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
:-
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
7:-
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
8:-
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.
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Example
9:-
If the percentage resistance drop of the single phase transformer is
(%R=2.5 %), and on the percentage reactance drop 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.
3
Example
10:-
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.
Example
11:-
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).
Example
12:-
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).
Example
13:- 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).