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How to find the equivalent resistance, reactance and impedance referred to primary and secondary side of a transformer

A 500/200v single phase transformer has primary resistance of 0.5Ω and reactance of 3.7Ω, while the secondary resistance and reactance are 0.03Ω and 0.25Ω respectively. Compute the equivalent values of resistance, reactance and impedance referred to;
I. the primary
II. the secondary

Equivalent resistance

(Values of resistance)R1(primary resistance) = 0.5Ω, R2 (secondary resistance) = 0.03Ω
and X1( primary reactance) = 3.7Ω, X2 (secondary reactance) = 0.25Ω
V1/V2 = 500/200V
The formula for equivalent resistance is;
Re( equivalent resistance) = R1 + R2 (V1/V2)²
Re = 0.5 + 0.03(500/200)²
Re = 0.5 + 0.03(2.5)²
Re = 0.5 + 0.03(6.25)
Re = 0.5 + 0.19
Re = 0.69Ω

Finding equivalent reactance( values of reactance)
Xe( equivalent reactance) = X1 + X2 (V1/V2)²
Xe = 3.7+ 0.25)500/200)²
Xe =3.7+ 0.25(2.5)²
Xe = 3.7+ 0.25(6.25)
Xe = 3.7 + 1.56
Xe = 5.26Ω

Impedance referred to the primary ( values of impedance referred to primary and secondary)
Z1² = R1² + X1²
Z1 = √[R1² + X1²]Z1 = √[0.5² + 3.7²]Z1 = √[0.25 + 13.69]Z1 = √[13.94]Z1 = 3.75Ω

Impedance referred to the secondary
Z2² = R2² + X2²
Z2 = √[R2² + X2²]Z2 = √[0.03² + 0.25²]Z2 = √[0.0009+ 0.063]Z2 = √[0.0639]Z2 = 0.25Ω

Oluwamuyide Peter

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