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Tutorial #1

**(Electric Machine)**

QN1 A 30 cm long circular iron rod is bent
into circular ring and 600 turns of windings are wound on it. The diameter of
the rod is 20mm and relative permeability of the iron is 4000. A time varying
current *i* = 5 sin 314.16t is passed through the winding. Calculate the
inductance of the coil and average value of emf induced in the coil. [1.89H, 1890V]

QN.2 For the Magnetic circuit shown below,
calculate the Amp-turn (NI) required establishing a flux of 0.75 wb in the
central limb. Given that m_{r} = 4000 for iron core.

[40.4 ´ 10^{3} Amp-turn]

QN.3 Calculate the net magnetic flux in the core of the following
magnetic circuit and show the

direction of magnetic flux in the
core. Given that cross sectional area of the core is 25 sq.cm

and m_{r} = 4000.
[23.56
mwb, clockwise ]

QN4 A circular iron core has a cross
sectional area of 5 sq. cm and mean length of 15 cm. It has two coils A and B
with 100 turns and 500 turns respectively. The current in the coil A is changed
from zero to 10amp in 0.1 sec. Calculate the emf induced in the coil B. Given
that the relative permeability of the core is 3000.
[62.5 V]

QN5 An iron
ring of mean length of 1.2m and cross-sectional area of 0.005 m^{2} is
wound with a coil of 900 turns. If a current of 2 amp in the coil produces a
flux density of 2T in the iron ring, calculate:

i)
The mmf

ii)
Total flux in the
core

iii)
Magnetic field
strength

iv)
Relative permeability
of the core. [ 1800AT, 6mwb, 15 AT/m, 637 ]

QN6. An iron
ring has a mean length of 1.5m and cross-sectional area of 0.01 m^{2}.
It has a radial air gap of 4mm. The ring is wound with 250 turns. What dc
current would be needed in the coil to produce a flux of 0.8 weber in the air gap?
Assume that µr = 400 and leakage factor is 1.25. [2.46 Amp]

QN7 An uneven
ring shaped core (as shown below) has µr = 100 and flux density in the larger
section is 0.75T. If the current through the coil is 500mA determine the number
of turns in the coil. [5669]

QN8 A
magnetic circuit shown below has cast iron core whose dimensions are given
below:

Length
(ab + cd) = 50 cm Cross sectional area
of path (ab + cd) = 25 sq.cm

Length
(ad) = 20 cm Cross sectional
area of path (ad) = 12.5 sq.cm

Length
(dea) = 50 cm Cross sectional
area of path (dea) = 25 sq.cm

Determine
the current ‘I’ required to produce a magnetic flux of 0.75 mWb in the central limb.

Given
that: Number turns in the coil = 500 and
µr = 2000. [ 0.22 A ]

#
Tutorial #2

**(Electric Machine –I)**

QN1 A 50 kVA, 50 Hz single phase
transformer has 500 turns on primary winding and 100 turns on secondary
winding. The primary winding is supplied by 3000V, 50 Hz ac voltage with full
resistive load connected on secondary side. Calculate:

i)
Emf induced in secondary winding

ii)
Primary and secondary windings currents

iii)
Maximum flux in the core.

Assume that it is an ideal
transformer.
[Ans: 600V, 16.66A, 83.33A,
27.02mwb]

QN3 A step up transformer supplies a
current of 5 amp to the load at 200 V. The power factor of the load is 0.8
lagging. Given that R_{1} = 0.5 ohm, X_{1} = 1 ohm, R_{2}
= 2 ohm, X_{2} = 4 ohm, k = 2,

R_{0} = 450ohms and X_{0} =
250 ohms. Calculate the magnitude and phase of V_{1} and I_{1}
with V_{2} as reference phasor and calculate the input power factor.

[V_{1} = 129.98Ð6.5^{0} V, I_{1} = 10.56Ð-37.88^{0} A and input pf = 0.71 lagging ]

QN4 A
230V/ 2300V single-phase transformer is excited by 230V ac voltage. The
equivalent resistance and reactance
referred to primary side are 0.1 ohm and 0.4 ohm respectively.

Given that R_{0} = 500
ohms and X_{0} = 200 ohms. The
load impedance is (400 + j600) ohm.

Calculate: a) Primary
current b) Secondary terminal
voltage c) Input power factor

[I_{1} = 30 A V_{2}
= 2075.4V, and input pf = 0.52 lagging ]

QN5 A 25 kVA, 6600V/ 250V single phase
transformer has the following parameters:

R_{1} = 8 ohm, X_{1}
= 15 ohm, R_{2} = 0.02 ohm, X_{2} = 0.05 ohm.

Calculate the full load voltage
regulation at a power factor a) 0.8
lag b) unity c) 0.8 lead.

[ 2.7 %, 1.3 %
and -0.782 % ]

QN6 A 20 kVA, 250V/2500V, 50Hz single phase
transformer gave the following test results:

No-load test ( on L.V. side )
: 250V, 1.4 A,
105 watts

Short circuit test (on H.V.
side): 120V, 8 A ,
320 watts

Calculate the equivalent circuit parameters
referred to primary side and draw the equivalent

circuit. [ Ro = 595.2 ohm, Xo = 187.26 ohm, R_{01} = 0.05 ohm
and X_{01} = 0.14 ohm ]

QN7 A single-phase 50 Hz transformer has 100 turns on
primary and 400 turns on secondary winding. The net cross-section area of the
core is 250 cm^{2}. If the primary winding is connected to a 230 V, 50
Hz supply, determine (a) the emf induced in the secondary winding and (b) the
maximum and rms value of the flux density in the core.
[920 V, 0.414 Wb/m^{2}, 0.293 Wb/m^{2}]

QN8 The no-load current of a transformer is 15 A at a p.f. of
0.2 when connected to a 460 V, 50 Hz power supply. If the primary winding has
550 turns, calculate :(a) the magnetizing and working component of no-load
current. (b) iron loss (c) maximum and
rms value of flux in the core.

[14.7 A, 3 A, 1380 W, 3.77 mWb, 2.66 mWb]

QN9 A 2000V/400V, 50 Hz, single phase transformer draws 2 A at a
p.f. of 0.2 lagging when it has no-load. Calculate the primary current and p.f.
When secondary current is 200 A at a p.f. of 0.8 lagging. Assume the voltage
drop in the winding to be neglected. [41.52 A, 0.78]

QN10. A 100 KVA, 1100/230V, 50 Hz transformer has an HV winding resistance
of 0.1Ω and a leakage reactance of 0.4 Ω. The low voltage winding has a
resistance of 0.006Ω and a leakage reactance of 0.01 Ω. Find the equivalent
winding resistance, reactance and impedance referred to HV and LV side.
[(0.237+j0.629) Ω, (0.0643+j0.0275) Ω]

QN11 A 50 KVA, 2200/110V transformer when tested gave the following
results:

OC test: 400 W 10 A 110
V

SC test: 808 W 20.5 A 90 V

Compute all the parameters
of the equivalent circuit referred to HV and LV sides of the transformer. Draw the
equivalent circuits also.

[HV side: 12120Ω, 4723.2Ω, 1.932Ω, 3.946Ω; LV side: 30.30Ω, 11.80Ω,
4.808*10^{-3}Ω, 9.865*10^{-3}Ω]

QN12 A 1000/500V 1-phase transformer draws a current of 2.4 A at
no-load with a p.f. of 0.35 lagging . With secondary terminals short circuited
by a thick wire, the primary winding is supplied by an ac voltage of 80 V, the
transformer draws a current of 25 A and consumes 250 W. Calculate the
equivalent circuit parameters referred to secondary side and draw the equivalent
circuit. [595.23Ω, 222.22Ω, 0.1Ω,
0.7925Ω]

QN13 With the secondary short circuited, if 200 V is applied to a
200 KVA, 1-phase, 3300/400 V transformer, the current through primary was the
full load value and the input power was 1650 W. Calculate the secondary p. d.
and percentage regulation when the secondary load is passing 300 A at 0.707
p.f. lagging with normal primary voltage. [388.41 V, 2.896%]

QN14 A 500 KVA, 50 Hz, 6600V/400V, 1- phase transformer have
primary and secondary winding resistances are 0.4 Ω and 0.001 Ω respectively.
If the iron loss is 3.0 KW, calculate the efficiency at (a) full load (b) half
full load. [98.64%, 98.438%]

QN15. A 200 KVA transformer has an efficiency of 98% at full load. If
the maximum efficiency occurs at three quarters of full load, calculate the
efficiency at half load. Assume p.f. of 0.8 at all loads. [97.9%]

QN16 An 11000/230V, 150 KVA, 50 Hz, 1-phase transformer has a core
loss of 1.4 KW and full load Cu loss of 1.6 KW. Determine (a) the KVA load for
maximum efficiency and the maximum efficiency (b) the efficiency at half full
load and full load at 0.8 p.f. lagging. [140.1312 KVA, 97.566%,
97%, 97.56%]

QN17. A 600 KVA, 1- phase transformer has an efficiency of 92% both
at full load and half load at unity p.f. Determine its efficiency at 60% of
full load at 0.8 p.f. lagging. [85.9%]

QN18 The primary and secondary of an auto-transformer are 230V and
75V respectively. Calculate the currents indifferent parts of the winding when
the load current is 200 A. Also calculate the saving in the use of copper. [65.2A,
134.8A, 32.6%]

QN19 If a three phase star/delta, 33 KV/11KV, 50 Hz, transformer is
loaded with a delta-connected load of 100 Ω per phase, calculate the primary
line current. [63.5 A]

QN20 A three phase delta/star, 11 KV/400V, 50 Hz, distribution
transformer has a star connected balanced load of (4+j6) Ω per phase. Calculate
the primary line current. [1.16 A]

QN21 A 300 KVA, 11 KV/400V, r/Y, three phase transformer
has star connected balanced load of 60 kW at power factor of 0.8 lagging in
each phase. Calculate primary line current. [11.81]

QN22 An 11KV/400V delta/star 3-phase transformer has balanced star
connected load of 60 KW at p.f. of 80% lagging per phase. Calculate the primary
line current. If the transformer has iron loss of 1.0 KW, calculate the
approximate efficiency of the transformer. Given that primary winding
resistance and leakage reactance are 25Ω per phase and 30Ω per phase
respectively. Secondary winding resistance and leakage reactance are 0.01Ω per
phase and 0.02Ω per phase respectively. [11.81A, 95.92%]

QN23 A 500 KVA, 33/11 KV, 3-phase, 50 Hz delta/star transformer has
resistances of 35 Ω per phase at high voltage side and 876 Ω per phases at low
voltage side. Calculate the efficiency at full load and one half of full load
respectively (a) at unity p.f. (b) at 0.8 p.f. lagging.

[98.54%,
98.2%, 98.35%, 98%]

QN24. For a transformer with 3-windings shown below, calculate the
primary current:

(a)
when the winding ‘B’ is connected to a resistive load of 2 Ω, keeping
winding ‘C’ open.

(b)
when the winding ‘C’ is connected to a resistive load of 4 Ω, keeping
winding ‘B’ as loaded in case(a) [25 A, 28.125 A]

#
Tutorial #3

**(Electric Machine –I)**

QN1 The data obtained from no-load
magnetization test of a dc shunt generator running at 800 rpm is as follow:

Field current(I_{f} in Amp) : 0
1.6 3.2
4.8 6.4 8
9.6 11.2

Emf ( E in volts ) : 10
148 285 390
460 520 560
590

The field winding resistance is 60 ohms.

a)
Draw the OCC and calculate the emf generated by the
machine at no-load.

b)
Find the critical resistance of the machine at 800 rpm. [ 550V, 91 ohms]

QN2 A 4-pole dc shunt generator has wave
wound armature. The armature and field winding resistances are 0.2 ohm and 60
ohms respectively. The brush contact drop is 1V per brush. The generator is
delivering a power of 3kW at 120V. Calculate :

a)
Total armature current coming out from the brush.

b)
Current in each armature conductor

c)
Generated EMF (E) [
27A, 13.5A, 127.4V ]

QN3 A dc series generator is running at 800
rpm and delivering a power of 6kW to the load at 120V. The armature and field
winding resistance are 0.1 ohm and 0.3 ohm respectively. When the load is
increased to 9kW, the speed is increased to 1200 rpm. Calculate the new values
of armature current and load terminal voltage. [46.85A, 145.27 V ]

QN4 A dc compound generator has to supply a
current of 120A at 120V. The shunt field, series field and armature winding
resistances are 30 ohm, 0.05 ohm and 0.1 ohm respectively. Calculate the emf
generated by the armature in the following two cases :

i)
Long shunt connection

ii)
Short shunt connection [ 138.6V,
138.42V ]

QN5 Calculate the resistance of the load
which consumes a power of 5 kW from a dc shunt generator whose load
characteristic is described by the equation : V_{L} = 250 – 0.5*I_{L}. [ 11.48 ohms ]

QN6 A short shunt cumulative compound dc generator supplies
7.5kw at 230V. The shunt field, series field and armature resistance are 100,
0.3and 0.4 ohms respectively. Calculate the induced emf and the load
resistance. [253.8V, 7.05W]

QN7. The resistance of the field circuit of a
shunt excited dc generator is 200W. When the output of
the generator is 100 KW, the terminal
voltage is 500V and the generated emf 525V.Calculate (a) the armature
resistance and (b) the value of the generated emf when the output is 60kw, if
the terminal voltage then is 520V.
[0.123W, 534.56V]

Contd…….

QN8. A
6 pole wave-wound dc shunt generator has 1200 armature conductors. The useful
flux per pole is 0.02wb, the armature resistance is 0.4W and the speed is 400 rpm.
If the shunt resistance is 220W, calculate the maximum current which the generator can
deliver to an external load if the terminal voltage is not to fall below 440V. [ 98 A ]

QN9 A separately excited dc generator running at 1200rpm supplies 200A at 125V to a
load of constant resistance. What will be the current when the speed is dropped
to 1000 rpm if the field current is unaltered? Given that armature resistance
=0.04W, total drop at brushes = 2 V.
[1.66.17A]

QN10. A dc generator is connected to 220V dc
mains. The current delivered by the generator to the main is 100A. The armature
resistance is 0.1W.The generator is driven at
a speed of 400rpm.Calculate:(a) the induced emf (b) the electromagnetic torque
(c) the power input and output of the armature when the speed drops to 350 rpm.
State weather the machine is generating or motoring. Assume constant flux.

[230V, 549.08N-m, 23kW, 37.73kW]

QN.11 A dc shunt machine, connected to 250V mains
has an armature resistance of 0.12W and the resistance of the
field circuit is 100W. Calculate the ratio of the
speed as a generator to the speed as a motor, the line current in each case
being 80A. [1.081]

QN12.
A 1500 kW, 500V, 16 pole, dc shunt generator runs at 150 rpm.What must be the
useful flux per pole if there are 2500 conductors in the armature and the
winding is lap connected and full-load armature copper loss is 25kW? Calculate
the area of the pole shoe if the air gap flux density has a uniform value of
0.9wb/m^{2}. Neglect charge in speed. Take R_{f} =55W.

QN13. A shunt generator delivers 50 KW at 250 V
and 400 rpm. The armature resistance is 0.02W and field resistance is 50W . Calculate the speed of the machine when
running as a shunt motor and taking 50 KW input at 250 V. [387 rpm]

QN14. A dc shunt generator has an output of 10 KW at 500 V; the
speed being 1000 rpm. The armature circuit resistance is 0.5 and the field
resistance is 250. Calculate speed when running as a shunt motor taking 50 KW
at 500 V.

***** End
******

#
Tutorial #4

**DC Generator**

**(Electric Machine –I)**

QN1 A 4-pole dc shunt generator has wave
wound armature. The armature and field winding resistances are 0.2 ohm and 60
ohms respectively. The brush contact drop is 1V per brush. The generator is
delivering a power of 3kW at 120V. Calculate :

d)
Total armature current coming out from the brush.

e)
Current in each armature conductor

f)
Generated EMF (E) [
27A, 13.5A, 127.4V ]

QN2 A dc series generator is running at 800
rpm and delivering a power of 6kW to the load at 120V. The armature and field
winding resistance are 0.1 ohm and 0.3 ohm respectively. When the load is
increased to 9kW, the speed is increased to 1200 rpm. Calculate the new values
of armature current and load terminal voltage. [46.85A, 145.27 V ]

QN3 A dc compound generator has to supply a
current of 120A at 120V. The shunt field, series field and armature winding
resistances are 30 ohm, 0.05 ohm and 0.1 ohm respectively. Calculate the emf
generated by the armature in the following two cases :

iii)
Long shunt connection

iv)
Short shunt connection [ 138.6V,
138.42V ]

QN4 Calculate the resistance of the load
which consumes a power of 5 kW from a dc shunt generator whose load
characteristic is described by the equation : V_{L} = 250 – 0.5*I_{L}. [ 11.48 ohms ]

QN5 A short shunt cumulative compound dc generator supplies
7.5kw at 230V. The shunt field, series field and armature resistance are 100,
0.3and 0.4 ohms respectively. Calculate the induced emf and the load
resistance. [253.8V, 7.05W]

QN6. The resistance of the field circuit of a
shunt excited dc generator is 200W. When the output of
the generator is 100 KW, the terminal
voltage is 500V and the generated emf 525V.Calculate (a) the armature
resistance and (b) the value of the generated emf when the output is 60kw, if
the terminal voltage then is 520V.
[0.123W, 534.56V]

QN7. A
6 pole wave-wound dc shunt generator has 1200 armature conductors. The useful
flux per pole is 0.02wb, the armature resistance is 0.4W and the speed is 400 rpm.
If the shunt resistance is 220W, calculate the maximum current which the generator can
deliver to an external load if the terminal voltage is not to fall below 440V. [ 98 A ]

QN8 A separately excited dc generator running at 1200rpm supplies 200A at 125V to a
load of constant resistance. What will
be the current when the speed is dropped to 1000 rpm if the field current is
unaltered? Given that armature resistance =0.04W, total drop at brushes = 2
V.
[1.66.17A]

QN9 A dc generator is connected to 220V dc mains.
The current delivered by the generator to the main is 100A. The armature
resistance is 0.1W.The generator is driven at
a speed of 400rpm.Calculate:(a) the induced emf (b) the electromagnetic torque
(c) the power input and output of the armature when the speed drops to 350 rpm.
State weather the machine is generating or motoring. Assume constant flux.

[230V, 549.08N-m, 23kW, 37.73kW]

QN11 A dc shunt machine, connected to 250V mains
has an armature resistance of 0.12W and the resistance of the
field circuit is 100W. Calculate the ratio of the
speed as a generator to the speed as a motor, the line current in each case
being 80A. [1.081]

QN12.
A 1500 kW, 500V, 16 pole, dc shunt generator runs at 150 rpm.What must be the
useful flux per pole if there are 2500 conductors in the armature and the
winding is lap connected and full-load armature copper loss is 25kW? Calculate
the area of the pole shoe if the air gap flux density has a uniform value of
0.9wb/m^{2}. Neglect charge in speed. Take R_{f} =55W.

QN13. A shunt generator delivers 50 KW at 250 V
and 400 rpm. The armature resistance is 0.02W and field resistance is 50W . Calculate the speed of the machine when
running as a shunt motor and taking 50 KW input at 250 V. [387 rpm]

QN14. A dc shunt generator has an output of 10 KW at 500 V; the
speed being 1000 rpm. The armature circuit resistance is 0.5 and the field
resistance is 250. Calculate speed when running as a shunt motor taking 50 KW
at 500 V.

***** End
******