#### In the last two articles, we learned about the effect of resistance and leakage reactance on the transformer. Now let us see the effect on the transformer with both resistance and leakage reactance i.e., nothing but the impedance.

## Resistance and Leakage Reactance or Impedance of a Transformer :

#### If R_{1} and X_{1} are the resistance and leakage reactance of the primary winding. Similarly, R_{2} and X_{2} are the resistance and leakage reactance of the secondary winding as shown below.

#### Then the impedances Z_{1} and Z_{2} due to resistance and reactance of the primary and secondary winding is given as,

#### There will voltage drops which causes power loss in the primary and secondary windings due to resistance ( as copper losses ) and due to leakage reactance ( as magnetic leakage flux ). Hence, the voltage across the primary and secondary windings is given by,

#### Where,- V
_{1} & V_{2} = Primary applied voltage and secondary terminal voltage. - I
_{1} & I_{2} = Primary and secondary currents. - E
_{1} & E_{2} = Primary and secondary induced EMFs. - I
_{1} Z_{1} & I_{2} Z_{2} = Power loss in the primary and secondary windings.

### Phasor Diagram with Different Loads :

#### The vector or phasor diagram for the above transformer with power loss for resistive, resistive-inductive, and resistive-capacitive loads are shown in the below figures respectively.

#### At first draw voltage vector V_{2}, and I_{2} representing secondary current in phase as well as in magnitude. Since voltage drop in the secondary winding i.e., drop due to resistance I_{2} R_{2} will be in phase with current I_{2}, and drop due to leakage reactance I_{2} X_{2} will leads current I_{2} by 90⁰. Now draw a line AB parallel to current I_{2} and equal to I_{2} R_{2} in magnitude and draw BC perpendicular to AB and equal to I_{2} X_{2} in magnitude such that line AC represents the total drop impedance I_{2} Z_{2}. So vector represents secondary induced emf E_{2}.

Draw no-load current I_{o}, and I_{2}' parallel to I_{2} ( and equal to K I_{2} ). The sum of I_{o} and I_{2}' gives I_{1}. Draw OD equal to induced emf E_{1}. So draw DG equal to I_{1} R_{1} and parallel to I_{1} and I_{1} X_{1} perpendicular to DG. So vector OH represents V_{1} in magnitude and phase.

## Equivalent Resistance and Leakage Reactance or Impedance of the Transformer :

#### The impedances Z_{1} and Z_{2} of the transformer on both the windings can be transferred either to the primary or secondary side and referred to as the transferred side. This shifting makes the calculations easy and simple.

### Equivalent Resistance and Leakage Reactance or Impedance Referred to primary side :

#### The equivalent impedance referred to the primary side can be done by transferring the secondary resistance and reactance to the primary side as shown below.

#### Here, the total resistance R_{01} ( R_{1} + R_{2}' ) referred to the primary side and total reactance X_{01} ( X_{1} + X_{2}' ) referred to the primary side is given by,

#### Therefore, the total impedance Z_{01} which is the algebraic sum of both resistance and leakage reactance referred to the primary side is,

### Equivalent Resistance and Leakage Reactance or Impedance Referred to secondary side :

#### Similarly, the equivalent impedance referred to as the secondary side can be done by transferring the primary resistance and reactance to the secondary side as shown below.

#### Here, the total resistance R_{02} ( R_{1}' + R_{2} ) referred to the secondary side and total reactance X_{02} ( X_{1}' + X_{2} ) referred to the secondary side is given by,

#### Therefore, the total impedance Z_{02} referred to the secondary side is,