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**Lecture No. 11 By. Sajid Hussain Qazi**

REFLECTED IMPEDANCE & POWER EQUIVALENT RESISTANCE, REACTANCE & PHASOR DIAGRAM OF TRANSFORMER Lecture No. 11 By. Sajid Hussain Qazi

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**REFLECTED IMPEDANCE In the previous section we found that,**

Dividing the first by the second, we have

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**REFLECTED IMPEDANCE However, since Then,**

The above equation states that the impedance of the primary circuit of an ideal transformer is the transformation ratio squared times the impedance of the load. Equation-1

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REFLECTED IMPEDANCE If a transformer is used, therefore, an impedance can be made to appear larger or smaller at the primary by placing it in the secondary of a step- down (a > 1) or step-up (a < 1) transformer, respectively. Note that if the load is capacitive or inductive, the reflected impedance will also be capacitive or inductive.

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Power of Transformer For the ideal iron-core transformer,

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**Example:- For the iron-core transformer of Figure shown**

a. Find the magnitude of the current in the primary and the impressed voltage across the primary. b. Find the input resistance of the transformer.

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Example:-

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**EQUIVALENT RESISTANCE, REACTANCE**

If we now reflect the secondary circuit through the ideal transformer using Eq. (1), as shown in Figure below, we will have the load and generator voltage in the same continuous circuit.

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**EQUIVALENT RESISTANCE, REACTANCE**

The total resistance and inductive reactance of the primary circuit are determined by, which result in the useful equivalent circuit of Figure shown.

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**EQUIVALENT RESISTANCE, REACTANCE**

The load voltage can be obtained directly from the circuit of Figure shown above through the voltage divider rule: Equation-2

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**Phasor Diagram of Transformer**

The figure shown above will also allow us to calculate the generator voltage necessary to establish a particular load voltage. The voltages across the elements of above figure have the phasor relationship indicated in Figure below...

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**Phasor Diagram of Transformer**

For an inductive load, the phasor diagram appears below, note that aVL leads I by the power-factor angle of the load.

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**Phasor Diagram of Transformer**

The effect of Re and Xe on the magnitude of Vg for a particular VL is obvious from Eq. (2). For increased values of Re or Xe, an increase in Vg is required for the same load voltage. For Re and Xe=0, VL and Vg are simply related by the turns ratio.

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