EE101 Lecture 4 Updated Electronics engineering

electrical and electronics engineering ac current and components

1. EE101, Lecture 4: Alternating Current and Components Assoc. Prof. Sema Dumanlı Oktar

2. Outline AC Fundamentals Capacitors and Inductors RC Circuits Transformers

3. Re: Direct and Alternative Current DC: Flow of electric charge that occurs in one direction Typically produced by batteries and direct current generator Not economically feasible to transmit because of high voltages needed for long-distance transmission AC: Alternating currents flow back and forth. AC is preferred over DC due to their ease of generation and distribution.

4. Alternating Currents DC AC

5. AC Voltages If we pass an alternating current through a resistor, we can observe across the resistor an AC voltage whose instantaneous value obeys Ohm’s law. This voltage can be written as Vp is the peak value, w is the angular frequency (rad/s), and t is time.

6. AC Voltages Note that f is the frequency in Hz. What about the power?

7. AC Voltages

8. AC Voltages Let us solve for the power

9. Capacitors If we align two conductive plates parallel to each other, separate them with an insulator, we have formed a capacitor. Capacitors store charge. The variable C is used to denote capacitance and the unit is Farads.

10. Capacitors

11. Capacitance Using the definition of current For a parallel plate capacitor, is the dielectric constant of free air and is 8.85 X 10-12 F/m.  

12. Capacitance

13. Real Capacitors

14. Capacitance is the relative dielectric constant   Material Relative Dielectric Constant Dielectric Strength (kV/cm) Vacuum 1.00000 ∞ Air 1.00054 8 Paper 3.5 140 Polystyrene 2.6 250 Teflon 2.1 600 Titanium Dioxide 100 60

15. Capacitance The overall power dissipation over time is zero. Capacitors do not dissipate power, they store energy when charging and return it to the circuit when discharging. The energy stored in a capacitor is given by

16. Capacitor-Water Analogy “Charging a capacitor is analogous to filling up a glass with water:” A. Sheikholeslami , "A Capacitor Analogy, Part 1 [Circuit Intuitions]," in IEEE Solid-State Circuits Magazine, vol. 8, no. 3, pp. 7-91, Summer 2016.   http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7559992&isnumber=7559939

17. Capacitor-Water Analogy “The water dropped initially into the glass wastes all of its potential energy. As the water height increases, the newly added water keeps more of its potential energy in the glass and wastes less.” A. Sheikholeslami , "A Capacitor Analogy, Part 1 [Circuit Intuitions]," in IEEE Solid-State Circuits Magazine, vol. 8, no. 3, pp. 7-91, Summer 2016.   http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7559992&isnumber=7559939

18. RC Circuits Imagine the circuit below with the capacitor charged to V .

19. RC Circuits What will the voltage across the capacitor look like? It will start from V . It will decrease until all the charge is dissipated and will drop to 0 V. As the current is flowing, an opposite voltage will appear across the resistor, slowing down the discharge.

20. RC Circuits We can write the following equations: The voltage is a function whose derivative is similar to itself. What can this function be? An exponential!!!

21. RC Circuits Thus, V(t) turns out to be V is the initial voltage, whereas is called the time constant and is given by =RC. C determines how much charge is stored,and R determines how fast it is dissipated. Their product determines the rate of decay.  

22. RC Circuits

23. RC Circuits This function is called the exponential decay. It is very common in many natural processes: Radioactive decay Newton’s law of cooling Chemical reaction rates depending on concentration of reactant. …

24. RC Circuits Now, let us take the following circuit

25. RC Circuits What does the voltage across the capacitor look like? We expect the capacitor to charge to the value of the voltage source. We expect that it charges fast in the beginning, slowing down as the capacitor voltage increases.

26. RC Circuits We can write the following equations:

27. RC Circuits

28. RC Circuits Universal voltage and current curves for RC circuit

29. RC Circuits What if the input were a pulse? The capacitor would repeatedly charge and discharge.

30. RC Circuits

31. Inductance When an electric current passes through an inductor, it creates a magnetic field. Energy is stored in space around the inductor as magnetic field builds up. This opposes any change in current. It is like momentum or inertia. In our water model, it is like a heavy paddle wheel placed in the current.

32. Inductance We can write the following equation for inductance:

33. Inductance

34. Transformers When two or more inductors share a common magnetic core, the resulting device is a transformer. When an AC voltage is applied to one of the windings of the transformer, it will create a magnetic field proportional to the number of turns. This magnetic field will be coupled to the next winding, creating an AC voltage depending on its number of turns.

35. Transformers Therefore,

36. Transformers Since an ideal transformer cannot create or dissipate power,

37. Transformers

38. Electrical Quantites Quantity Variable Unit Unit Symbol Typical Values Defining Relations Important Equations Charge Q Coulomb C 10 -18 – 1 Mag of 6.24X10 -18 charges I = dq/dt Current I Ampere A 10 -6 – 10 3 1A = 1C/s KCL Voltage V Volt V 10 -6 – 10 6 1V=1N-m/C KVL Power P Watt W 10 -6 – 10 6 1W = 1J/s P = IV Energy U Joule J 10 -15 – 10 12 1J = 1N-m U = QV Force F Newton N 1N=1kg-m/s 2 Time t Second s Resistance R Ohm W 1 – 10 7 V = IR Capacitance C Farad F 10 -15 – 10 Q = CV Inductance L Henry H 10 -6 – 1 V = L di/dt

39. Next Lecture Introduction to Semiconductors Rules and Regulations