1
Example
1:- A (40 KVA, 50 Hz) single phase transformer has (400) turns on the
primary windings and (100) turns on the secondary windings, the supply voltage is
(2000 V) on the primary. Determine the followings:-
1- The secondary voltage when the transformer is operating as open circuit.
2- The full load current of the both sides (primary and secondary).
3- The maximum value of the flux (ɸ
max
).
4-
Example 2
:-
A single phase transformer has (1.1 Volt /turn) . when the primary
winding is supplied by (220 V, 50 Hz) the secondary winding voltage is (550 V).
Determine the followings:-
1- The number of the primary and secondary windings.
2- The cross section area of the iron core if the flux density is (B= 1.2 Tesla).
Example 3
:-
A (200 KVA) single phase transformer (V
1
=6600 V & V
2
= 400 V), the
number of the secondary windings is (N
2
= 80 turn). If the transformer is operating at
(50 Hz), then determine the followings:-
1- The number of the primary windings (N
1
).
2- The maximum value of the flux (ɸ
max
).
3- If the transformer is operating at (25 Hz), and the flux increased by (10%) of its
value then determine the followings:-
a- The new value of the primary voltage (V
1
).
b- The new value of the transformer power in (KVA), assuming the values of the
primary and secondary (I
1
& I
2
) remains constant.
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Example 4:
-
A single phase transformer (V
1
=300 V & V
2
= 3300 V), at the no load
the current is (I
o
= 0.6 A) and the power is (P
o
=60 W) when the supply voltage is
connected to the low voltage side and the high voltage side is open circuited , then
determine the followings:-
1- The power factor at no load (PF).
2- The tow components of the no load current.
2
Example 5
:-
A single phase transformer (V
1
=440 V & V
2
= 110 V), at the no load
the current is (I
o
= 5 A) at power factor (Pf = 0.2 lag), the secondary delivered the
load with (I
2
=120 A) at power factor (0.8 lag). Determine the primary winding
current (I
1
).
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Example 6
:-
The numbers of the primary and the secondary turns windings of a
single phase transformer are (N
1
= 1000 turn and N
2
=200 turn) respectively. When
the load current on the secondary windings is (I
2
= 125 A) at a power factor (0.8 lag).
The primary current was (I
1
=30 A) at power factor (0.707 lag). Determine the no
load current and its power factor.
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Example 7
:-
A single phase transformer with a turns ratio (a=1/19.5), (R
1
=25 Ω,
X
1
=100 Ω, R
2
=0.06 Ω, X
2
=0.25 Ω), the no load current is ( I
o
=1.25 A) and leading
the flux by (30 ̊) . The secondary delivered the load by (I
2
=200 A) at a terminal
voltage of (500 V) and power factor of (0.8 lag), using the vector diagram (V.D)
determine the primary supplied voltage (V
1
) and its power factor (PF).
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Example
8:-
A (30 KVA) single phase transformer (V
1
=2000 V & V
2
= 200 V),
(R
1
=3.5 Ω, X
1
=4.5 Ω, R
2
=0.015 Ω, X
2
=0.02 Ω). Then determine the followings:-
1- The values of (R
eq1
, X
eq1,
and Z
eq1
) referred to the primary winding side (H.V Side).
2- The values of (R
eq2
, X
eq2,
and Z
eq2
) referred to the secondary winding side (L.V Side).
3- The total copper losses by the three methods.
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Example
9:-
A (10 KVA) single phase transformer (V
1
=450 V & V
2
= 120 V), if the
results of the open circuit and short circuit tests are shown below:-
V
o.c
= 120 V , I
o.c
= 4.2 A , P
o.c
= 80 W on the L.V side.
V
s.c
= 9.65 V , I
s.c
=22.2 A, P
s.c
=120 W on the H.V side.
Determines the equivalent circuit of the transformer referred to the high voltage side.
3
Example
10:-
If the percentage resistance of the single phase transformer is
(%R=2.5 %), and on the percentage reactance is (%X= 5 %). Determine the lagging
power factor (PF) at which the voltage drop is maximum value. And then determine
the value of the drop as a percentage value.
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Example
11:-
A single phase transformer (V
1
=200 V & V
2
= 400 V), if the results of
the open circuit and short circuit tests are shown below:-
V
o.c
= 200 V , I
o.c
= 0.7 A , P
o.c
= 70 W on the L.V side.
V
s.c
= 15 V , I
s.c
=10 A , P
s.c
=85 W on the H.V side.
Determines the secondary voltage when the transformer delivering (5 KW) at power
factor (0.8 lag).
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Example
12:-
A (10 KW) single phase transformer (V
1
=220 V & V
2
= 440 V), if the
iron losses are (P
iron
=200 W) and the cupper losses are (P
cu
=300 W), find the
efficiency of the transformer at:-
1- Full load. 2- 0.5 Full load.
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Example
13:-
If the cupper losses of a single phase transformer are (P
cu
=100 W),
then determine the values of the cupper losses at (0.5 F.L, 0.75 F.L and 0.9 F.L).
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Example
14:-
A (10 KVA) single phase transformer (V
1
=450 V & V
2
= 120 V), if
the results of the open circuit and short circuit tests are shown below:-
V
o.c
= 450 V , I
o.c
= 1.12 A , P
o.c
= 80 W on the H.V side.
V
s.c
= 9.68 V , I
s.c
=22.2 A , P
s.c
=120 W on the H.V side.
Then determines the followings:-
1- The equivalent circuit referred to the H.V side.
2- The efficiency at full load (F.L) and power factor (0.8 lag).
3- The efficiency at half full load (0.5 F.L) and power factor (0.8 lag).
4- The voltage regulation factor (% Reg) at full load (F.L) and power factor (0.8 lag).
4
Example
15:-
A single phase transformer (V
1
=250 V & V
2
= 500 V), if the results of
the open circuit and short circuit tests are shown below:-
V
o.c
= 250 V , I
o.c
= 1 A , P
o.c
= 80 W on the L.V side.
V
s.c
= 20 V , I
s.c
=12 A , P
s.c
=100 W on the H.V side.
Then determines the followings:-
1- The equivalent circuit referred to the primary (L.V) side.
2- The primary supply voltage in order to obtain (500 V and 10 A) in the secondary at
power factor (0.8 lag).
3- The efficiency when the load current is (10 A), (V
2
= 500 V) and the PF=0.8 lag.
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Example
16:-
A (5 KVA) single phase transformer (V
1
=230 V & V
2
= 2300 V), if
the iron losses at rated voltage are (P
iron
=40 W) and the cupper losses at the rated
current are (P
cu
=112 W), determine the efficiency of the transformer at :-
1- (1.25 KVA) and (PF=0.8 lag).
2- (3.57 KVA) and (PF=0.8 lag).
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Example
17:-
A (5 KVA) single phase transformer (V
1
=250 V & V
2
= 500 V), if the
results of the open circuit and short circuit tests are shown below:-
V
o.c
= 250 V , I
o.c
= 0.75 A , P
o.c
= 60 W on the L.V side.
V
s.c
= 9 V , I
s.c
=6 A , P
s.c
=21.6 W on the H.V side.
Then determines the followings:-
1- The no load current components.
2- The efficiency at full load and unity power factor.
3- The secondary voltage at full load and :-
a) Unity power factor. b) P.F=0.8 lag. c) P.F=0.8 lead.
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Example
18:-
A single phase transformer (V
1
=440 V & V
2
= 110 V) , (R
1
=0.3 Ω,
R
2
=0.02 Ω), the iron losses at rated voltage are (P
iron
=150 W). Determine:-
1- The secondary current when the efficiency is maximum value.
2- The maximum efficiency at unity power factor (PF=1).
5
Example
19:-
A (1000 KVA) single phase transformer, the iron losses are
(P
iron
=8.8KW) and the cupper losses are (P
cu
=9.8 KW). determine the followings:-
1- The efficiency at (125% F.L) and (PF= 0.85 lag).
2- The load (output power) at which the maximum efficiency occur.
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Example
20:-
A (25 KVA) single phase transformer (V
1
=2200 V & V
2
= 220 V), if
the results of the open circuit and short circuit tests are shown below:-
V
o.c
= 220 V , I
o.c
= 4 A , P
o.c
= 150 W on the L.V side.
V
s.c
= 90 V , I
s.c
=10 A , P
s.c
=350 W on the H.V side.
Then determines the followings:-
1- The primary voltage at (PF=0.8 lag) and if the secondary voltage is (220 V).
2- The voltage regulation factor (%Reg).
3- The efficiency at full load and (PF= 0.8 lag).
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Example
21:-
A single phase transformer (V
1
=110 V & V
2
= 220 V), when the
transformer is operating at full load the secondary voltage became (210 V) find the
regulation factor (%Reg).
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Example
22:-
A (100 KVA) single phase transformer delivered lighting load, the
total losses at full load are (3 KW) sharing equally between (P
iron
& P
cu
). Through the
day the transformer operates as bellow:-
- At full load for (3 Hours).
- At half full load for (4 Hours).
- No load for the remaining time.
Determine the all day efficiency of the transformer at unity power factor.
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Example
24:-
A single phase auto transformer (V
1
=500 V & V
2
= 400 V), the load
current is (I
load
=100A). Show the current distribution and determine the saving of the
cupper.
6
Example
23:-
The maximum efficiency of a single phase transformer is (98%) and
occurs at (15 KVA & 1 PF). Through the day the transformer operates as bellow:-
- ( 2 KW & PF =0.5 lag) for 12 Hours.
- (12 KW & PF =0.8 lag) for 6 Hours.
- (18 KW & PF =0.9 lag) for 6 Hours.
Determine the all day efficiency of the transformer.
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Example
25:-
A (5 KVA) single phase transformer (V
1
=480 V & V
2
= 120 V), it is
used as auto transformer to delivered a load with (480 V) from supply voltage of
(600V), sketch the winding connection in this case and then determine the rated
power of the transformer assuming the values of the winding currents remains
constant at the rated values.
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Example
26:-
A (50 KVA) single phase transformer (V
1
=33000 V & V
2
= 230 V), If
the percentage impedance (%Z=4 %), and the cupper losses equal (1.8 %) of the full
load power. Determine the followings:-
1- The percentage reactance (%X).
2- The ohmic values of (R
eq
, X
eq
, Z
eq
) referred to the primary side.
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Example
27:-
For a single phase transformer the percentage cupper losses at full
load is (1.5 %) and the percentage reactance (%X=3.5 %). Determine the percentage
value of the regulation factor at :-
a) Unity power factor. b) P.F=0.8 lag. c) P.F=0.8 lead.
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Example
28:- A (440 V, 50 Hz) single phase transformer, the iron losses at the rated
voltage and frequency are (2500 W). and the iron losses is (850 W) at (220 V &
25Hz), Determine the values of the hysteresis losses and eddy current losses.
7
Example
29:- Two single phase transformer with equal voltage ratio and equal KVA
rating have impedance of (0.5+j3 Ω) and (0.6+j10 Ω) referred to secondary winding.
If they are connected in parallel determine how they will share total load of (100KW)
of power factor (PF=0.8 lag).
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Example
30:- Two single phase transformer are connected in parallel. One
transformer has an ohmic drop of (0.5%) at full load and an inductive drop (8%) at
full load. The other transformer has an ohmic drop of (0.75%) and an inductive drop
(4%). Show how they are share a load of (180KW) at power factor (PF=0.9 lag)
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