Problem 505: A compound dynamo supplies a load of 20 kW at 400 V through a feeder having a resistance eual to 0!" ohm! #he shunt and series $eld resistances are %5 ohms and 0!0& ohm respectively! 'etermine the total electromotive force (hen the generator is connected long shunt! Assume a brush contact drop of " V per brush and an armature resistance of 0!" ohm! A! *! +! '!
4"%!)4 V 4"2!50 V 4"5!,& V 42"!44 V
Problem 50&: A long shunt compound generator has the follo(ing parameters: -a.0!"Ω/ -se . 0!05 Ω and -sh . "20 Ω! #his machine supplies po(er a aggregate dc load of "0 kW! At this load the armature generates 24& volts! 'etermine the terminal voltage! A! 25"!55 V *! 25,!%& V +! 25)!%2 V '! 24,!)) V Problem 50,: A compound generator is to be operated/ as a at1compounded long shunt compound generator! #o obtain the same rated voltage at full load and at no load (hen operated as a shunt generator/ it is necessary to increase the $eld current by 0!20 A! #he shunt $eld (inding has "000 turns per pole/ and the series $eld (inding has 4 turns per pole! f the full load armature current of the compound generator is 35 A and the series $eld resistance is 0!025 ohm/ calculate the divert resistance reuired! A! 0!0&% Ω *! +! 0!042 0!02% Ω Ω '! 0!0)4 Ω Problem 50%: #he armature/ series $elds and shunt $eld resistances of a "25 kW/2501V long shunt cumulative compound '+ generator are 0!025 Ω/ 0!0" Ω and )0 Ω/ respectively! f the stray po(er loss at rated load is 5 kW/ determine the motor brake horsepo(er reuired to drive this machine! Assume a brush drop of 2 V and a stray load loss of " of the output! A! "%2!)2 hp *! 20"!)) hp
+! "30!%5 hp '! 2"0!5& hp Problem 503: A long shunt compound generator delivers "00 A/ 250 V at rated load! #he resistances of the various (indings are: -a . 0!" Ω/ -ip . 0!02 Ω/ -s h . "00 Ω and -se . 0!0 25 Ω! f the stray po(er losses amount to "!% kW/ solve for the overall eciency of the generator! A! 30!52 *! %,!4) +! %%!)2 '! %&!)& Problem 5"0: A certain 5!5 kW/ "251V '+ long shunt compound generator (as operated as a shunt motor at no load for determination of stray po(er losses! With ")5 V eual to the generated emf at full load applied to the armature and at normal speed of ",00 rpm/ the current input to the armature (as found to be 2!5 A! #he armature/ shunt $eld and series $eld resistances are 0!2 Ω/ 2 5 Ω/ and 0!25 Ω respectively! 'etermine the eciency of the generator at rated load! A! %4!52 *! %)!5, +! %0!2" '! %2!2) Problem 5"": A compound dynamo supplies a load of 20 kW at 400 V through a feeder having a resistance eual to 0!" ohm! #he shunt and series $eld resistances are %5 ohms and 0!0& ohm respectively! 'etermine the total electromotive force (hen the generator is connected short shunt! Assume a brush contact drop of " V per brush and an armature resistance of 0!" ohm! A! *! +! '!
4"5!4% 4""!42 V V 4"&!2) V 4"2!42 V
Problem 5"2: A short shunt compound generator has the follo(ing has an armature/ series $eld and shunt $eld resistances are 0!04 ohm/ 0!0) ohm and %0 ohms respectively! #he generator serves a 20 kW/ 200 V load through a feeder (ith an euivalent resistance of 0!" ohm! 6olve for the po(er generated by the armature! A! 2)!%4 kW *! 2"!)0 kW
+! 22!23 kW '! 2"!32 kW Problem 5"): A short shunt compound generator has an armature/ shunt $eld and series $eld resistances of 0!02 Ω/ %0 Ω and 0!0) Ω respectively! #he generator7s induced emf is 5"0 V (hen the terminal voltage is 500 V! 8o( much load current is delivered under this condition! A! "3,!4, A *! "30!4& A +! "34!5) A '! "32!,2 A Problem 5"4: A short shunt compound generator delivers "50 A at a terminal voltage is 2)0 V! #he shunt $eld current is 2!5 A! #he resistances of the armature/ series $eld and diverter are 0!0)2 Ω/ 0!0"5 Ω and 0!0) Ω respectively! +alculate the electrical eciency of the generator at this load! A! 3&!4 *! 3)!% +! 34!2 '! 35!, Problem 5"5: #(o shunt '+ generators 9" and 92 are rated at "00 and "50 kW at ""0 V respectively! #heir eternal load characteristics may be considered as straight line! #he drop in the terminal voltage from no1 load to full1load is "0 volts for 9" and 20 volts for 92! +alculate the no1 load voltages of these generators (hen they are operated in parallel to supply a load of 2000 A/ (hich is divided bet(een them in proportion to their ratings! A! *! +! '!
9"" 9" 9"
. . .
"2)!, "2"!, "2"!,
V/ V/ V/
922 . ")"!, "))!, V 92 . "))!, V 92 . ")"!, V
Problem 5"&: #(o shunt generators operating in parallel are giving a total output of )20 kW! 9;<;-A#=A->A#?-; <'?+;' ;>@ -;66#A<+; A 0!02 ohm 450 * 0!025 ohm 4&0
@ind the bus bar voltage!
*! 4, +! &4 '! )&
Problem 52": A 50 kW/ 220 V dc generator has a voltage regulation of "0! t is connected in parallel (ith a battery of ""5 cells/ each (ith an emf of 2 V and internal resistance of 0!0" ohm! What current (ill the battery carry if by accident the load is trip1oB from the bus A! 0 A *! %!02 A +! &!"5 A '! ,!20 A Problem 522: #(o identical &00 kW/ 2)0 V dc generators are operating in parallel and take eual shares of an %00 kW/ 250 V bus load! #he ratings of the generator are as follo(s: >A+8<; PA-A>;#;9;<;-A#=- " 9;<;-A#=- 2 -egulation CD 2 4 -ated Po(er CkWD 500 400 f the load drops to 2"00 A/ determine the ne( operating bus voltage! A! 252 V *! 25& V +! 254 V '! 25) V Problem 524: #(o shunt generators are operating in parallel and taking eual shares of a 2400 A/ 2)0 V bus load! #he ratings of the generator are as follo(s: >A+8<; PA-A>;#;9;<;-A#=- " 9;<;-A#=- 2 -egulation CD ) 4 -ated Po(erCkWD 500 &00 -ated VoltageCVD 250 250 f an additional &001A load is connected to the bus/ determine the current delivered by each generator at this condition! A! "5"& A/ "4%4 A *! "525 A/ "4,5 A +! "&"2 A/ ")%% A '! "&55 A/ ")45 A #est "5
Problem 525: A simple lap (ound armature has 5%0 conductors and carries of "25 amperes per armature current path! f the u per pole is 20 mWb! +alculate the electromagnetic torue developed by the armature A! 2"0!&4 <1m *! 252!,2 <1m +! 2)0!,, <1m '! 20,!&) <1m Problem 52&: A &1pole lap (ound shunt motor takes )00 A (hen the speed is 500 rpm! #he u per pole is 0!0& Wb and the armature has %,0 turns!
(eaken the u by 2 from no1load to full load/ determine speed of the motor at no1load! Assume the armature resistance to be 0!"5 ohm! A! "202 rpm *! "22" rpm +! ""22 rpm '! "0"0 rpm Problem 5)0: #he nameplate rating of a shunt motor is "50 hp/ &00 volts/ 205 A/ ",00 rpm! #he resistance of the shunt $eld circuit is 240 ohms and the total armature circuit resistance is 0!"5 ohm! +alculate the speed regulation of the motor! A! 4!0, *! 4!%3 +! 5!25 '! 5!"% Problem 5)": A '+ shunt motor runs at &00 rpm on a 2401volt supply (hile dra(ing a line current of )0 A! ts armature and $led resistances are 0!5 Ω and "20 Ω respectively! What resistance should be placed in series (ith the armature circuit in order to reduce the speed to 400 rpm! Assume no changes in the armature or $eld current! A! 2!&3 Ω *! 2!4" Ω +! 2!0, Ω '! 2!%)Ω Problem 5)2: A "201V shunt motor has an euivalent of 0!5 Ω and a $eld resistance of &0 Ω! A full load/ the motor takes "0 A and the speed is "000 rpm! At (hat speed must this motor maybe driven as a generator to deliver "0 A to an eternal load at "20 V A! ""5% rpm *! "0%& rpm +! "2&2 rpm '! "045 rpm Problem 5)): A bet1 driven "50 kW shunt (ound '+ generator is running at 450 rpm and is supplying full load to a bus bar at 240 V! At (hat speed (ill it run if the belt breaks and the machine continues to run taking %!5 kW from the bus bar #he armature and $eld resistance are 0!05 ohm and %5 ohms respectively! #he brush contact drop is "!5 volt per brush!
A! *! +! '!
)35 rpm )%% rpm 402 rpm )5% rpm
Problem 5)4: A shunt motor dra(s a current of 40 A from a "20 V source and runs at "200 rpm at rated load! #he armature and $eld circuit resistance are 0!" Ω and &0 Ω respectively! 'etermine the speed of the motor at half load! Assume a brush drop of 2 V at rated load and " V at half load! A! ""%0 rpm *! "2)% rpm +! "2)0 rpm '! "02& rpm Problem 5)5: A '+ shunt motor has a full load rating of "5 hp/ 2)0 volts/ 5,!" amperes/ "400 rpm! #he armature circuit resistance is 0!") ohm and the $eld circuit resistance is ""5 ohms!
'! "!22 ohms
Problem 5)%: A "01hp 2)0 V '+ motor of %5 full load eciency of %& is located 450 ft from the supply mains! f the motor7s starting current is "!,5 times the full load current/ (hat is the smallest cross1sectional area of cooper (ire reuired (hen the allo(able voltage drop in the feeder at starting is limited to 24 volts A! )0 >+> *! 2% >+> +! 2& >+> '! 2, >+> Problem 5)3: #he nameplate rating of a shunt motor is "50 hp/ &00 volts/ 205 A/ ",00 rpm! #he resistance of the shunt $eld circuit is 240 ohms and the total armature circuit resistance is 0!"5 ohm! f the motor is to be deliver full1load torue at "/200 rpm/ (hat value of resistance must be added to the armature circuit A! 0!%)) ohm *! 0!%02 ohm +! 0!%2, ohm '! 0!%&2 ohm Problem 540: A "20 V shunt motor dra(s a current of ,, A at rated load! #he armature and shunt $eld resistances are 0!2 Ω and &0 ohms respectively! A multi1tap starter rheostat is inserted in the armature circuit to limit the starting current! f the rheostat has a resistance of "!,)2 ohms/ determine the percentage tap used such that the starting current (ill be limited to "50 of its full load value A! &0 *! 50 +! 55 '! 45 Problem 54": A "01hp po(er 220 V '+ shunt motor has an armature and $eld resistance of 0!25 ohm and "00 ohms respectively! #he full load eciency is %) ! 'etermine the value of starting resistance in order that starting current (ill not eceed 200 percent of full1load value! A! 2!%% Ω
*! 2!53 Ω +! 2!"5 Ω '! 2!45 Ω Problem 542: A 50 8P/ 550 V shunt (ound motor dra(s a line current of 4!5 A at no load! #he shunt $eld resistance is 2,5 ohms and the armature resistance eclusive of brushes/ is 0!) ohm/ the brush drop at full load is 2 V! At full load/ the motor dra(s a line current of %4 A! +urrent the eciency at full load! A! 32!0 *! %%!5 +! 3"!2 '! %3!3 Problem 54): A "001volt shunt motor is developing & hp (hile operating at an overall eciency of %& ! #he armature and shunt $eld resistance are 0!0& and 50 ohms respectively! 'etermine stray po(er losses! A! ),% W *! )&, W +! )32 W '! )&4 W Problem 544: #he shaft po(er of a shunt motor is ,!% hp! t dra(s 50 A from "20 V! #he $eld (inding dra(s "!2 A! What is the eciency of the motor A! 34!, *! 3) +! 3&!3 '! 3%!2 Problem 545: A 500 V shunt motor running at ,20 rpm takes an armature current of 50 A! #he euivalent armature resistance is 0!4 ohm! What resistance must be placed in series (ith the armature to reduce the speed to 540 rpm (hile maintaining the same torue A! 2!2 ohms *! 2!& ohms +! 2!4 ohms '! 2!% ohms Problem 54&:
A current shunt motor has an resistance of 0!05 ohm! t dra(s 50 A at a terminal voltage of "20 V! Assume other miscellaneous losses at "! 'etermine the output horsepo(er of the motor! A! %!5 hp *! ,!" hp +! &!% hp '! ,!% hp Problem 54,: #he armature and $eld resistance of a shunt machine are 0!2 ohm and ""0 ohms respectively! While running as a generated emf is 250 V at "200 rpm! f the machine is run as a shunt motor/ it takes 4 A at 220 V! A a certain load the motor takes )0 A at 220 V! 8o(ever on load/ the armature reaction (eakens the $eld by 2 ! @ind the motor speed at his load! A! ""20 rpm *! "050 rpm +! "042 rpm '! "025 rpm Problem 54%: A shunt motor/ (hich has a $eld resistance of 220 ohms and an armature resistance of 0!% ohm takes 2& A from a 2&0 V supply (hen running at 500 rpm on full load! n order to control the speed of the motor a "!21ohm resistor is connected in series (ith the armature! +alculate the speed at (hich the motor (ill run (hen supplying full load torue! A! 4)% rpm *! 445 rpm +! 424 rpm '! 4,2 rpm Problem 543: #he input and output po(ers of a 220 V/ shunt motor are )0 and 2% kW respectively! #he $eld and armature circuit resistance are 40 ohms 0!0"25 ohm respectively! 'etermine the eciency of the motor if the output po(er is reduced to "0 kW! A! %)!5& *! %%!&, +! %4!3) '! %&!4% Problem 550: A 220 V series motor takes "5 A and runs at ,00 rpm! #he armature resistance including the resistance of the series (inding is
0!% ohm! At (hat speed (ill it run if a 21ohm resistance is connected in series (ith supply voltage Assume the motor is taking the same current! A! 533 rpm *! &0" rpm +! 5,2 rpm '! 5%) rpm
Problem 55": #he euivalent armature resistance of a series motor is 0!" ohm! When connected across a ""01V mains/ the armature takes 20 A and its speed is "000 rpm! 'etermine its speed (hen the armature takes 50 A from the same mains/ (ith the $eld increased by "0! A! %03 rpm *! 345 rpm +! %5& rpm '! %%4 rpm Problem 552: A 400 V series motor has a $eld resistance of 0!2 ohm and an armature resistance of 0!" ohm! #he motor takes )0 A of current at "000 rpm (hile developing full load torue! What is the motor develops &0 of full load torue! A! ")02!4 rpm *! "25&!2 rpm +! "23,!& rpm '! "")5!5 rpm Problem 55): A "0 hp/ 2)01V/ "200 rpm series motor having rated load eciency of %5!5! #he armature resistance including brushes is 0!) ohm! #he $eld resistance is 0!25 ohm! Assuming the u varies directly as the armature current/ (hat value of resistance should be placed in series (ith this motor (hen starting/ in order that the starting current maybe limited to a value that (ill eert a starting torue eual to "50 of its rated torue A! 4!, ohms *! 4!4 ohms +! 5!" ohms '! )!% ohms Problem 554: #he $eld and armature resistances of a 2201V series motor are 0!2 Ω and 0!" Ω/ respectively! #he motor takes )0 A of current (hile
running at ,00 rpm! f the total iron and friction losses are )50 W/ determine the motor eciency! A! 30!& *! 3"!5 +! %3!4 '! 32!2 Problem 555: A "001V series motor is used to drive a load through a pulley! #his machine has an armature resistance of 0!2 ohm and a series of $eld resistance of 0!25 ohm! When a torue of 25 <1m is applied to the pulley/ the speed is &00 rpm! f stray po(er losses at this load is )00 W/ calculate the armature current! A! 20!&2 A *! 2"!%3 A +! 22!,2 A '! 2)!4" A Problem 55&: A 400 V series motor/ having an euivalent armature circuit resistance of 0!5 ohm/ takes 44 A of current (hile running at &50 rpm! What is the motor speed for a line current of )& A A! %0) rpm *! %22 rpm +! %"2 rpm '! %0& rpm Problem 55,: #he resistance of each of the t(o coils of a series motor is 0!04 ohm/ armature resistance/ 0!04 ohm! #he motor takes 50 A at "00 V (hile running at %00 rpm and the coils are in series! What (ill it speed if the coils are re1connected in parallel (hile the load torue is doubled A! %00 rpm *! 400 rpm +! 20 rpm '! &50 rpm Problem 55%: =n full load a 50 V series motor takes "00 A and runs at %20 rpm! #he armature and series $eld resistances are 0!" and 0!04 ohm respectively! What (ill be its speed (hen developing half1full load torue and (ith a 0!0% ohm diverter connected across the series $eld (inding! Assume u is proportional to $eld current! A! "5&) rpm *! "&)4 rpm
+! ")53 rpm '! "423 rpm Problem 553: A 400 V series motor (orking (ith unsaturated $eld is taking &0 A and running at %40 rpm! #he total resistance of the motor is 0!" ohm! A (hat speed (ill the motor run (hen developing half1full load torue! A! *! +! '!
""3) rpm "202 rpm ""&, rpm ")52 rpm
Problem 5&0: A long shunt compound motors takes a current of 42 A from a 2)0 V source! #he generator parameters are: -a . 0!" Ω/ -se . 0!2 ' and -sh . 50 Ω! f the friction and (indage losses amount to 400 W/ determine the eciency of the machine! A! %2024 *! %0!5& +! %"!22 '! ,3!5) Problem 5&": A 2)0 V/ long shunt machine has the follo(ing parameters: -a . 2!0Ω/ -sh . 4&0 Ω and -se . 0!25 Ω! When the machine is run at no1 load at its normal speed and rated voltage/ the armature dra(s 0!& A! 'etermine the armature current dra(n if the machine delivers an output of 5 bhp! A! 24!)5 A *! 2"!22 A +! 20!)& A '! 22!%) A Problem 5&2: A 25 hp/ 250 V long shunt compound motor takes 5 A (hen running light and runs at ""50 rpm! Armature resistance/ 0!"5Ω/ 6hunt $led resistance/ 200Ω and series $eld resistance/ 0!05 Ω! At rated load the motor takes %&!5 A and runs at ,20 rpm! 'etermine the ratio of torue developed from no1load to full load! A! ":2& *! ":)4 +! ":22 '! ":)% Problem 5&):
A 200 V shunt motor has armature and shunt $eld resistance of 0!"5 Ω and "25 Ω/ respectively! When running light/ it takes & A and runs at "200 rpm! A series (inding of 0!05 ohm is added to make it long shunt cumulatively compounded! #his (inding increases the u per pole by 25 (hen the motor is taking its full load current of "0 A!
%%, rpm %30 rpm %&% rpm %&5 rpm
Problem 5&4: A 220 V '+ motor has an armature resistance of 0!4 ohm/ a shunt $eld resistance of ",5 ohms and a series $eld resistance of 4 ohms! #his machine is connected as a short shunt compound motor to 220 V mains! +alculate the po(er developed by the armature current is )0 A!
motor is found to be 3"0 rpm and the balanced on a 0!"& m brake arm reads ""!3 kg! #he dead (eight of the arm is found to be "!03 kg! What is the output hp of the door motor A! 3!40 hp *! "0!)% hp +! %!2& hp '! 3!5% hp Problem 5&%: A shunt motor (ith an armature and $eld resistance of 0!055 and )2 ohms respectively/ is to be tested for its mechanical eciency by means of a rope brake! When the motor is running at "400 rpm/ the longitudinal pull on the & Finch diameter pulley is 5, pounds! #he readings of the line ammeter and voltmeter are )5 and "05/ respectively! +alculate the eciency! A! ,,!"0 *! ,5!)2 +! ,%!2% '! ,3!"2 Problem 5&3: A shunt motor (as tested by means of a pony brake having a length arm of )!5 feet and a tare (eight of 5!, lbs! #he current dra(n by the machine from a 240 V line (as 50!3 A (hen the scale reading (as 24 lbs and the speed of the motor (as "2"5 rpm! +alculate the rotational losses of the motor! #he armature and the shunt $eld resistances of the machine are 0!25Ω and "20 Ω/ respectively! A! &,4 W *! &32 W +! &20 W '! ,05 W Problem 5,0: +alculate the force that (ill be eerted on the scale in a pony brake test (hen a 201hp/ "/400 rpm motor is operating at full load! #he length of the brake arm is )ft! and the tare (eight of the brake is )!,5 lb! A! )0!45 lbs *! 2%!,& lbs +! 2"!54 lbs '! )&!)) lbs #;6# "& Problem 5,":
What is the speed of a "00 W/ 2)0 volt/ three1phase/ four pole/ &0 8G alternator A! 450 rpm *! 300 rpm +! "200 rpm '! "%00 rpm Problem 5,2: A si1pole/ )1phase A+ generator has ,2 slots/ the coil span is "2! What is the pitch factor A! "!000 *! 0!3)3 +! 0!3%5 '! 0!3&& Problem 5,): A three1phase alternator has & slots per pole per phase! 'etermine the distribution factor! A! 0!3,, *! 0!35& +! 0!3&) '! 0!34% Problem 5,4: A )0 >VA/ "5 kV three1phase alternator (ill have a per phase nominal impedance of HHHHH! A! ,!5 ohms *! 3 ohms +! "5 ohms '!
coils are all connected in series! #he (inding is (ye1connected! 'etermine the open circuit emf of the alternator! A! 5)2!" V *! 504!2 V +! 5"2!4 V '! 5,2!4 V Problem 5,,: A four1pole/ three1phase/ 50 8G/ star connected Ac generator has 24 stator slots! #here are & conductors per slot and a sinusoidally distributed u per pole of &) mWb! @ind the terminal voltage on open circuit/ if the coil span factor is unity! A! 54&!05 V *! 5,3!44 V +! 5&%!4% V '! 55%!&2 V Problem 5,%: A three1phase/ &1pole/ ,21slot armature of a synchronous generator is (ound using a t(o1layer lap coil having 20 conductors per coil (ith a pitch of %)!))! #he u per pole is 4/%00/000 ma(ells! f the rotor of the generator is driven at a speed of "200rpm/ calculate the induced emf per phase! A! 5/&%0 V *! 5/)30 V +! 5/5&4 V '! 5/%54 V Problem 5,3: A ">VA/ "" kV/ three1phase (ye1connected synchronous generator has a synchronous reactance of 5 ohms and a negligible resistance per phase! At a certain $eld current the generator delivers rated load at 0!3 lagging po(er factor at "" kV! @or the same ecitation/ (hat is the terminal voltage at 0!3 leading po(er factor full1 load A! ""!& kV *! ""!4 kV +! ""!) kV '! ""!5 kV Problem 5%0: A three1phase star connected A+ generator s rated at 2!5 >VA/ "" kV/ &0 8G! #he generator has a negligible resistance and a synchronous reactance of & ohms per phase! t delivers full1load current at 0!%0 lagging po(er factor at rated voltage! What (ill be the
terminal voltage for the same ecitation and load current/ if the po(er factor is 0!%0 leading A! "4!2 kV *! ")!5 kV +! "5!) kV '! "2!, kV Problem 5%": A "200 kVA/ &&00 volt/ )1phase I1 connected alternator has an eBective resistance of 0!40 and a reactance of & ohms per phase! t delivers full1load current at 0!%0 lagging po(er factor at rated voltage! What (ill be the terminal voltage for the same ecitation and load current/ if the po(er factor is 0!%0 leading A! 45&0 V *! 3%,% V +! ,%3% V '! 4250 V Problem 5%2: A 2500 kVA/ &&00 V synchronous turbo alternator is operating at full1load at 0!% pf lagging! #his machine has a synchronous reactance per phase is "0!4 ohms and a negligible resistance! +alculate the percentage voltage regulation A! 4%!5& *! 42!)5 +! 45!%4 '! 4)!3& Problem 5%): A 501 kVA/ 5501volt single1phase alternator dra(s a $eld current "0 A at rated load! With the same $eld current/ the open circuit emf and short1circuit current are )00 V and "50 A! #he ohmic resistance of the armature bet(een terminals is 0!"5 ohm! #he ratio of eBective to ohmic resistance maybe taken as "!5! 'etermine the regulation at 0!% po(er factor lagging! A! 2,!% *! 2&!4 +! 25!5 '! 24!3 Problem 5%4: A generator is rated "00 >W/ ")!% kV and 30 po(er factor! #he eBective resistance is "!5 times the ohmic resistance! #he ohmic resistance is obtained connecting t(o terminals to a '+ source! #he current and voltage are %,!& A and V respectively! What is the eBective resistance per phase
A! *! +! '!
0!05") ohm 0!0&%5 ohm 0!)42 ohm 0!0&", ohm
Problem 5%5: #o get the armature resistance of a "00 >W/ ")!% kV and 30 po(er factor generator/ t(o terminals are connected to a '+ source! #he measured current and voltage are %,!& amperes and & volts respectively! What is the '+ resistance per phase A! 0!022) ohm *! 0!0)42 ohm +! 0!0&%5 ohm '! 0!0&", ohm Problem 5%&: A 2 >VA/ 2!)1kV three1phase I1connected alternator operates at rated kVA at a po(er of %0 ! #he dc armature (inding resistance bet(een terminals is 0!0% Ω! #he $eld takes ,0 A at "25 V from an eciter euipment! @riction and (indage loss is 20 kW/ iron losses )& kW and stray load losses are 2!0 kW! +alculate the eciency of the alternator! Assume the eBective armature1(inding resistance is "20 of the '+ resistance! A! 34!0 *! 32!" +! 3)!2 '! %3!5 Problem 5%,: 'etermine the eciency of a "500 kVA/ 2)00 V/ )1phase/ I1 connected alternator/ (hich operates at rated output (ith a po(er factor of %0 ! #he '+ armature resistance at ,0 degree + bet(een terminals is 0!0% ohm! #he $eld takes ,0 A at "20 V from the eciter euipment! @riction and (indage losses are "5! kW/ iron loss is )5 kW and stray load losses is "!5 kW! Assume the eBective armature (inding resistance is "!5 times the '+ value! A! 34!5& *! 30!)" +! 3)!)5 '! 32!&2 Problem 5%%: A 2/500 kVA/ three1phase/ &0 8G/ &!& kV (ye1connected alternator has a $eld resistance of 0!45 Ω and armature resistance of 0!05 Ω per phase! #he $eld current at full load 0!%5 pf/ is 200 A! #he
stray po(er losses amount to %2 kW! +alculate the eciency of the alternator at full load/ 0!%5 pf lagging! A! 3)!, *! 34!% +! 35!2 '! 3&!) Problem 5%3: A &!& kV/ I1connected/ )1phase alternator has a synchronous reactance of & Ω per phase and a negligible resistance! At a certain $eld current the armature is kno(n to induce 5!% kV per phase! +alculate the maimum po(er that can be developed by the alternator at this ecitation! A! "2 >W *! "" >W +! 3!% >W '! "0 >W Problem 530: An ""/000 volts three1phase (ye1connected turbo alternator has a synchronous reactance of & ohms and negligible reactance per phase! When the $eld current is % A/ the open circuit voltage is "2/000 volts! 'etermine the armature current (hen alternator developed maimum po(er! A! "45& A *! ","2 A +! "&4) A '! "5&& A Problem 53": A three1phase/ "" kV (ye connected synchronous alternator has a synchronous reactance of % ohms per phase but negligible resistance! f the ecitation is such that the open circuit voltage is "4kV/ determine the po(er factor at the maimum output! A! 0!,%& *! 0!,,2 +! 0!,3) '! 0!,0% Problem 532: A three1phase A+ generator is supplying po(er to a load of )200 kW at 2)00 volts and a po(er factor of &0 ! Assume that the loss of the line/ the generator armature and the load is eual to "0 of the load/ (hat (ould be the savings of (atts if the po(er factor (ere raised to %0 A! "00/000
*! "40/000 +! %0/000 '! 2)0/000 Problem 53): A three1phase 50 >VA/ ")!% kV/ )&00 rpm/ &0 8G grid connected generator (ith a synchronous reactance of )/% ohms per phase operating (ith a lagging po(er factor of 0!%% at rated voltage and current! 'etermine the ne( po(er factor if the rotor current is decreased by 5 ! A! 0!320 *! 0!3)5 +! 0!30, '! 0!3,, Problem 534: A )1phase 50 >VA/ ")!% kV/ )&00 rpm/ &0 8G grid connected generator (ith a synchronous reactance of )!% ohms per phase operating (ith a lagging of 0!%% at rated voltage and current! f the load decreases such that its prime mover po(er is decreased by 25 and the rotor current decreases same percentage/ (hat (ill be the ne( pf A! 0!32% *! 0!33% +! 0!3%, '! 0!303 Problem 535: A )1phase 50 >VA/ ")!% kV/ )&00 rpm/ &0 8G grid connected generator (ith a synchronous reactance of )!% ohms per phase operating (ith a lagging pf of 0!%% at rated voltage and current! f the machine is to provide a lagging reactive po(er of 40 >VA- and still operating at its rated current/ (hat percent change in the rotor current is reuired A! "0!4% *! "0!24 +! ""!)0 '! "2!2% Problem 53&: A three1phase turbo alternator has a reactance of "5 ohms and negligible resistance/ the machine dra(s an armature current of 250 amperes at 0!% pf lagging (hen running on "2/000 volts in$nite busbars! f the steam admission is constant but the emf is raised by 20 ! +alculate the ne( operating pf! A! 0!54,
*! 0!5%& +! 0!503 '! 0!5,5 Problem 53,: A three1phase/ 20 kV/ synchronous alternator has a reactance of "0 ohms and a negligible resistance! #he machine dra(s an armature current of "50 A/ 0!%0 pf lagging! f the steam admission is constant and $eld current is adEusted raising the induced the emf by 25 determine the value of the ne( armature current! A! 442 A *! 452 A +! 42" A '! 4)) A Problem 53%: A standby 'iesel generator set (ill have the follo(ing loads: nductive load dra(ing 50 kVA at 0!% po(er factor: Kightning load dra(ing 20 kVA at "!0 po(er factor! At (hat po(er factor (ill the generator operate A! *! +! '!
0!%55 lagging 0!%,2 lagging 0!%2" lagging 0!%34 lagging
Problem 533: A 250 V/ )0 8G generator supplies po(er to a parallel circuit consisting of a 20 hp motor (hose eciency is 30 at 0!%0 pf lagging and a second load that dra(s an apparent po(er of , kVA at unity pf! 'etermine the system reactive po(er! A! 2)!5%2 kVA*! "2!4)5 kVA+! "0!)4" kVA'! 20!)%4 kVAProblem &00: #(o )1 φ/ 4"&0 V/ &0 8G alternators are operated in parallel! #he total load of the system is "050 W at ,5 lagging pf! f alternator A is carrying ,00 kW at %0 pf lagging/ determine kVA- of alternator *! A! 40" kVA*! 405 kVA+! 4"" kVA'! 40% kVAProblem &0":
#(o alternators A and * are operating in parallel supplying a load dra(ing "000 kVA at 0!%0 po(er factor lagging! f alternator A contributes 50 kVA at 0!&0 po(er factor lagging/ determine the po(er factor of alternator *! A! 0!32% lagging *! 0!%52 lagging +! 0!30" lagging '! 0!3,, lagging Problem &02: #(o identical three1phase I1connected alternators A and * share eually a load of "0 >W at ))1kV and %0 lagging pf! #he synchronous reactance of each machine is 4 ohms per phase and the armature resistance is negligible! Alternator A has its $eld ecitation adEusted to carry "25 A lagging current/ (hat is the current supplied by alternator * A! 3& A *! 3, A +! 3% A '! 35 A Problem &0): Alternator A C"00 kVA/ ) φ/ 240 V/ &0 8G/ "%00 rpmD! #he load of alternator A is &0 kW at 30 pf lagging and the load of alternator * is %0 kW at ,0 pf lagging! 'etermine pf of load! A! 0!,55 lagging *! 0!,%4 lagging +! 0!%3) lagging '! 0!%&& lagging Problem &04: #(o )1phase/ I1connected turbo alternators supply a load of )000 kW at &!& kV and at 0!%5 po(er factor lagging! Alternator A contributes &00 kVA- at 0!32 po(er factor lagging! 6olve for the po(er factor of alternator *! A! 0!,2& *! 0!,32 +! 0!,04 '! 0!,&% Problem &05: #(o alternators are operating in parallel supplying a common load of 4250 kW at 0!%5 po(er factor lagging! Alternator A contributes &00 kVA- at 0!32 po(er factor lagging! 6olve for the po(er factor of alternator *!
A! *! +! '!
0!%") lagging 0!%)4 lagging 0!%04 lagging 0!%20 lagging
Problem &0&: #(o I1connected alternators A and * running in parallel supply the follo(ing loads at )!) kV Koad ": %00 kW at unity pf Koad 2: &00 kW at 0!% pf lagging Koad ): 400 kW at 0!,0, pf lagging f alternator A is adEusted to carry an armature current of "50 A at 0!%5 pf lagging/ (hat is the armature current of alternator * A! 20% A *! "%0 A +! 200 A '! "30 A Problem &0,: #(o A+ generators running in parallel supply the follo(ing loads: 400 kW at unity pfL 500 kW at 0!3 pf laggingL &00 kW at 0!%&& pf lagging! =ne machine is loaded to "000 kW at a pf of 0!32 lagging/ (hat is the operating po(er factor of the second machine! A! 0!3&4 lagging *! 0!l32" lagging +! 0!3)2 lagging '! 0!35" lagging Problem &0%: #(o alternators are connected in parallel! #he total load is 4250 kW at 0!%5 pf lagging! Alternator A operates (ith a load of 2"25 kW at 0!,0, pf lagging! 'etermine the kVA load of alternator *! A! 2245 *! 20,% +! 2"%5 '! 24"0 Problem &03: 6ipalay >ines/ has t(o )1phase/ &0 8G A+ generators operating in parallel! #he $rst unit has a capacity of "000 kVA and the second unit has a capacity of "500 kVA! #he $rst is driven by a prime mover so adEusted that the freuency fall from &" 8G at no1load to 53!& 8G at full1load! #he second has a diBerent speed1load characteristics/ the freuency fall from &"!4 8G at no1load to 53!2 hM at full1load! When these alternators are Eointly delivering 2000 kW/ (hat is the load of each generator
A! *! +! '!
%%4 kW/ """& kW %&, kW/ "")) kW 3"5 kW/ "0%5 kW %04 kW/ ""3& kW
Problem &"0: #(o alternators are driven by shunt motors! #he shunt motors have speed1load droop characteristics of ) and 4 respectively! alternators are in parallel and each carrying 50 kW! #here is automatic speed1load control! An additional 50 kW is s(itched What are the resulting loads of the alternators assuming that speed1load control of each is not adEusted A! ,%!5, kWJ ,"!4) kW *! %2!5" kWJ &,!43 kW +! ,5 kWJ ,5 kW '! %0!)" kWJ &3!&3 kW
#he no on! the
Problem &"": #here are t(o alternators/ "00 kW/ )1phase in parallel are driven by shunt motors (hose speed1load characteristics are as follo(s: Alternator
induced per turn is % volts/ determine the cross sectional of the core in cm2! A! 232 *! ),5 +! 2%% '! )&2 Problem &"4: #he net cross section of a transformer is 20 suare inches! #he maimum u density is "" kilogausses! #he freuency is &0 8G! f there are "/000 turns in the primary/ determine the primary induced emf! A! ),%0 V *! )345 V +! )530 V '! )%50 V Problem &"5: +alculate the total magnetic u in a &01cycle transformer in (hich the induced emf per turn of the (inding is eual to 2 V! A! *! +! '!
,!50 mWb ,!02 mWb ,!50 mWb ,!42 mWb
Problem &"&: #he lo( side of a certain (elding transformer has 2 turns and delivers )00 A! f the high voltage side has )0 turns/ ho( much current o(s through it A! "0 A *! "2 A +! 20 A '! "5 A Problem &",: A single1phase transformer is rated 4/"&0 V and 250 V secondary! t has "/500 turns in the primary and a voltage regulation of %! What should be the number of turns in secondary (inding A! %% turns *! 32 turns +! 30 turns '! %& turns Problem &"%: #he current densities in the primary and secondary (indings of a step do(n transformer are "250 and "500 A per suare inch/
respectively! #he ratio of transformation is "0:" and the mean length per turn of the primary is "5 greater than that of the secondary! f the primary (inding resistance is 20 ohms/ calculate the resistance of the secondary (indings! A! 0!202 ohm *! 0!2"3 ohm +! 0!203 ohm '! 0!220 ohm Problem &"3: A certain transformer has a ratio of % is to "! #he primary (inding resistance is 0!002%) ohm per turn and has ""55 more turns than the secondary (inding! f the copper losses in the primary is 20 less than in the secondary/ $nd resistance of the secondary (inding! A! 0!0,) ohm *! 0!030 ohm +! 0!0&% ohm '! 0!0%4 ohm Problem &20: A "0 kVA/ 2440J2401V single1phase transformer has the follo(ing resistances and reactances! @ind the primary voltage reuired to produce 240 V at the secondary terminals at full1load/ (hen the po(er factor is 0!% lagging! r" . ) Ω/ " . "5 Ω r2 . 0!0) Ω/ 2 . 0!"50 Ω A! 2450 V *! 25,2 V +! 243& V '! 243& V Problem &2": A "01kVA/ 2/000J400 V/ single1phase distribution transformer has a primary and secondary (inding impedances of 5!0 N E"0 and 0!2 N E0!45 ohms/ respectively! +alculate the voltage across the secondary terminals at full1load/ %0 po(er factor lagging/ (hen the primary is supplied (ith 2/000 volts A! 400 V *! )34 V +! )%5 V '! ),3 V Problem &22: A single1phase transformer rated ,5 kVA/ %000 volts primary 240 volts secondary/ is given the short circuit test! With the secondary terminals short1circuited/ 440 volts C&0 8GD is impressed on the
primary/ (hich then dra(s rated currents and ""25 (atts! 6olve for the percentage impedance of the transformer! A! 5!23 *! 4!3) +! 5!50 '! 5!") Problem &2): A short circuit test (as performed upon a "01kVA/ 2)00J2)0 volt transformer (ith the follo(ing results: ;sc . "), voltsL Psc ."32 WL lsc . 4!)4 A! +alculate in primary terms the reactance of the transformer! A! )"!5& ohms *! 23!%% ohms +! "0!"3 ohms '! "2!45 ohms Problem &24: A single1phase/ 25 kVA/ 4%00J240 volt transformer (as given a short circuit tests: With the secondary terminals short1circuited/ 3)!,5 volts (as applied on the primary so that the ammeter reads rated current and the (attmeters reads "&2!,4 (atts/ all on the primary side! 6olve for the percentage resistance of the transformer! A! "!35 *! )!)3 +! )!02 '! 2!2) Problem &25: #he follo(ing data (ere obtained (hen a short circuit test (as performed upon a "00 kVA/ 2400J240 volts distribution ttransformer: ;sc. ,2 voltsL l sc . 4"!& AL P sc . "/"%0 W! All instruments are on the high side during the short circuit test! +alculate the euivalent resistance an reactance of the transformer! A! 0!%&2 ohm/ "!53 ohms *! 0!&%2 ohm/ "!,) ohms +! 0!,52 ohm/ "!,) ohms '! 0!,52 ohm/ "!53 ohms Problem &2&: A ")!% kVJ4%0 V/ "0 >VA three1phase transformer has 5 impedance! What is the impedance in ohms referred to the primary A! 0!352 ohm *! 0!0) ohm +! 5!"25 ohms '! 3!0" ohms
Problem &2,: A short circuit test (as performed on a 20 kVA/ 2000J200 V single1phase transformer! With the secondary (inding short1circuited/ full1load current o(s in the primary (inding (ith "00 V applied on it! #he (attmeter connected in the primary read )00 W! 'etermine the terminal voltage on full1load unity pf! A! "3%!& V *! "3)!4 V +! "3&!, V '! "35!2 V Problem &2%: #he follo(ing data (ere obtained (hen a short1circuit test (as performed upon a "00 kVA/ 2400J240 volts distribution transformer: s;c . ,2 voltsL lsc . 4"!& AL P sc . "/"%0 W! All instruments are on the high side during the short circuit test! +alculate the percent regulation at a po(er factor of 0!,5 lagging! A! 2!54 *! 2!%& +! 2!&2 '! 2!," Problem &23: A 2001 kVA transformer (ith impedance of 5 and the po(er factor of the load is %5! #he primary voltage is &/000 volts (hile copper loss 5 kW! @ind the percentage regulation! A! 5!0) *! 5!2" +! 4!4) '! 4!0) Problem &)0: A "50 kVA/ three1phase transformer supplies "00 kVA at 50 lagging po(er factor! #he transformer7s (inding impedance is 2 resistance and 5 reactance/ based on "50 kVA! 'etermine the voltage regulation of the transformer at this load! Assume "00 voltage! A! )!55 *! 5!)) +! 4!24 '! 4!05 Problem &)": A short circuit test (as performed upon a "01kVA/ 2)00J2)0 volt transformer (ith the follo(ing results: ;sc . "), voltsL Psc . "32 (L lsc .
4!)4 A! +alculate the percent regulation at a lagging po(er factor of 0!,0,! A! 5!2% *! 5!55 +! 5!), '! 5!,2 Problem &)2: A "00 kVA/ &&00J&00 V/ &0 8G single1phase transformer operating at rated condition has the follo(ing losses: hysteresis loss . 520 WL eddy current loss . ),0 W and copper loss . 2000 W! f this transformer is to be used on a 50 8G system/ determine its ne( kVA rating/ assume the same total losses and maimum core u! A! %)!% *! 34!) +! %,!4 '! 3"!% Problem &)): When "20 V/ &0 8G is applied to the primary (inding of a transformer/ the core loss is 240 W/ 50 V/ 25 8G is applied the core loss is 50 W! 'etermine the core loss (hen 2)0 V/ 50 8G is applied to the primary (inding! A! ,0)!5 W *! 342!& W +! %&)!& W '! %,4!, W Problem &)4: #he eddy current and hysteresis losses of a 4/4001V/ &0 8G single1phase distribution transformer are 2%0 and 5&0 (atts/ respectively! 'etermine the core loss (hen the transformer is connected across a 4/&001volt/ 5018G source! A! 3,, W *! 3%) W +! 334 W '! 3&, W Problem &)5: n a 400 V/ 50 cJs transformer/ the total iron loss 2500 W! When the supplied p!d! is 220 V at 25 cJs/ the corresponding loss is %50 W! +alculate the eddy current loss at normal freuency p!d! A! 2)), W *! 2"&5 W +! 20"0 W '! 22"& W
Problem &)&: When a 220 V/ &0 8G is impressed on a certain transformer at no load/ the total core loss is 200 W! When the freuency of the impressed voltage is changed to 25 8G and the magnitude of the voltage is made such as to maintain the same maimum u density as before/ the core loss fails to ,5 W! +alculate the hysteresis losses at &0 8G! A! *! +! '!
"&) W "&& W "," W "&3 W
Problem &),: A "00 kVA/ 4"&0J2)0 V/ &0 8G single1phase transformer has percentage impedance of "!,5 N E4!0! ts eciency (hen operating at rated conditions at ,5 pf lagging is 3,! 'etermine the eciency/ if the transformer is loaded at rated load and voltage but at 50 8G! Assume the ratio of eddy current losses to hysteresis losses at &0 8G to be 2!5! A! 3,!)" *! 3&!3, +! 3,!&" '! 3&!42 Problem &)%: #he full1load copper loss of a ,5 kVA single1phase transformer is thrice the iron losses! At half load unity pf/ the eciency is 3,! 'etermine the full1load eciency at 0!% pf lagging! A! 35!,, *! 3%!45 +! 34!,% '! 3,!%& Problem &)3: A 50 kVA/ 2)00J2)0 volt/ &01cycle transformer is tested in the laboratory so that its characteristics maybe determined! #he standard test reuires an open circuit test and short circuit test! =pen circuit test l . &!5 A ; . 2)0 V P . "%, W 6hort circuit test l . 2"!, A ; . ""5 V P . 5,0 W 'etermine the eciency of the transformer at half1load/ unity pf! A! 3,!55 *! 3%!,0 +! 3%!45 '! 3,!%0 Problem &40:
#he iron loss transformer is " of load copper loss one half of the rated A! 35!)) *! 3,!%2 +! 34!24
of a 251kVA/ &0 8G single1phase distribution the rated output at unity po(er factor and the full1 )&0 W! 'etermine the eciency (hen operating output at ,0 po(er factor lagging!
'! 3&!2& Problem 4&": 9iven that full1load copper losses are eactly t(ice the iron losses in a 501kVA transformer/ and that the uarter load eciency is 3&!5! +alculate the full load eciency at unity po(er factor! A! 3,!4% *! 3%!"2 +! 3,!&4 '! 3&!25 Problem &42: A "5 kVA/ 2)00J2)01volt transformer is under test! With the lo( side supplied (ith rated voltage and the high side open1circuited/ input po(er through a (attmeter reads 245 W! With the high side supplied (ith &5 V (hile the lo( side short1circuited/ input po(er at rated current reads )50 W! 'etermine the maimum eciency that can be epected from this transformer at unity pf! A! 3,!23 *! 3&!25 +! 3,!%) '! 3%!2" Problem &4): A "01kVA/ 2)00J2)0 transformer has an euivalent resistance referred to the secondary (inding of 0!05 ohm! #he core loss of this transformer is ,5 W! At (hat kVA load (ill this transformer operate at maimum eciency A! %!", kVA *! 3!0% kVA +! 3!)2 kVA '! %!30 kVA Problem &44: #he core loss of a 5 kVA single1phase transformer (ith normal voltage applied to the primary is ,5 (atts! #he maimum eciency occurs at &0 of full1load kVA! What is the full1load eciency of the transformer at 0!%0 po(er factor A! 35!"&
*! 3)!)% +! %3!52 '! 3"!)& Problem &45: A "001kVA transformer has 34 eciency at full load and at 50 full1load (ith unity pf in both cases! 'etermine the maimum eciency of the transformer at unity pf load! A! 3&!2, *! 35!&% +! 3)!44 '! 34!)2 Problem &4&: A "001kVA transformer has a maimum eciency of 3% at "0 underload and unity pf! ;valuate the eciency at uarter load/ 0!%0 pf lagging! A! 3&!) *! 35!) +! 34!, '! 3,!, Problem &4,: A " >VA/ &&J"" kV/ &0 8G transformer has an euivalent series impedance of "!0 N E 5 ohms referred to the lo( voltage side and a no1 load loss of 5500 (atts at rated terminal voltage! What is the maimum eciency at 0!% pf lagging A! 3%!)4 *! 3,!42 +! 3%!02 '! 3&!)% Problem &4%: #he all day eciency of a "0 kVA single1phase transformer is 34!, (hen loaded as follo(s: full load unity pf for 4 hours and no load the rest of the day! f the full1load copper loss at unity pf is 400 (atts/ calculate the core loss! A! ,5 kW *! ,0 kW +! ,2 kW '! ,% kW Problem &43: A 25 kVA distribution transformer operates at 20 overload/ 0!) pf lagging for " hourL at full load/ 0!3 lagging pf for ) hoursL 50 load at unity pf for % hoursL and "0 load at 0!% leading pf for the rest of
the day! f the core loss is "50 (atts and full load copper loss is 500 W/ (hat is the all day eciency of the transformer A! 34!2) *! 32!%& +! 3,!"4 '! 3&!&% Problem &50: @ind the all1day eciency of a transformer having a maimum eciency at 3% percent at "5 kVA at unity pf and loaded as follo(s: "2 hours 1111111111111 2 kW at 0!5 pf lagging & hours 111111111111111 "2 kW at 0!% pf lagging & hours 111111111111111 at no load A! 35!) *! 3"!, +! 34!& '! 3)!) Problem &5": A )0 kVA 2400J240 V/ &0 8G transformer has a full load po(er at unity over the period of 24 hours! #he maimum eciency is 35 and it occurs at full load! +alculate the all1day eciency if loade as follo(s: & hours at full load & hours at uarter load A! 3"!5) *! 32!54 +! 30!), '! 3)!%& Problem &52: A "000 OVA/ &/&00J400 volts &0 cycle single phase core type transformer has the follo(ing average daily load: @ull load at 0!% pf for % hours 8alf load at 0!,0, pf for "0 hours
follo(s: full load at unity pf for % hours/ one1half load at unity for % hours and no load the rest of the day! +alculate the all1day eciency! A! 3&!)& *! 3,!2) +! 3&!4, '! 3%!)2 Problem &54: A &!3 kVJ&00 V/ multi1tap/ single1phase distribution transformer is connected the far end of a distribution line for (hich the rear end voltage is maintained at &!3 kV! #he euivalent impedance of the transformer referred to lo( voltage side is 0!05 N E0!25 Ω per phase! #he impedance of each line is " N E2 Ω! t is reuired to maintain a terminal voltage of &00 V (hen the line current of )00 A at %0 pf lagging is delivered to the load! What approimate percentage tapping is reuired in the primary side
Problem &55: A &0 8G alternator generates a single1phase voltage of "20 V and has a reactance of 0!25 ohm! #he alternator feeds a line/ (hich is essentially resistive (ith an impedance of 0!" ohm! #he line is terminated (ith a 2:" step up transformer! What should be the load impedance to be connected to the secondary side to have maimum po(er transfer to it A! 0!5 N E "!2 *! +! 0!4 0!5 F E "!0 "!2 '! 0!4 N E "!0 Problem &5&: A transformer consists of primary (inding (ith 500 turns and t(o secondary (indings of "251turn secondary (inding has &0 ohms connected to its terminals and the )&1turn secondary (inding has ) ohms connected to its terminals! f the primary is connected to "201V/ &0 8G source/ determine the current in the primary (indings! A! 0!))2 A *! 0!4"2 A +! 0!2)5 A '! 0!25, A
Problem &5,: A )1phase/ &0 8G transformer has primary/ secondary and tertiary (indings! #he primary (inding is delta connected and rated &/&00 V! the secondary (inding is delta connected and rated "000 V! #he tertiary (inding is (ye connected and rated 440 V! f the secondary (inding has a )1phase balanced load of "00 kVA at %0 pf lagging and the tertiary (inding has a balanced )1phase load of 50 kW at unity pf/ (hat is the current in the primary (inding and its operating pf A! "2!52 A/ 0!30% *! ,!2) A/ 0!302 +! "2!52 A/ 0!302 '! ,!2) A/ 0!30% Problem &5%: A 201kVA/ 5001V load is to be supplied by an ideal step1up autotransformer from a 4001V source! @ind the current in the common (inding! A! )0 A *! 40 A +! 50 A '!
#;6# "% Problem &&": What should be the kVA rating of each t(o transformers in an open1delta bank (hen the three1phase balanced load is 230!4 kVA A! "55!&0 kVA *! ",)!40 kVA +! "50!25 kVA '! "&,!&& kVA Problem &&2: A V or open delta connected transformer bank/ composed of t(o identical units/ serves a balanced )1phase load of "& kVA at 2)0 volts! 6olve for the minimum siGe in kVA of the transformer needed! A! % kVA *! 3!24 kVA +! "& kVA '! %!25 kVA Problem &&): A V Copen deltaD connected transformer bank serves a balanced )1phase load of 40 kVA at 2)0 V and 0!%&& pf lagging! 6olve for the minimum kVA of each transformer neede to accommodate the load (ithout overloading! A! 25 *! 24 +! 2) '! 20 Problem &&4: #(o single1phase distribution transformers are banked in V Copen deltaD! f each transformer is rated ),!5 kVA/ solve for the maimum )1 phase load that the bank can carry (ithout overrloading/ considering that the load has a po(er factor of 0!%5 lagging! A! 52!5 W *! 43!5 W +! 5)!& W '! 55!2 W Problem &&5: An open delta bank/ consisting of t(o single1phase transformers is operating (ith a balanced three1phase load of 50 kVA/ 440 V at 0!% pf lagging and a single1phase load of "0 kW resistive connected across c1a leg! 'etermine the minimum ratings of the t(o transformers! Assume a phase seuence of a1b1c!
A! *! +! '!
)%!%0 kVA/ )4!0& kVA )4!)2 kVA/ ))!40 kVA )5!)% kVA/ )3!52 kVA )0!%) kVA/ )3!52 kVA
Problem &&&: #(o C2D single1phase distribution transformers/ connected in open delta (ill supply po(er to a 200 hp/ )1phase induction motor/ operating at 0!,0 po(er factor and 0!30 eciency! 6olve for the minimum siGe in kVa of each transformer needed to supply the po(er (ithout being overloaded! A! ")&!,) kVA *! "24!45 kVA +! ")0!)% kVA '! "23!4% kVA Problem &&,: #he ?tility +ompany supplies t(o single1phase transformers banked in open delta! f each transformer is rated ,51kVA capacity/ (hat is the maimum )1phase load in kilo(atts that the bank can carry (ithout suBering overload considering that the load has a lagging po(er factor of 0!%0! A! "04 kW *! ""2 kW +! ")0 kW '! ""4 kW Problem &&%: #(o identical "1phase transformers connected in open delta serve a )1phase motor load of 250 hp/ 0!,0 pf lagging! 0!30 eciency! 6olve for the minimum siGe in kVA of each transformer reuired to serve the load (ithout overloading! A! "50!)) *! ",0!3" +! "&0!4) '! "%5!") Problem &&3: An open1delta connected transformer bank serves a balanced )1 phase load of 40 kVA at 2)0 V and 0!%&& pf lagging! 6olve for the real po(er and pf at (hich each transformer is operating! A! ""!54 kW at 0!5 pf/ 2)!03 kW at unity pf *! "2!22 kW at 0!5 pf/ 22!42 at unity pf +! ""!54 kW at 0!%&& pf/ 2)!03 kW at 0!,0, pf '! "2!22 kW at 0!%&& pf/ 22!42 kW at 0!,0, pf Problem &,0:
An open delta/ three1phase transformer consisting t(o single1 phase transformers is operating (ith a balanced three1phase load of 50 kVA/ 4401V at a lagging pf of 0!%! 'etermine the operating pf of each transformer! A! 0!)3) lagging/ 0!33) lagging *! 0!)%) lagging/ 0!%%, lagging +! 0!)%) lagging/ 0!33) lagging '! 0!)3) lagging/ 0!%%, lagging Problem &,": #(o single1phase transformers are connected in V Copen deltaD and serving a delta connected impedance load/ each impedance is eual to "&∠)&!%,Q ohms! f the transformer voltages impressed on the impedances are: Vab . 240∠0Q/ Vab . 240∠240Q/ Vab .240∠"20Q volts 6olve for the kVA delivered by each transformer! A! ,!2%/ 5!20 *! 5!%,/ &!&" +! &!%4/ 5!&4 '! &!24/ &!24 Problem &,2: #(o single1phase transformers in an open1delta bank served a three1phase balanced load of 230!4 kVA! f a third transformer is added for delta operation/ (hat percent increase in load does this represent A! ,)!2 *! %4!& +! %0!5 '! ,3!4 Problem &3): #hree1single phase transformers each rated ,5 kVA are banked in delta supplying )1phase load dra(ing "&0 kVA at solve 0!% lagging po(erand factor! f one a transformer is removed for repairs/ for the amount of overloading of the remaining units! A! )0 kVA *! "0 kVA +! 20 kVA '! 25 kVA Problem &,4: A &&001volt/ &0 8G/ 21phase net(ork is connected to a three1 phase/ 41(iresystem by a 6cott1connected transformer combination! f there are "500 turns on the 21phase side/ calculate the number of turns on the )1phase side reuired for the main and teaser transformers! Voltage per phase on the )1phase side is 240 V!
A! *! +! '!
34 turns/ %) turns 3) turns/ %4 turns 35 turns/ %2 turns 32 turns/ %5 turns
Problem &,5: A balanced )1phase transformers bank has delta1connected primary an (ye1connected secondary (indings! #he primary to secondary (inding voltage ratio is 2400J2,,! 6olve for the primary line current if the lo(1side CsecondaryD load dra(s a line current of "000 A! A! 200 A *! ""5 A +! "50 A '! ",5 A Problem &,&: A three1phase "50 kVA/ 4"&0 V/ o!% lagging pf load is to be supplied by three single1phase transformer having a turns ratio of 2! +alculate the current that o(s in the primary (indings if the transformers are connected delta1delta! A! *! +! '!
"0!4" A &!0" A 20!%2 A "2!02 A
Problem &,,: What should be the turns ratio of a three1phase transformer to transform "0/000 kVA from 2)0 kV to 4"&0 V if the transformer is to be connected delta1(ye A! 34 *! 3% +! 3& '! 3, Problem &,%: A bank of three 50:" single1phase transformers connected (ye1 delta is used to step do(n the 8V transmission line rated ")% kV! 'etermine the magnitude of the step do(n voltage! A! "2& kV *! &!30 kV +! ")%!55 kV '! "53!)5 kV Problem &,3:
#he potential transformer of a line has a ratio ")2/000J&&!#hese are connected (ye1delta! #he voltmeter reads &4 volts! What is the voltage of the line A! 22"!, kV *! ""2!5 kV +! ")5!2 kV '! ")2 kV Problem &%0: A po(er transformer rated 50/000 kVA/ )4!5 kVJ")!% kV is connected (ye1grounded primary and delta on the secondary! 'etermine the full load phase current on the secondary side! A! 2032 A *! ",25 A +! "443 A '! "20% A Problem &%": A &3J")!% kV/ "0 >VA three1phase transformer is connected (ye1 grounded delta! What is the kV rating of the secondary (inding A! *! +! '!
,!3, "5 2)!3 ")!%
Problem &%2: #he P#s of a 220 kV transmission line have ratio of ")2!,& kVJ&&!),5 kV and are connected (ye1(ye! A voltmeter connected line to ground reads && volts! What is the transmission line voltage A! 22%!&) kV *! 220!"0 kV +! 22)!"5 kV '! 225!25 kV Problem &%): A po(er transformer rated 50/000 kVA/ )4!5 kVJ")!% kV is connected (ye1(ye! What are the line currents at full load A! 525!2 A/ ",25!4 A *! %)&!, A/ 2032 A +! 4%)!" A/ "20,!, A '! "443!) A/ )&2)!2 A Problem &%4: #(o transformers are connected in parallel to supply a common load of ",5 kVA! #ransformer A is rated "00 kVA (ith euivalent impedance of "2!5 ohms! @ind the kVA load of each transformer!
A! *! +! '!
,%/ 3, ,&/ 33 %0/ 35 ,5/ "00
Problem &%5: #(o distribution transformers are connected in parallel supplying a load of "25 kVA! f transformer A is rated 50 kVA/ (ith "4 ohms euivalent reactance and transformer * is rated ,5 kVA (ith "" ohms euivalent reactance! 6olve for the loading in kVA of each transformer! A! 55 kVA/ ,0 kVA *! 50 kVA/ ,5 kVA +! 5% kVA/ &, kVA '! 52 kVA/ ,) kVA Problem &%&: A "251kVA distribution transformer (ith 4 impedance is connected in parallel (ith another transformer rated ,51kVA and (ith ) impedance! *oth have the same voltage ratio! VA and the other at "5 >VA! @or a given )0 >VA load (ith a lagging pf of 0!%! 'etermine the load carried by each transformer A! "%!50 >VA/ ""!50 >VA *! "%!,5 >VA/ ""!25 >VA +! "5!25 >VA/ "4!,5 >VA '! "&!45 >VA/ ")!55 >VA Problem &%%: A 5001kVA single1phase transformer RAS (ith percentage impedance of 0!0"0 N E 0!05 is connected in parallel (ith a 2501kVA transformer R*S (ith a percentage impedance of 0!0"5 N E0!04! f the transformers are serving a single1phase load rated %001kVA/ %0 lagging pf/ determine the operating pf of each transformer! Assume the transformers have the same turns ratio! A! A . 0!,&2/ * . 0!0%) *! A . 0!,,2/ * . 0!%5& +! A . 0!,&2/ * . 0!%5& '! A . 0!,,2/ * . 0!%0)
Problem &%3: #he >;-AK+= has t(o single1phase transformers (ith eual turns ratio and ratings and are operated in parallel to supply a load of 2%0 kW at 0!%0 lagging pf! #ransformer A has a resistance of 2 and a reactance of %! #ransformer * has a resistance of " and a reactance of &! 'etermine the po(er delivered by the transformers A and * to the load! A! A . "2) kW/ * . *! A . "25 kW/ * . +! A . "22 kW/ * . '! A . "2, kW/ * .
"5, kW "55 kW "5% kW "5) kW
Problem &30: #(o single1phase transformers (ith eual ratings and turns ratio are operated in parallel to supply a load of 0!30! #ransformer A has a resistance of " and a reactance of &! #ransformer * has a resistance of 2 and a reactance of 5! +alculate the po(er delivered by each transformer! A! %) kW/ 3, kW *! ,3 kW/ "0" kW +! %% kW/ 32 kW '! %0 kW/ "00 kW Problem &3": #(o single1phase transformers A and * are connected in parallel to serve a &001A single1phase load at 0!%0 pf lagging! #he euivalent impedance of the transformers are 2 N E ) and 2!) N E 5 ohms/ respectively! 'etermine the ratio of the kW output of transformer A to the kW output of transformer *! Assume the transformers have eual ratings and turns ratio! A! "!5& *! "!%% +! "!&% '! "!,4