electric circuit analysis's presentation

ECA chapter 1 descriptions

1. ELECTRIC CIRCUIT ANALYSIS - I Department of Electrical Engineering, COMSATS Institute of Information Technology, Islamabad

2. Topics: CHARGE AND CURRENT VOLTAGE Power and Energy Circuit Elements Resistance Conductance Series Resistors and Voltage Division Parallel Resistors and Current Division The equivalent conductance in series Current divider: Wye-Delta Transformations Nodal Analysis Mesh Analysis Superposition Source Transformation Thevenin’s Theorem Norton’s Theorem Capacitors: Inductor: The Source Free RC Circuit: The Source Free RL Circuit: Step Response of RC Circuit: Step Response of RL Circuit: Source Free Series RLC Circuit: Step Response Of Series RLC Circuit: Source Free Parallel RLC Circuit: Step Response of Parallel RLC Circuit :

3. CHARGE AND CURRENT C harge: is the subatomic property of all the materials in nature measured in coulombs (C) C urrent : is the direct flow of electric charge in an electric circuit measured in amperes (A). The relationship between current I and quantity of charge Q: I = Q ÷ t Q = It t = Q ÷ I Where current is measured in amperes(A), 1 ampere = 1 coulomb/second TYPES OF CURRENT: Direct current: A direct current (dc) is a current that remains constant with time. If the current does not change with time, but remains constant, we call it a direct current (dc). Alternative current: An alternating current (ac) is a current that varies sinusoidally with time.

4. Example:

5. VOLTAGE Voltage (or potential difference) is the energy required to move a unit charge through an element, measured in volts (V). Unit of voltage: 1 volt = 1 joule/coulomb = 1 newton-meter/coulomb Example:

6. Power and Energy P ower is the amount of energy transferred or converted per unit time. The unit of power is the watt, equal to one joule per second. Power is a scalar quantity. The formula is  P = E/t , where P means power, E means energy, and t means time in seconds. This formula states that power is the consumption of energy per unit of time. Energy is  the ability to do work The SI unit of energy is same as that of work, which is  joule (J) .

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8. Circuit Elements: IDEAL INDEPENDENT SOURCE: An ideal independent source is an active element that provides a specified voltage or current that is completely independent of other circuit elements. Independent Voltage Sources: Independent Current Source: An ideal dependent (or controlled) source is an active element in which the source quantity is controlled by another voltage or current . IDEAL DEPENDENT SOURCE Types of dependent sources 1. voltage-controlled voltage source (VCVS). 2. current-controlled voltage source (CCVS). 3. voltage-controlled current source (VCCS). 4. current-controlled current source (CCCS).

9. Resistance   A measure of the opposition to current flow in an electrical circuit . Resistance is measured in ohms, symbolized by the Greek letter omega (Ω). Ohm’s law  A formula used to calculate the relationship between voltage, current and resistance in an electrical circuit. The formula for Ohm's law is V=IR. The ohm (symbol: Ω) is the unit of electrical resistance in the International System of Units (SI). Linear resistor: A resistor that obeys Ohm’s law is known as a linear resistor Non-Linear resistor: A nonlinear resistor does not obey Ohm’s law.

10. Conductance Conductance is the ability of an element to conduct electric current it is measured in siemens (S). A useful quantity in circuit analysis is the reciprocal of resistance R, known as conductance and denoted by G: Conductance is the inverse of resistance: G = 1/R. Conductance is measured in units of Siemens or mhos.

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12. Series Resistors and Voltage Division: The equivalent resistance is  equal to the algebraic sum of the individual resistances .  Req=R1+R2+R3+R4+R5 Or Req=R1+R2+R3+.........+Rn (for n number of resistors) For n Resistance

13. Parallel Resistors and Current Division The equivalent resistance can be computed  using the reciprocal of the resistance For n number of Resistors

14. The equivalent conductance in series

15. Current divider: Given the total current i entering node a in Fig. 2.31, how do we obtain current and We know that the equivalent resistor has the same voltage, Example:

16. Wye-Delta Transformations: Dalta and Pi

17. Example:

18. Nodal Analysis The number of nonreference nodes is equal to the number of independent equations that we will derive. At node 1, applying KCL gives

19. Example:

20. Mesh Analysis A mesh is a loop which does not contain any other loops within it.

21. Examples :

22. Superposition The superposition principle states that the voltage across (or current through) an element in a linear circuit is the algebraic sum of the voltages across (or currents through) that element due to each independent source acting alone Examples :

23. Source Transformation: Examples :

24. Thevenin’s Theorem:

25. Examples :

26. Norton’s Theorem:

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28. Capacitors: Series and Parallel Capacitors:

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30. Examples :

31. Examples :

32. Inductor: Series and Parallel Inductors:

33. Examples :

34. The Source Free RC Circuit: Time constant: Examples :

35. The Source Free RL Circuit:

36. Examples :

37. Step Response of RC Circuit: Examples :

38. Step Response of RL Circuit:

39. Examples :

40. Source Free Series RLC Circuit:

41. Examples :

42. Step Response Of Series RLC Circuit:

43. Examples :

44. Source Free Parallel RLC Circuit:

45. Examples :

46. Step Response of Parallel RLC Circuit:

47. Examples :