What is the relationship of the Current in the primary and secondary coil with the voltage and number of turns in the coils of transformer ?

Dear Student,

Please find below the solution to the asked query:

Ideal transformer equations (eq.)

By Faraday's law of induction:

$$\begin{gathered} V_S=-N_S\frac{d\varphi }{dt}....\left(1\right) \\ and \\ {V}_P=-N_P\frac{d\varphi }{dt}....\left(2\right) \end{gathered}$$

Combining ratio of (1) & (2)

$Turns ratio=\frac{V_P}{V_S}=\frac{-N_P}{-N_S}=a....\left(3\right)$
where
for step-down transformers, a > 1
for step-up transformers, a < 1

By law of conservation of energy, apparent, real and reactive power are each conserved in the input and output

$S=I_P{V}_P=I_S{V}_S....\left(4\right)$

Combining (3) & (4) with this end note yields the ideal transformer identity
$\frac{V_P}{V_S}=\frac{I_S}{I_P}=\frac{N_P}{N_S}=\sqrt{\frac{L_P}{L_S}}=a....\left(5\right)$

By Ohm's law and ideal transformer identity
$Z_L=\frac{V_S}{I_S}....\left(6\right)$

Apparent load impedance Z'L (ZL referred to the primary)
$Z{\text{'}}_L=\frac{V_P}{I_P}=\frac{a{V}_S}{{\displaystyle \raisebox{1ex}{$I_S$}\!\left/ \!\raisebox{-1ex}{$a$}\right.}}=a^2\frac{V_S}{I_S}=a^2{Z}_L.....\left(7\right)$

Hope this information will clear your doubts about the topic.

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