TRANSFORMER THEORY
Transformers
Core losses are caused by two factors: hysteresis and eddy current losses. Hysteresis loss is that
energy lost by reversing the magnetic field in the core as the magnetizing AC rises and falls and
reverses direction. Eddy current loss is a result of induced currents circulating in the core.
The efficiency of a transformer can be calculated using Equations (138), (139), and (1310).
(138)
Efficiency
Power Output
Power Input
P_{S}
P_{P}
x 100
(139)
Efficiency
Power Output
Power Output
Copper Loss
Core Loss
x 100
(1310)
Efficiency
V_{S} I_{S} x PF
(V_{S} I_{S} x PF)
Copper Loss
Core Loss
x 100
where
PF = power factor of the load
Example 1:
A 5:1 stepdown transformer has a fullload secondary current of 20 amps. A
short circuit test for copper loss at full load gives a wattmeter reading of 100 W.
If R_{P} = 0.3W, find R_{S} and power loss in the secondary.
Solution:
Copper Loss
I^{2}_{P} R_{P}
I^{2}_{S} R_{S}
100 W
To find I_{P}:
N_{P}
N_{S}
I_{S}
I_{P}
I_{P}
N_{S}
N_{P}
I_{S}
1
5
20
4 amps
To find R_{S}:
I^{2}_{S} R_{S}
100
I^{2}_{P} R_{P}
R_{S}
100
I^{2}_{P} R_{P}
I^{2}_{S}
100
0.3(4)^{2}
20^{2}
0.24
ES13
Page 12
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