## 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

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