A one-phase transformer has 400 and 1000 turns in primary and secondary, respectively. The cross-sectional area of the core is 60 cm². The primary of the transformer is connected to a supply of one-phase, 50 Hz, 500 V. Determine the secondary voltage of the transformer.

Concept:

Transformation ratio: It is defined as the ratio of the secondary voltage to the primary voltage. It is denoted by 'K'.

\(K = \frac{{{N_2}}}{{{N_1}}} = \frac{{{V_2}}}{{{V_1}}} = \frac{{{I_1}}}{{{I_2}}}\)  ----- (1)

Turns ratio or Voltage ratio: It is defined as the ratio of primary winding turns to secondary winding turns. It is denoted by 'a'.

\(a = \frac{{{1}}}{{{K}}} = \frac{{{N_1}}}{{{N_2}}} = \frac{{{V_1}}}{{{V_2}}} = \frac{{{I_2}}}{{{I_1}}}\)   ----- (2)

N₁ = primary winding turns

N₂ = secondary winding turns

V₁ = primary winding voltage

V₂ = secondary winding voltage

I₁ = current through the primary winding

I₂ = current through the secondary winding

Calculation:

Given:

N₁ = 400, N₂ = 1000, V₁ = 500, V₂ =?

from eq (2), we can write

\(\frac{{{V_1}}}{{{V_2}}} = \frac{{{N_1}}}{{{N_2}}}\)

\(\frac{{500}}{{{V_2}}} = \frac{{400}}{{1000}}\)

V₂ = 1250 V