Electrical and electronics eng Ac_networks.pptx

Ac network theory

1. Ac networks GROUP 4A Rumbidzai magwaza f r184636v Kudzanai chizeya r183169a Tawanda chivasa r181239r Tapiwa takura r1710989g Tatenda mashava r1711512q Humphrey zivanai r183207x Tawanda mhiripiri r141980v Ephraim dube r183340b Tanatswa mujeni r185706x Jethro durwayi r184390j

2. Energy-Storage(Dynamic) circuit elements Two distinct mechanisms that lead to the storage of energy in a electromagnetic field are namely capacitance and induction Capacitance - the ability of a system to store an electric charge.The ratio of the change in an electric charge in a system to the corresponding change in its electric potential.

3. Energy-Storage(Dynamic) circuit elements INDUCTION -the process by which a body having electric or magnetic properties produces magnetism, an electric charge, or an electromotive force in a neighboring body without contact. Inductance is the name given to the property of a circuit whereby there is an e.m.f. induced into the circuit by the change of flux linkages produced by a current change.

4. The Ideal Capacitor Capacitor -is a device that can store energy in the form of a charge separation when appropriately polarized by an electric field (i.e., a voltage). A typical capacitor is made of two parallel conducting plates separated by an insulator. Capacitors are used extensively in electrical and electronic circuits. For example, capacitors are used to smooth rectified a.c . outputs, they are used in telecommunication equipment – such as radio receivers – for tuning to the required frequency, they are used in time delay circuits, in electrical filters, in oscillator circuits, and in magnetic resonance imaging (MRI) in medical body scanners, to name but a few practical applications.

5. Typical capacitor

6. capacitor two parallel conducting plates of crosssectional area A, separated by air (or another dielectric1 material, such as mica or Teflon). The presence of an insulating material between the conducting plates does not allow for the flow of DC current; thus, a capacitor acts as an open circuit in the presence of DC currents In the presence of an voltage source , electrons travel from the voltage source to the capacitor and charge one of the plates with excess electrons. The electric field from these electrons repel electrons from the opposing plate and equal but positive charge develops on that plate. The repelled electrons from the positive plate travel to the source. As such, the total charge stored in a capacitor is zero but consists of two separated amount of equal charges with different polarity. In this way, a capacitor can store energy in the form of electric field between the two plates, which is proportional to the voltage between the two plates.

7. Ideal capacitors where Q = CV C is called the capacitance of the element and is a measure of the ability of the device to accumulate, or store, charge. It is the constant of proportionality N.B that the total charge stored in a capacitor is zero, the charge mentioned here is the charge on one of the plates (the plate marked with + of voltage v). The unit of capacitance is the coulomb/volt and is called the farad (F). The farad is an unpractically large unit; therefore it is common to use microfarads (1 µF = 10−6 F) or picofarads (1 pF = 10−12 F).

8. Ideal capacitor Where Capacitance C = unit Farad (F) As the number of electrons flowing into the negative plate is equal to the number of electrons flowing out of the positive plate, the current flowing into one plate of capacitor is exactly equal to the current flowing out of the other plate. That follows to q = Cv but voltage applied to the capacitor plates changes in time, so will the charge that is internally stored by the capacitor: q(t) = Cv (t) (1)  

9. Ideal capacitor The change with time in the stored charge is analogous to a current. Given by i (t) = (2) that electric current corresponds to the time rate of change of charge Differentiating equation (1) gives the relationship between the voltage and current in a capacitor  

10. Ideal capacitor i (t) = C (3) That defines the circuit law of capacitors If the differential equation that defines the i -v relationship for a capacitor is integrated, the following relationship for the voltage across a capacitor is obtained : (4) Equation 4 indicates that the capacitor voltage depends on the past current through the capacitor, up until the present time, t. Of course, one does not usually have precise information regarding the flow of capacitor current for all past time, and so it is useful to define the initial voltage (or initial condition) for the capacitor according to the following, where t0 is an arbitrary initial time::  

11. Ideal capacitor (5) Capacitor voltage can now be given by (6) The significance of the initial voltage, V , is simply that at time t some charge is stored in the capacitor, giving rise to a voltage, vC (t ), according to the relationship Q = CV . Knowledge of this initial condition is sufficient to account for the entire past history of the capacitor current.

12. Ideal capacitors Capacitors connected in series and parallel can be combined to yield a single equivalent capacitance Capacitors in parallel add. Capacitors in series combine according to the same rules used for resistors connected in parallel.

13. Ideal capacitors Capacitors connected in series and parallel can be combined to yield a single equivalent capacitance Capacitors in parallel add. Capacitors in series combine according to the same rules used for resistors connected in parallel.

14. Energy stored in capacitors The instantaneous power in a circuit element is equal to the product of voltage and current:

15. Energy stored in capacitors Formula for energy stored in a capacitor FORMULA

16. Energy stored in capacitors An example

17. Problem on energy stored in a capacitor (a) Determine the energy stored in a 3 μF capacitor when charged to 400V (b) Find also the average power developed if this energy is dissipated in a time of 10 μs .

18. Answer

19. The Ideal inductor The ideal inductor is an element that has the ability to store energy in a magnetic field. Inductors are typically made by winding a coil of wire around a core, which can be an insulator or a ferromagnetic material As current flows through the wire, a magnetic field is produced. When a conductor is moved across a magnetic field so as to cut through the lines of force (or flux), an electromotive force ( e.m.f. ) is produced in the conductor. If the conductor forms part of a closed circuit then the e.m.f. produced causes an electric current to flow round the circuit. Hence an e.m.f. (and thus current) is ‘induced’ in the conductor as a result of its movement across the magnetic field.

20. The Ideal inductor (a) shows a coil of wire connected to a centre -zero galvanometer, which is a sensitive ammeter with the zero-current position in the centre of the scale. (a) When the magnet is moved at constant speed towards the coil (Fig(a)), a deflection is noted on the galvanometer showing that a current has been produced in the coil.

21. The Ideal inductor (b) When the magnet is moved at the same speed as in (a) but away from the coil the same deflection is noted but is in the opposite direction (see Fig. (b)) (c) When the magnet is held stationary, even within the coil, no deflection is recorded. (d) When the coil is moved at the same speed as in (a) and the magnet held stationary the same galvanometer deflection is noted. (e) When the relative speed is, say, doubled, the galvanometer deflection is doubled.

22. The Ideal inductor (f) When a stronger magnet is used, a greater galvanometer deflection is noted. (g) When the number of turns of wire of the coil is increased, a greater galvanometer deflection is noted.

23. The Ideal inductor Figure (c) shows the magnetic field associated with the magnet. As the magnet is moved towards the coil, the magnetic flux of the magnet moves across,or cuts, the coil. It is the relative movement of the magnetic flux and the coil that causes an e.m.f. and thus current, to be induced in the coil. This effect isknown as electromagnetic induction.

24. Ideal inductor In an ideal inductor, the resistance of the wire is zero, so that a constant current through the inductor will flow freely without causing a voltage drop. In other words, the ideal inductor acts as a short circuit in the presence of DC currents. If a time-varying voltage is established across the inductor, a corresponding current will result, according to the following relationship: where L is called the inductance of the coil and is measured in henrys (H), where : 1 H = 1 V-s/A Henrys are reasonable units for practical inductors; millihenrys ( mH ) and microhenrys (µH) are also used.

25. Ideal inductor The behavior of an ideal inductor is defined, with the expression relating capacitor current and voltage: Inductors in series add. Inductors in parallel combine according to the same rules used for resistors connected in parallel.

26. Inductors in series and parallel

27. Energy Storage in Inductors An inductor possesses an ability to store energy. The energy stored, W, in the magnetic field of an inductors given by:

28. Energy Storage in Inductors Question An 8 H inductor has a current of 3A flowing through it. How much energy is stored in the magnetic field of the inductor? answer

29. Example