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sandy.bridge
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Homework Statement
The problem at hand involved determining the equivalent circuit model of the transformer and then determining its efficiency. I for the life of me cannot get the results that he has provided us with, so perhaps someone here can either confirm my results or indeed confirm his.
Here are my steps:
For open circuit,
[tex]\theta_{OC}=arccos((186W)/((240V)(5.41A)))=81.7639° [/tex]
[tex]Y_E=(5.41A)/(240V)e^{-j81.76°}=0.003229-j0.02231[/tex]
[tex]R_{G,S}=1/0.003229=310Ω,X_{M,S}=1/0.02231=44.825Ω[/tex]
Short circuit test:
[tex]\theta_{SC}=arccos(617W/((48V)(20.8A)))=51.3°[tex]
[tex]R_{eq,p}=1.42615Ω, X_{eq,p}=1.81426Ω[/tex]
I put everything in terms of the LV side and hence [itex]R_{G,S},X_{M,S}[/itex] remain the same. The primary equivalents are divided by a factor of a=2400/240-100.
Full load on secondary side at 0.8 PF:
[tex]I_S=(50 000VA)/(240V)e^{-j36.9°}[/tex]
hence
[tex]V_p/a=(0.0142262+j0.0181426)(208.33e^{-j36.9°})+240V=484.641e^{j0.146956}[/tex]
[tex]P_{Cu}=(208.33A)^2(0.0142262Ω)=617W[/tex]
[tex]P_{Core}=(484.641V)^2/(309.7W)=758W[/tex]
[tex]P_{Supplied}=(240V)(208.33A)cos(36.9°)=39984W[/tex]
The efficiency turns out to be 96.7%.
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