An alternating emf VP from an ac source is applied across the primary coil of a transformer, shown in figure.

This sets up an alternating current fP in the primary circuit and also produces an alternating magnetic flux through the primary coil such that

V_p = -N_p \(\cfrac{dΦ_P}{dt}\)………….. (1)

where N_p is the number of turns of the primary coil and Φ_p is the magnetic flux through each turn.

Assuming an ideal transformer (i.e., there is no leakage of magnetic flux), the same magnetic flux links both the primary and the secondary

coils, i.e., Φ_p = Φ_s .

As a result, the alternating emf induced in the secondary coil,

V_s = – N_s \(\cfrac{dΦ_S}{dt}\) = - N_s \(\cfrac{dΦ_P}{dt}\)……………… (2)

where N_s is the number of turns of the secondary coil.

From Eqs. (1) and (2),

\(\cfrac{V_s}{V_p}\) = \(\cfrac{N_s}{N_p}\) or V_s = V_p \(\cfrac{N_s}{N_p}\)…………… (3)

Case (1) : If N_s > N_p , V_s > V_p . Then, the transformer is called a step-up transformer. 

Case (2) : If N_s < N_p , V_s < V_p . Then the transformer is called a step-down transformer

Ignoring power losses, the power delivered to the primary coil equals that taken out of the secondary coil, so that V_pI_p = V_sI_s …………. (4) 

From Eqs. (3) and (4),

\(\cfrac{I_p}{I_s}\) = \(\cfrac{V_s}{V_p}\) = \(\cfrac{N_s}{N_p}\)