Answer to Question #210538 in Electrical Engineering for Zwi

Question #210538

The no-load voltage of a single phase transformer is 3300 / 400 V. It takes 7A at a power factor of 0.3 lagging on no-load. Determine the following: 

(a) The magnetizing current of the transformer.

(b) The magnetizing reactance of the transformer.

(c) The core loss current of the transformer.

(d) The core loss resistance of the transformer

(e) The iron losses of the transformer.

(f) The primary current if the load on the secondary is 80 A at a power factor of 0.85 leading.


1
Expert's answer
2021-06-28T06:18:02-0400

(a)

The magnetizing current of the transformer is

Im=IosinϕIo=7Acosϕ=0.3ϕ=cos10.3ϕ=72.5°sinϕ=0.95Im=7×0.95=6.68AI_m=I_o\sin\phi\\ I_o=7A\\ \cos\phi=0.3\\ \phi=\cos^{-1}0.3\\ \phi=72.5\degree\\ \sin\phi=0.95\\ I_m=7\times 0.95=6.68A \\

(b)

The magnetizing reactance of the transformer is

Xo=E1ImE1=3300VIm=6.68AXo=33006.68Xo=494ΩX_o=\frac{E_1}{I_m}\\ E_1=3300V\\ I_m=6.68A\\ X_o=\frac{3300}{6.68}\\ X_o=494\Omega

(c)The core loss current of the transformer is

Iw=IocosϕIw=7×0.3Iw=2.1AI_w=I_o\cos\phi\\ I_w=7\times 0.3\\ I_w=2.1A\\

(d) The core loss resistance of the transformer is

Ro=E1IwRo=33002.1Ro=1571.4ΩR_o=\frac{E_1}{I_w}\\ R_o=\frac{3300}{2.1}\\ R_o=1571.4\Omega\\

(e) The iron losses of the transformewr is

Pi=Iw2RoPi=2.12×1571.4Pi=6390WP_i=I_w^2R_o\\ P_i=2.1^2\times1571.4\\ P_i=6390W\\

(f) The primary current I1 if the load on the secondary is 80 A at a power factor of 0.85 leading is calculated as follows

ϕ1=72.5°ϕ2=cos10.85=31.8°ϕ=72.5+31.8=104.3°I2=(K)I2K=4003300=433I2=80AI2=9.7A\phi_1=72.5\degree\\ \phi_2=\cos^{-1}0.85=31.8\degree\\ \phi=72.5+31.8=104.3\degree\\ I_2'=(K)I_2\\ K=\frac{400}{3300}=\frac{4}{33}\\ I_2=80A\\ I_2'=9.7A

I1=Io2+I22+2IoI2+cosϕI1=72+9.72+2(7)(9.7)+cos104.3I1=16.7AI_1=\sqrt{I_o^2+I_2'^2+2I_oI_2'+\cos\phi}\\ I_1=\sqrt{7^2+9.7^2+2(7)(9.7)+\cos104.3}\\ I_1=16.7A


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment