 l"-L
1. Psing the data of pro".15 calculate the tor$ue that !ill develop if the >ux density is reduce "y 5 percent !hile the current is increase to 4 amp. Fiven& O+ 4-Q4x (.5R + 4? I+4amp 8+?.5in C+4.25in *lots+1 M/N onductors+1 M/N #e$Kd& T+< *oln&
+ (O x I x C11.x1 + (1x1x./x4?x4x4.25 11.x1 +221.?4l"s. T+ x r T+221.?4l"s x (?.25in2 x (1L12in T+?l"-L
1?. 3hat total current must the armature of a dc motor carry, given the S. informaon& armature slots + ?2= conductor per slot + = pole arcs cover ?.5 percent of circumference= >ux density + 5/, lines per s$uare inch= armature core length + / inch= armature core diameter + 21 inch= no. of armature paths in parallel + = tor$ue + 15 l"-L. Fiven& )+ M?.5N *lot+?2 O+5/ 8+21in T+15l"-L #e$Kd& I+< *oln&
r+ Q(21in2 x (1L12inR2 r+ ./?5L + Tr + 15l"-L./?5L +12l"s I+ Q(12 x (11.x1RQ(5/ x ( x (.?5 x (?2 x (/R I+5.amp
1/. 3hat must "e the total armature !inding current in pro".1? if the tor$ue increases to 12 l"-L !hile the >ux density drops "y 4 N. Fiven& T+12 O+5/-Q5/ x (.4R +55/ r+ ./?5 )+ M?.5N *lot+?2 *oln&
+ Tr + 12l"-L./?5L +1?1.4l"s I+ Q(1?1.4 x (11.x1RQ(55/ x ( x (.?5 x (?2 x (/R I+114.2amp
