Principle of Transformer

Principle of Transformer

$\Phi={\Phi _m}\sin \omega t$

$e = - \partial \frac{d}{{dt}}(\Phi T) = - T\frac{{d\Phi }}{{dt}}({\Phi _m}\sin \omega t) = - T\omega {\Phi _m}\cos \omega t$

$= T\omega {\Phi _m}\sin (\omega t - \frac{\pi }{2})$

$e = {E_m}\sin (\omega t - \frac{\pi }{2})$

${E_m} = T\omega {\Phi _m}$

${E_{rms}} = E = \frac{{{E_m}}}{{\sqrt 2 }}$

$E = \frac{{T\omega {\Phi _m}}}{{\sqrt 2 }} = \frac{{T(2\pi f){\Phi _m}}}{{\sqrt 2 }}$

$E = 4.44{\Phi _m}fT$

${E_1} = 4.44{\Phi _m}f{T_1}$

${E_2} = 4.44{\Phi _m}f{T_2}$

${B_m} = \frac{{{\Phi _m}}}{A}$

$\frac{{{E_1}}}{{{T_1}}} = 4.44{\Phi _m}f$

$\frac{{{E_2}}}{{{T_2}}} = 4.44{\Phi _m}f$

$\frac{{{E_1}}}{{{T_1}}} = \frac{{{E_2}}}{{{T_2}}}$

$\frac{{{E_1}}}{{{E_2}}} = \frac{{{T_1}}}{{{T_2}}}$

$a = \frac{{{E_1}}}{{{E_2}}} = \frac{{{T_1}}}{{{T_2}}}$

$\frac{{{V_1}}}{{{V_2}}} = \frac{{{T_1}}}{{{T_2}}} = a$

$\Phi = {\Phi _M}\sin \omega t$

${e_1} = {E_{1m}}\sin (\omega t - \frac{\pi }{2})$

${e_2} = {E_{2m}}\sin (\omega t - \frac{\pi }{2})$