Find the estimated current taken by the primary side if a single-phase transformer with a voltage ratio of 440/110 V takes a no-load current of 5 A at 0.2 power factor lagging and the secondary supplies a current of 120 A at a power factor of 0.8 lagging. Given that cos(41°36’) = 0.748.

Equivalent circuit diagram of the transformer

The primary current is given by:

Also, 

where, I_o = No-load current

I₂ = Secondary current

Calculation

I2 = 120 A at a power factor of 0.8 lagging = 120∠-36.54° 

Io = 5 A at 0.2 power factor lagging = 5∠-78.46° 

I₁ = 5∠-78.46° + (0.25) (120∠-36.54°)

I1 = 5∠-78.46° + 30∠-36.54°

I1 = 5(0.2 - j0.97) + 30(0.8-j0.6)

I1 = 1 - j4.89 + 24 - j18

I1 = 

Additional Information Conversion from rectangular form to polar form

The rectangular form of a coordinate is represented by 

The polar form of a coordinate is represented by 

where, 

 Conversion from polar to rectangular form

The polar form of a coordinate is represented by 

The rectangular form of a coordinate is represented by 

where,