3. Lecture 03 Av 335 - Transformer and Motional EMF.pptx

lecture

1. AV-335 Transmission lines and waveguides Dr. Hidayat Ullah Lecture No 3 Transformer and Motional EMF Book(s) consulted: Elements of Electromagnetics, Matthew, N. O. Sakidu Chapter 9, Section(s) 9.3

2. TRANSFORMER AND MOTIONAL EMFs Having considered the connection between emf and electric field, we may examine how Faraday’s law links electric and magnetic fields. For a circuit with a single turn (N = 1) In terms of E and B, where y has been replaced by and S is the surface area of the circuit bounded by the closed path L. It is clear from eq. (9.5) that in a time-varying situation, both electric and magnetic fields are present and are interrelated. (9.5)

3. TRANSFORMER AND MOTIONAL EMFs The variation of flux with time as in eq. (9.1) or eq. (9.5) may be caused in three ways: By having a stationary loop in a time-varying B field By having a time-varying loop area in a static B field By having a time-varying loop area in a time-varying B field Each of these will be considered separately. (9.1) (9.5)

4. A. Stationary Loop in Time-Varying B Field (Transformer emf) In Figure 9.3 a stationary conducting loop is in a time-varying magnetic B field. Equation (9.5) becomes This emf induced by the time-varying current (producing the time-varying B field) in a stationary loop is often referred to as transformer emf in power analysis, since it is due to transformer action. FIGURE 9.3 Induced emf due to a stationary loop in a time varying B field

5. A. Stationary Loop in Time-Varying B Field (Transformer emf) Applying Stokes theorem to middle term This is one of the Maxwell’s equations for time-varying fields. It shows that the time varying E field is not conservative The Stoke’s theorem states that “the surface integral of the curl of a function over a surface bounded by a closed surface is equal to the line integral of the particular vector function around that surface.”

6. B. Moving Loop in Static B Field (Motional emf) When a conducting loop is moving in a static B field, an emf is induced in the loop. We recall from eq. (8.2) that the force on a charge moving with uniform velocity u in a magnetic field B is We define the motional electric field E m as If we consider a conducting loop, moving with uniform velocity u as consisting of a large number of free electrons, the emf induced in the loop is This type of emf is called motional emf or flux-cutting emf because it is due to motional action.

7. B. Moving Loop in Static B Field (Motional emf) Motional emf is kind of emf found in electrical machines such as motors, generators, and alternators. Figure 9.4 illustrates a two-pole dc machine with one armature coil and a two bar commutator. Although the analysis of the dc machine is beyond the scope of this text, we can see that voltage is generated as the coil rotates within the magnetic field.

8. B. Moving Loop in Static B Field (Motional emf) Another example is depicted in Figure 9.5, where a rod is moving between a pair of rails. In this example, B and u are perpendicular, so F m becomes

9. B. Moving Loop in Static B Field (Motional emf) By applying Stokes’s theorem

10. Application of Faraday’s Law: Magnetic Induction AC Generator Water turns wheel  rotates armature  changes flux  induces emf  drives current

11. Single-Phase Generator

12. Transformers This is a step-up transformer – the emf in the secondary coil is larger than the emf in the primary. AC current in primary coil creates an AC B-field in the soft iron core which then induces an emf in the secondary coil.

13. B. Moving Loop in Static B Field (Motional emf) The following points should be noted while applying the equation. The integral in eq. (9.10) is zero along the portion of the loop where u = 0 . Thus dl is taken along the portion of the loop that is cutting the field where u has nonzero value. The direction of the induced current is the same as that of E m or u x B . The limits of the integral in eq. (9.10) are selected in the direction opposite to the induced current, thereby satisfying Lenz’s law. In Figure 9.5, for example, the integration over L is along -ay, whereas induced current flows in the rod along ay. (9.10)

14. C. Moving Loop in Time-Varying Field In the general case, a moving conducting loop is in a time-varying magnetic field. Both transformer emf and motional emf are present. Thus, the total emf is

15. EMFs Transformer EMF: a stationary loop in a time-varying B field Motional EMF: a time-varying loop area in a static B field Moving Loop in time-varying Field: a time-varying loop area in a time-varying B field