Question 3.29: A transformer has turn ratio of a = 10. The results of two o...

(a)   X_{m} =\frac{240}{4} =50\Omega ,X_{m}=2\pi fL_{1}
L_{1} =\frac{200}{2\pi \times 50} =0.159 H
1950=\sqrt{2} \pi N_{2} \phi _{max}=\sqrt{2} \pi \psi _{max}
\psi _{max} =\frac{1950}{\sqrt{2} \pi } =8.78 Wb–T
M=\frac{\psi _{max}}{i_{1}\left(max\right) } =\frac{8.78}{\sqrt{2} \times 4} =1.55 H
(b)  E_{1} =\sqrt{2} \pi fN_{2}\phi _{max} =\sqrt{2} \pi \psi _{max}
\frac{\psi _{max} }{i_{2}\left(max\right) } =M, \psi _{max} =\sqrt{2} \times 0.42\times 1.55=199.6 A
L_{2} =\frac{2000}{\sqrt{2}\pi \times 50 } \cdot \frac{1}{\sqrt{2}\times 0.41 } = 15.53 H
Coupling coefficient, k=\frac{1.55}{\sqrt{0.159\times 15.53} } =0.986