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A single-phase two-winding transformer is rated at 23 kVA, 600/120 V, 50 Hz. An impedance load with a magnitude of 1.003 ohm is connected to the secondary winding. The load has a power factor of 0.76 lagging when the load voltage is 116 V. Assume that the transformer is ideal. Calculate the value of the load impedance referrred to the primary side.

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Final answer:

To find the load impedance referred to the primary side of an ideal transformer, we use the square of the turns ratio and multiply by the secondary side impedance. Given a 600/120 V transformer and 1.003 ohm load impedance on the secondary, the reflected primary impedance is 25.075 ohms.

Step-by-step explanation:

The question asked relates to the concept of transformer impedance reflection in the field of electrical engineering. An ideal single-phase two-winding transformer is given with primary and secondary ratings, and the task is to calculate the equivalent impedance of a load, connected to the secondary side, but referred to the primary side of the transformer. In an ideal transformer, the impedance reflection is given by the square of the turns ratio (Np/Ns)2.

To calculate the reflected impedance to the primary side (Zp) from the secondary side (Zs), we use the formula:

Zp = Zs(Np/Ns)2

First, we calculate the turns ratio which is simply the ratio of the primary voltage to the secondary voltage:

Turns ratio (Np/Ns) = Vp/Vs = 600V/120V = 5

Knowing that the load impedance on the secondary side is 1.003 ohm, we can now calculate the reflected impedance to the primary side:

Zp = 1.003 Ω × (5)2

Zp = 1.003 Ω × 25

Zp = 25.075 Ω

Thus, the value of the load impedance referred to the primary side is 25.075 ohms.

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