LAB_19 - Transformers - Lab 19 Transformers Genius is one...

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Lab 19 207 Transformers Summary A transformer is a coupled electrical circuit, whose distinguishing feature is that the coupling between the two conducting loops is due to magnetic flux rather than electrical current. Transformers are used in power transmission, radio, television, computers, oscilloscopes and power supplies. Educational Objectives After performing this experiment, students should be able to: 1. Measure transformer action. 2. Build a step-down transformer. 3. Measure the mutual inductance of two coils. Background Information A transformer is created when two inductors are arranged so that some of the flux of one is linked with the other. This flux linkage can be obtained by building the inductors on a common core. The core can simply be a hollow structure (air core transformer), or it can be a magnetic material such as ferrite. From Faraday’s Law we know that a voltage is induced in a coil which contains a time-varying magnetic flux, regardless of the source of the flux. Let us therefore consider a second coil, having N 2 turns, posi- tioned in the neighborhood of the first coil, having N 1 turns, as shown in Fig 1a. In this case we have formed a simple transformer having two pairs of terminals in which coil 1 is referred to as the primary winding (the one that is driven by a source) and coil 2 as the secondary winding (the one which connects to the load). “Genius is one percent inspiration and ninety-nine percent perspiration.” - Thomas Alva Edison
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Lab 19 208 Case 1: Open-Circuited Secondary To introduce several important inductive quantities, let us begin by examining the open-circuited second- ary case, Fig 1a. When coil 1 is driven by a source, a current I 1 is produced. This current produces a mag- netic flux ϕ 11 . where ϕ 11 is the flux of I 1 that links coil 1 and not coil 2, called the leakage flux, and ϕ 21 is the flux of I 1 that links coil 2 and coil 1, called the mutual flux. Since the secondary is an open circuit, no current flows in coil 2, and the flux linkage λ 2 of coil 2 is: Therefore, the secondary voltage V 2 is given by: In a linear transformer, the flux ϕ 21 is proportional to I 1 . Thus we may write: where M 21 is a mutual inductance in henries (H). In terms of this mutual inductance, the open-circuit sec- ondary becomes: Figure 1a - Open circuited secondary (1) (2) (3) (4) Primary Secondary V 2 (open) N 2 N 1 V 1 ϕ ϕ ϕ 11 1 21 = + L λ ϕ 2 2 21 = N V N d dt 2 2 21 = ϕ N M I 2 21 21 1 ϕ =
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Lab 19 209 Let us now find the primary voltage V 1 . We know that: where λ 1 , the flux linkage of coil 1, is given by: As in the case of a single inductor, the inductance L 1 of the primary winding, sometimes called the self-
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