Lecture 5

inductive load

• Here, I2 lags E2 (actually V2) by 2.

• Current I2’ is in anti-

phase with I2 and equal to it in magnitude.

• I1 is the vector sum of I2’

and I0 and lags behind V1 by 1.

Transformer with Winding Resistance but No Magnetic Leakage

• An ideal transformer was supposed to possess no resistance, but in an actual transformer, there is always present some resistance of the primary and secondary windings

• Due to this resistance, there is some voltage drop in the two windings.

• The result is that:

1. The secondary terminal voltage V2 is vectorially less than the secondary induced emf E2 by an amount I2R2 where R2 is the resistance of the secondary winding. Hence V2 is equal to the vector difference of E2 and resistive voltage drop I2R2.

• V2=E2-I2R2 vector difference

2. Similarly, primary induced emf E1 is equal to the vector difference of V1 and I1R1 where R1 is the resistance of the primary winding.

• E1=V1-I1R1 vector difference

Magnetic Leakage

• In the case of ideal transformer it has been assumed that all the flux linked with primary winding also links the secondary winding.

• But in practice, all flux linked with primary does not link the secondary but part of it i.e. completes its magnetic circuit by passing through air rather than around the core

• This flux is known as primary leakage flux and is proportional to the primary ampere-turns alone because the secondary turns do not link the magnetic circuit of L1.

• This flux L1, which is in time phase with I1, induces an emf eL1 in primary but none in secondary.

• Similarly, secondary part sets up leakage flux L2 which linked with secondary winding alone (and not with primary turns).

• This flux L2, which is in time phase with I2, produces a self-induced emf eL2 in secondary (but none in primary).

• At no-load and light loads, the primary and secondary ampere-turns are small hence leakage fluxes are negligible.

• But when load is increased, both primary and secondary windings carry huge currents.

• The effect of induced emf due to the leakage flux is equivalent to a small inductive coil in series with each winding such that voltage drop in each series coil is equal to that produced by leakage flux where X1=eL1/I1 and X2=eL2/I2.

• The terms X1 and X2 are known as primary and secondary leakage reactances.

1. The leakage flux links one or the other winding but not both, hence it in no way contributes to the transfer of energy from the primary to secondary winding.

2. The primary voltage V1 will have to supply reactive drop I1X1 in addition to I1R1. Similarly, E2 will have to supply reactive drop I2X2 in addition to I2R2.

Transformer with Resistance and Leakage Reactance

In Fig. 32.28 as shown the primary and secondary windings of a transformer with reactances taken out of the windings.

The primary impedance and voltage equations are given by

1

11tan21

21111 R

XXRjXRZ 1111

)11

(11

IZEIEV jXR

Similarly, secondary impedance and voltage equations are given by

2

21tan22

22222 R

XXRjXRZ

2222)22

(22

IZVIVE jXR

Transformer on resistive load

• vectors for resistive drops are drawn parallel to current vectors whereas reactive drops are perpendicular to the current vectors.

• In the case of resistive load, the secondary voltage V2 and I2 are in phase.