1. The voltage of a d.

c generator , when supplying a current of 75A to a load, is measured to

be 108.8V at the switch-board. At the load , the voltage recorded is 105V and when the
load is switched off the voltage rises to 110V. Find the internal resistanse of the generator
, the resistance of the supply cables and estimate the fault current if a ‘short-circuit’ of
negligible resistance occurred at the load terminals. (Ans: 0.016Ω , 0.0507Ω , 1650A )

2. A moving-coil instrument has a resistance of 10Ω and requires a current of 15mA to give
full-scale deflection. Calculate the resistance value of the resistor necessary to enable it to
be used to measure (a) currents up to 25A, (b) voltages up to 500V. ( Ans: 𝑹𝑺𝑯 = 0.006Ω ,
𝑹𝑺𝑬 = 33.33kΩ )

3. Two groups of resistors A and B are connected in series . Group A consists of four resistors
of values 2Ω, 4Ω, 6Ω and 8Ω connected in parallel and group B consists of two resistors of
values 10Ω and 15Ω in parallel. If the current in the 4Ω resistor is 1.5A, calculate (a) the
current in each of the remaining resistors, (b) the supply voltage, (c) the voltage drop
across the groups A and B. (Ans :3A, 1A, 0.75Ω, 1.5A, 43.5V, 6V, 37.5V )
4. The ammeter on a switchboard , scaled 0 – 300A is accidentally damaged. The associated
shunt is marked 300A , 150mV . A small ammeter, scaled 0 – 1A with a resistance of 0.12Ω ,
is available , and the possibility of using this is considered. Find if such an arrangement is
possible , and if so , how it could be achieved using surplus resistors which are also available.
( Ans: 0.03Ω )
5. The open-circuit voltage of a cell, as measured by a voltmeter of 100Ω resistance, was 1.5V,
and the p.d. when supplying current to a 10Ω resistance was 1.25V , measured by the same
voltmeter. Determine the e.m.f. and internal resistance of the cell.
6. MMMC. Three batteries A, B and C have their negative terminals connected together. Between
the positive terminals of A and B there is a resistor of 0.5Ω and between B and C there is a resistor
of 0.3Ω.

Battery A 105V, internal resistance 0.25Ω

Battery B 100V, internal resistance 0.2Ω

Battery C 95V, internal resistance 0.25Ω

Determine the current values in the two resistors and the power dissipated by them.

7. MMEA/MMMC. A battery consisting of 48 cells , having an internal resistance of 0.02ohms per

cell, is to be charged so that the e.m.f per cell is raised from 1.8 to 2.2V . Determine the maximum
number of carbon lamps of a parallel bank, which may be switched on in series with the circuit ,
so that the current from the 200V mains does not exceed 10A at the commencement of charging .
If the circuit remains unaltered, calculate the current flowing through the battery when the charge
is approaching completion. Each lamp is marked 110V, 32 c.p and requires 3.5W per candle
power. ( Answer: 10 lamps in parallel, 7.89A in completion)
8. MMEA/MMMC. The Earth-lamps on a main switch board comprise two 240V, 60W lamps
connected in the usual manner. The p.d at the busbars is 220V. Damage by sea water occurs to a
distribution cable so that the isolation resistance to earth is reduced to 16 ohms and 6 ohms for
+ve and –ve cables respectively. Find by calculation (a) which of the two lamps burns the brighter,
and (b) the additional load on the generator occasioned by the fault. The resistance of the cables
and the ship’s structure may be neglected, and that of the lamps taken as constant at the value
corresponding to the 60W rating. ( Answer: (a)+ve lamp brighter, (b)2.2kW )
9. MMMC. A balanced Wheatstone bridge consists of four resistors labeled clockwise P , Q, R, S, the
supply being connected to the junction of PS and QR, R is 450Ω. If P and Q are interchanged then
a 5 Ω resistor has to be placed in parallel with R to maintain balance . Find S and the ratio of P
and Q.
10. In an electric motor the armature has 800 conductors each carrying a current of 8A. The
average flux density of the magnetic field is 0.6T. The armature core has an effective length
of 250mm and all conductors may be taken as lying on an effective diameter of 200mm.
Determine the torque and mechanical power developed when the armature is revolving at
1000 rev / min. ( Ans : 96 N m , 10.05 kW )
11. A coil of 250 turns is wound uniformly over a wooden ring of mean circumference 500mm
and uniform cross-sectional area of 400 𝒎𝒎𝟐 . If the current passed through the coil is 4A
find (a) the magnetising force (b) the total flux . ( Ans: 2000 amp-turns/m , 1.0048 𝝁Wb )
12. The magnet system of a moving- coil instrument provides a flux density in the air gap of
0.25 T. The moving-coil of 120 turns , is carried on a former of ( active side ) length 25mm
and width 18 mm ( between air-gap centres ) . If the coil carries a current of 2mA , calculate
the turning moment on it.

13. The magnetic field in the air-gap of a two-pole motor has a flux density of 0.8T. The
armature is wound with 246 conductors, each of 400mm effective length, mounted at 150mm
effective radius , and at full load each conductor carries a current of 20A. Assuming that the
actual torque produced is equivalent to that due to two-thirds of the number of conductors
cutting the lines force at right-angles , find (a) the torque in newton metres, and (b) the
shaft power developed at 500 rev / min. ( Ans : 157.5 N m , 8.24 kW )

14. A coil of 200 turns is rotated at 1200 rev/ min between the poles of an electromagnet . The
flux density of the field is 0.02 T and the axis of rotation is at right angles to the direction
of the field . The effective length of the coil is 0.3 m and the mean width 0.2 m. Assuming
that the e.m.f. produced is sinusoidal, Calculate ( a ) the maximum value of e.m.f. ( b ) the
frequency. ( Ans: 30.144V , 20Hz )
15. A coil of 800 turns is wound on a wooden former and a current of 5A is passed through
it to produce a magnetic flux of 200 micro-webers. Calculate the average value of e.m.f.
induced in the coil when the current is (a) switched off in 0.08 seconds. (b) reversed in
0.2 seconds.
16. When driven at 1000 rev/min with a flux/pole of 20 mWb, a d.c. generator has an e.m.f. of
200 V . If the speed is increased to 1100 rev/min and at the same time the flux/pole is
reduced to 19m Wb/ pole , what is then the induced e.m.f. ? ( Ans: 209V )
17. Find the generated e.m.f./conductor of a 6-pole d.c. generator having a magnetic flux/ pole
of 64 m Wb and a speed of 1000 rev/min . If there are 468 conductors , connected is six
parallel circuits, calculate the total generated e.m.f. of the machine . Find also the total power
developed by the armature when the current in each conductor is 50 A .( Ans: 499.2V , 149.76
kW )
18. A coil of 1200 turns is wound on an iron core and with a certain value of current flowing
in the circuit , a flux of 4mWb is produced . When the circuit is opened, the flux falls to its
residual value of 1.5 mWb in 40 ms . Calculate the average value of the induced e.m.f. (
Ans: 75V )
19. If the instantaneous value of a current is represented by i = 70.7sin 520t, calculate the
current’s ( a ) maximum value, ( b ) r.m.s value, ( c ) frequency,( d ) instantaneous value 0.0015s
after passing through zero. ( Ans: 70.7A, 49.94A, 82.8Hz, 49.65A )
20. Two alternators are arranged to be coupled to the same prime-mover in a manner which
allows the phase angle , between their generated e.m.fs., to be varied . If the machines are
connected in series and generate 100V and 200 V respectively , find the total output voltage
when the phase difference is; ( a ) zero , ( b ) 60° ( c ) 90° ( d ) 120°, and ( e ) 180°. ( Ans:
300V, 264.8V, 223.7V, 173.2V, 100V )
21. A simple transmission line has a resistance of 1Ω and a reactance at normal frequency of
2.5Ω. It supplies a factory with 750kW, 0.8pf (lagging) at a voltage of 3.3kV. Determine the
voltage at the generator and its power factor. Find also the output of the generator and
draw the phasor diagram. ( Ans: 3.98kV, 0.73(lagging), 825kW )
22. Two inductive circuits A and B are connected in series across 230V, 50 Hz mains. The
resistance values are A 120Ω , B 100Ω . The inductance values are A 250mH, B 400mH.
Calculate (a) the current (b) the phase difference between the supply voltage and current
(c) the voltage across A and B (d) the phase difference between these voltages. ( Ans:
0.766A, 42°46' , 109.6V, 122.9V, 18°20' )
23. A circuit, consisting of a resistor and a capacitor connected in series across a 200V, 40Hz
supply, takes a current of 6.66A. When the frequency is increased to 50Hz and the voltage
maintained at 200V, the current becomes 8A. Calculate the value of resistance and
capacitance and sketch a phasor diagram ( not to scale ) for either frequency. ( Ans: 10.25Ω,
139µF )
24. A 100W lamp for a 100V supply is placed across a 220V supply. What value of resistance
must be place in series with it so that it will work under its proper conditions ? If a coil
is used instead of the resistor and if the resistance of the coil is small compared to its
reactance, what is the inductance of the coil ? The frequency is 50Hz. What is the total
power absorbed in each case ? ( Ans: 120Ω , 0.624H , 220W , 100W )
25. A choke when connected across 206V a.c. mains, passed a current of 10A and dissipates
500W. If it is connected in series with apparatus having an impedance of 5Ω and a capacitive
reactance of 4Ω, find the impedance and power factor of the complete circuit. ( Ans: 17.88Ω,
0.44(lagging) )
26. A moving-iron voltmeter with a resistance of 1732Ω and an inductance of 0.625 H registers
110V with maximum deflection on a 50 Hz, a.c circuit. It is required to be placed in a 230V,
50 Hz a.c circuit in series with a non-inductive resistor. Find the value of R, the required
resistor.
27. A coil of resistance 10Ω and inductance 0.1 H is connected in series with a capacitor of
capacitance 150 µF , across a 200V , 50 Hz supply . Calculate (a) the inductive reactance(b)
the capacitive reactance (c) the circuit impedance (d) the circuit current (e) the circuit
power factor (f) the voltage drop across the coil (g) the voltage drop across the capacitor
.
28. The low voltage release of an a.c motor starter consists of a solenoid into which an iron plunger
is drawn against a spring . The resistance of the solenoid is 35. When connected to 220V,
50Hz a c supply the current taken is at first 2A, and when the plunger is drawn into the
‘full in’ position the current falls to 0.7A. Calculate the inductance of the solenoid for both
position of the plunger and the maximum value of the flux linkages into weber turns for the
full in position of the plunger.
29. A coil of 0.84H inductance and 50Ω resistance is connected in series with a capacitor of
14µF capacitance. (a) Find the frequency for resonance and the potential differences across
the capacitor, across the coil and across the two, when a current of 5A at this frequency,
is flowing, (b) find the three potential differences when the same current flows at 60Hz. (
Ans: 46.38Hz, 1224.45V, 1250V, 250V, 946.5V, 1604V, 684.5V )
30. A circuit consists of two branches in parallel. Branch A consists of a 20Ω resistor in series
with a 0.07H inductor, while branch B consists of a 60µF capacitor in series with a 50Ω
resistor . Calculate the mains current and the circuit power factor, if the voltage is 200V at
50Hz.
31. Two loads are connected in parallel. Load A is 800kVA at 0.6 (lagging). Load B is 700kVA
at 0.8 power factor (lagging). Find the total kW, kVA, and overall power factor of the joint
loads.
32. A 220V, single-phase alternator supplies the following loads: ( a ) 20kW at unity power
factor for lighting and heating. ( b ) A 75kW induction motor having an efficiency of 90.5
per cent poerating at a power factor of 0.8( lagging ). ( c )A synchronous motor taking 50kVA
at a power factor of 0.5( leading ). Find the total kVA, current and the power factor of the
combined load.
33. The load taken from a single-phase supply consists of : (a) Filament lamp load of 10kW at
unity power factor. (b) Motor load of 80kVA at 0.8 power factor (lagging). (c) Motor load
of 40kVA at 0.7 power factor (leading). Calculate the total load taken from the supply in
kW and in kVA and the power factor of the combined load. Find the mains current if the
supply voltage is 250V. ( Ans : 102kW, 104kVA, 0.98(lagging), 416A )
34. If an alternator supplies the following loads: (a) 200kW lighting load at unity power factor,
(b) 400kW induction motor load at 0.8(lagging) power factor, (c) 200kW synchronous motor
load, find the power factor of the synchronous motor load, to give an overall power factor
of 0.97(lagging). ( Ans : 0.89(leading) )
35. A 40kW load, operating at 0.707 power factor (lagging) , is supplied from 500V, 50Hz mains.
Calculate (a) the capacitor value required to rise the line power factor to unity (b) the
capacitance required to rise the power factor to 0.95 (lagging).
36. A 400V, 50Hz, 20kW, single-phase induction motor has a full-load efficiency of 91.15 per cent
and operates at a power factor of 0.87 (lagging). Find the kVAr value of the capacitor to be
connected in parallel to improve the circuit power factor to 0.95 (lagging). Find also the
capacitance value of this capacitor.
37. A single-phase motor running from a 230V, 50Hz supply takes a current of 11.6A when
giving an output of 1.5kW, the efficiency being 80 per cent. Calculate the capacitance required
to bring the power factor of the supply current to 0.95(lagging) . Calculate also the kVAr
rating of the capacitor. ( Ans: 76µF, 1.26kVAr )
38. MMMC . A parallel circuit consists of a branch A of resistance 10 Ω, inductance 38 mH and
capacitance 312.8 μF and a branch B of negligible resistance and inductive reactance of 12Ω.
Derive graphically the total current and its phase angle if the system is connected to a 440 V, 50 Hz
supply.
39. MMMC. A system is supplying a 100kW lighting load at unity power factor and a 300 kW induction
motor at 0.85 power factor (lagging) is to have its power factor improved to 0.95(lagging) by the
use of 100 kW synchronous motor. Determine the power factor and kVA of synchronous motor.
40. A 3-phase, star-connected alternator supplies a delta-connected induction motor at 600V.
The current taken is 40A. Find (a) the phase voltage of the alternator (b) the current in
each phase of the motor. (c) If the motor operates at a power factor of 0.8(lagging) and
an efficiency of 88 per cent, find the kVA rating of the alternator and power output of the
motor.
41. A 500V, 3-phase, star-connected alternator supplies a star-connected induction motor which
develops 45kW. The efficiency of the motor is 88 per cent and the power factor is
0.9(lagging). The efficiency of the alternator at this load is 80 per cent. Determine (a) the
line current, (b) the power output of the alternator, (c) the output power of the prime-
mover. ( Ans: 65.6A, 51.14kW, 64kW )
42. A 500V, three-phase alternator supplies a balanced delta-connected load in parallel with a
balanced star-connected load. The delta load is 30kW at a power factor of 0.92(leading)
and the star load is 40kW at a power factor of 0.85(lagging). Calculate the line current and
the power factor of the supply. ( Ans: 82.1A, 0.98(lagging) )
43. A 400V, 3-phase system takes 40A at a power factor of 0.8 (lagging). An over-excited
synchronous motor is connected to raise the power factor of the combination to unity. If
the mechanical output of the motor is 12kW and the efficiency is 91 per cent, find the kVA
input to the motor and its power factor. Find also the total power taken from the supply
mains. ( Ans: 21.21kVA, 0.62(leading), 35.38kW )
44. MMMC. A 440V load of 400kW at 0.8 (lagging) power factor is jointly supplied by two alternators
A and B. The kW load on A is 150kW and the kVAr load on B is 150kVAr (lagging). Determine the
kW load on B, the kVAr load on A, the power factor of operation on each machine and the current
loading of each machine. ( Here three-phase alternators have been assumed)
45. MMMC. Three equal resistors are connected to a three phase system. If one resistor is removed,
find the reduction in load if they are connected in (a) Star, (b) Delta . (16marks)
46. A three-phase, marine, dry type, transformer is used to step-down the voltage of three-
phase, star-connected alternator to provide the supply for 120V lighting. The transformer
has a 4:1 phase turns ratio and is delta connected on the primary side and star connected
on the secondary side. If the lighting is supplied at the line voltage of the transformer, what
must be the phase voltage of the alternator? ( Ans : 160V )
47. A 200 kVA, 6600 / 415 V, three-phase transformer connected in delta / star supplies a 120kW,
415V, 50 Hz, three-phase motor whose power factor and efficiency are 0.8 ( lagging ) , and
83% respectively. Neglecting the transformer losses, calculate the current in each transformer
𝟒𝟑𝟓.𝟒
winding . ( Ans : secondary A, primary 9.13 A )
√𝟑
48. A three-phase transformer has 560 turns on the primary and 42 turns on the secondary. The
primary windings are connected to a line voltage of 6.6 KV. Calculate the secondary line voltage
when the transformer is connected (a) Star-Delta, (b) Delta- Star.
49. A 440V transformer has 3000 turns on the primary. If a tapping is to be available for 400V,
find its position on the winding. If one secondary winding suitable for 200, 220, and 240V
is also to be provided, find the necessary number of turns and the position of the tappings.
50. Find the core cross-sectional area in square mm, the number of turns and the position of the
tapping point for a 50KVA, 50Hz, single-phase, 3700/2500V auto-transformer, assuming that the
e.m.f. per turn is 7V and the maximum flux density is 1.5T.
51. For the no-load test on a transformer, the ammeter was found to read 0.18 A and the
wattmeter 12 W. The reading on the primary voltmeter was 400 V and that on the secondary
voltmeter was 240 V. Calculate, the magnetizing component of the no-load current, the iron-
loss component and the transformation ratio. Find the equivalent resistance and reactance
of the no-load circuit. ( Ans: 0.178 A, 0.03 A, 1.66 : 1, 13.33 kΩ, 2247Ω )
52. A marine, dry-type, 17.5 kVA, 460 / 115 V, single-phase, 50 / 60 Hz transformer has primary
and secondary resistances of 0.36 Ω and 0.02Ω respectively and the leakage reactances of
these windings are 0.82Ω and 0.06Ω respectively. Determine the voltage to be applied to
the primary to obtain full-load current with the secondary winding short-circuited. Neglect
the magnetizing current .
53. A 660/220 V , single-phase transformer has a primary resistance of 0.29Ω and a secondary
resistance of 0.025Ω. The corresponding reactance values are 0.44Ω and 0.04Ω. Estimate the
primary current which would flow if a short-circuit was to occur across the secondary
terminals. ( Ans: 694.7 A )
54. A 175KVA, 6600/440V , single-phase transformer has an iron loss of 2.75KW. The primary and secondary
windings have resistance of 0.4Ω and 0.0015Ω respectively. Calculate the efficiency on full load when the
power factor is 0.9.
55. A 20kVA, 2000 / 220 V, single-phase transformer has a primary resistance of 2.1Ω and a
secondary resistance of 0.026Ω. If the total iron loss equals 200W, find the efficiency on (
a ) full load and at a power factor of 0.5 ( lagging ); ( b ) half load and at a power factor of
0.8 ( leading ).
56. A single-phase power transformer supplies a load of 20 kVA at power factor of 0.81 (
lagging ). The iron loss of the transformer is 200 W and the copper loss at this load is 180
W. Calculate : ( a ) the efficiency ; ( b ) if the load is now changed to 30 kVA at power factor
of 0.9 ( lagging ), calculate the new efficiency. ( Ans : 97.6% , 97.9% )
57. For a 25 kVA, 450 / 121 V, single-phase transformer, the iron and full-load copper losses
are respectively 165 W and 280 W. Calculate ( a ) the efficiency at full load, unity power
factor and at half full-load 0.8 power factor ( lagging ), ( b ) the load at which the efficiency
is a maximum. ( Ans : ( a )98.1%, 97.75%, ( b ) 19.2 kVA )
58. A 50kVA, 3.3 kV / 230 V , single-phase transformer has an impedance of 4.2 percent and a
copper loss of 1.8 percent at full load. Calculate the percentage reactance and ohmic value
of resistance, reactance and impedance referred to the primary side. Estimate the primary
short-circuit current, assuming the supply voltage to be maintained. ( Ans : 361 A )
59. A 660/220 V , single-phase transformer has a primary resistance of 0.29Ω and a secondary
resistance of 0.025Ω. The corresponding reactance values are 0.44Ω and 0.04Ω. Estimate the
percentage regulation for a secondary load current of 50 A at a power factor of 0.8 ( lagging
). ( Ans: 2.25% )
60. A marine, dry-type , 17.5 kVA, 450 / 121 V, 50 / 60Hz, single-phase transformer gave the
following data on test :
O.C Test : 450 V, 1.5 A, 115 W at 50 Hz;
S.C Test : 15.75 V , 38.9 A, 312 W at 50 Hz;
Estimate the voltage of the secondary terminals and the efficiency of the transformer when
supplying full-load current, at a power factor of 0.8 ( lagging ), from the secondary side.
Assume the input voltage to be maintained at 450 V, 50 Hz. ( Ans : 117.1 V, 96.8% )
61. A lighting transformer rated at 10 kVA has a full-load loss of 0.3 kW, which is made up
equally from the iron loss and the copper loss. The duty cycle consists of full load for 3
hours, half full-load for 4 hours and no-lod for the remainder of 24 hour period. If the load
operates at unity power factor, calculate the all-day efficiency. ( Ans : 92.25% )
62. A 50 kVA, 440 / 110 V, single-phase transformer has an iron loss of 250 W. With the
secondary winding short-circuited, full-load currents flow in the windings when 25 V is
applied to the primary; the power input being 500 W. For this transformer determine ( a
)the percentage voltage regulation at full-load, 0.8 power factor( lagging ) ; ( b )the fraction of
full-load at which the efficiency is a maximum. ( Ans : ( a ) 4.15 % down , ( b ) 0.7071 )
63. A 220V shunt motor takes 10.25 A on full load . The armature resistance is 0.8 Ω and the
field resistance is 880Ω. The losses due to friction, windage and the iron amount to 150W.
Find the output power and the efficiency of the motor on full load.
64. A dc shunt motor has an armature resistance of 0.9Ω and takes an armature current of 18
A from 230 V mains. Calculate the power output and overall efficiency of the motor, if the
rotational losses are measured to be 112 W and the shunt field resistanceis 300 Ω.
65. A 500 V shunt motor takes a current of 5 A on no load. The resistances of the armature
and field circuits are 0.22Ω and 250Ω respectively. Estimate the efficiency when the motor
current is 100A. State the assumption made in estimating the efficiency.
66. A ship’s 110 V dc “lubricating oil” pump shunt motor is tested by being run light at its
correct voltage and at rated speed. It takes 4.5 A. Estimate the efficiency of the motor when
loaded to take its rated line current of 40 A. The resistance of the armature including the
brushes is 0.12 Ω and the resistance of the field 100 Ω.
67. A 220 V shunt generator is rated to have a full-load current of 200A. Its armature resistance
is 0.06Ω and its field resistance is 55Ω. The rotational losses at correct speed and excitation,
are measured to be 3 kW. Find the output power rating of the prime-mover and also the
load current for maximum efficiency.
68. A 50 kW, 500 V shunt generator is tested by the Swinburne method. When run light as a
motor it takes a no-load current of 10.1 A at the correct voltage and speed. Ra = 0.25Ω and
Rf = 500Ω . Assess the efficiency at full load as a generator.
69. Two shunt generators A and B , each with straight line load characteristics are operating in
parallel. The characteristics are :
Machine Open Circuit Voltage Terminal Voltage at 50amperes

A 460V 420V

B 440V 410V

Determine how the machines would share a load of 100A and determine the common busbar
voltage.