**Equivalent Resistance**. In Fig. 25 is shown a transformer whose primary and secondary windings have resistances *of R _{1} and R*

_{2}*respectively (shown external to the windings). The resistance of the two windings can be transferred to anyone of the two windings. If both the resistances are concentrated in one winding the calculations become simple since then we can work in one winding only.*

In the secondary, copper loss is I_{2}^{2}R_{2}. This loss is supplied by primary which takes a current of I_{1}. Hence, if R_{2}‘ is the equivalent resistance referred to primary which would have caused the same loss as R_{2} in secondary, then

Similarly, equivalent primary resistance as referred to secondary is

In Fig. 26, secondary resistance has been transferred to primary side (leaving secondary circuit resistanceless),

Similarly, the equivalent resistance of the transformer as referred to the secondary (Fig. 27)

R_{02} =R_{2} +R_{1}‘ =R_{2} +K^{2}R_{1} … (7)

The following points are worth remembering:

(i) When shifting resistance *to the secondary, multiply *it by *K ^{2}. *

(ii) * *When shifting resistance *to the primary, divide *by *K ^{2}. *

**Leakage reactance**. Leakage reactance can also be transferred from one winding to the other in the same way as resistance (Fig. 28 and Fig. 29).

**Total Voltage Drop in a Transformer **

(i) **Approximate voltage drop**. When there is no-load on the transformer, then,

V_{1} = E_{1} (approximately).

and E_{2} = KE_{1} = KV_{1}

Also E_{2} = _{0}V_{2}, where _{0}V_{2} is secondary terminal voltage on no-loud

E_{2} = _{0}V_{2} =KV_{1}

V_{2} = secondary voltage on load.

Refer Fig. 32. The procedure of finding the approximate voltage drop of the transformer as referred to secondary is given below:

- Taking O as center, radius OC draw an arc cutting OA produced at E.

The total power voltage drop I_{1}Z_{02} = AC = AE which is approximately equal to AG.

- From B draw BF perpendicular on OA produced. Draw CG perpendicular to OE and draw BD parallel to OEApproximate voltage drop = AG = AF + FG = AF + BD [= I
_{2}R_{02}cos ɸ + I_{0}X_{02}sin ɸThis is the value of approximate voltage drop for a*lagging power factor.*Figs. 33 and 34 refer to*unity*and*leading power factor*respectively..

- The approximate voltage drop for a
*leading power factor*becomes:

(I_{2}R_{02} cos ɸ – I_{2}X_{02} sin ɸ)

- The approximate voltage drop for a transformer
*in general*is given by :

(I_{2}R_{02} cos ɸ ± I_{1}X_{02} sin ɸ) … (12)

- The voltage drop as
*referred to primary*is given by:

(I_{1}R_{01} cos ɸ ± I_{1}X_{02} sin ɸ

*Percentage*voltage drop in*secondary*

*ii) ***Exact voltage drop**. When we refer to Fig. 32 we find that exact drop is *AE *and not *AG. *If quantity *GE *is added *to AG *the exact value of voltage drop will be obtained.

From right angled triangle *OCG, *we get

CG^{2} = OC^{2} – OG^{2} = (OC + OG) (DC – OG)

= (DC + OG) (DE – OG) = GE × 2OC

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