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Linear Circuit Analysis

Linear Circuit Analysis. Chapter # 1: Basic Concepts. Introduction. Electrical circuit and Electromagnetic theory are two fundamental theories for all branches of electrical engineering

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Linear Circuit Analysis

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  1. Linear Circuit Analysis Chapter # 1: Basic Concepts

  2. Introduction • Electrical circuit and Electromagnetic theory are two fundamental theories for all branches of electrical engineering • In electrical engineering, we are often interested in communicating or transferring energy from one point to another • To do this we require an interconnection of electrical devices

  3. Examples of Electric Circuits (1) • An Electric Circuit is a connection of electrical elements

  4. Examples of Electric Circuits (2) • Test text

  5. Basic Concepts - Chapter 1 1.1 Systems of Units. 1.2 Electric Charge. 1.3 Current. 1.4 Voltage. 1.5 Power and Energy. 1.6 Circuit Elements.

  6. 1.1 System of Units (1) As electrical engineers, we deal with measurable quantities Six basic units

  7. 1.1 System of Units (2) The derived units commonly used in electric circuit theory Decimal multiples and submultiples of SI units Unit of Conductance: Siemens or mho

  8. 1.2 Electric Charges • Charge is an electrical property of the atomic particles of which matter consists, measured in coulombs (C). • The charge e on one electron is negative and equal in magnitude to 1.602  10-19 C which is called as electronic charge. • The charges that occur in nature are integral multiples of the electronic charge.

  9. 1.3 Current (1) • Electric current i = dq/dt. The unit of ampere can be derived as 1 A = 1C/s. • A direct current (dc) is a current that remains constant with time. • An alternating current (ac) is a current that varies with time. (alternate or reverse direction).

  10. 1.3 Current (2) • The direction of current flow

  11. 1.3 Current (3) Example 1 A conductor has a constant current of 5 A. How many electrons pass a fixed point on the conductor in one minute?

  12. 1.3 Current (4) Solution Total no. of charges pass in 1 min is given by 5 A = (5 C/s)(60 s/min) = 300 C/min Total no. of electronics pass in 1 min is given

  13. Class Activity (1) • Example 1.2: The total charge entering a terminal is given by q=5t sin4t mC. Calculate the current at t=0.5 sec. Matlab code for creating and plotting the function: >> t=-1:0.01:10; >> q=5.*t.*sin(4*pi*t); plot(t,q); >> xlabel('Time'); ylabel('Amplitude'); grid

  14. Class Activity (2) • Example 1.2: The total charge entering a terminal is given by q=5t sin4t mC. Calculate the current at t=0.5 sec.

  15. Class Activity (3) • Example 1.2: The total charge entering a terminal is given by q=5t sin4t mC. Calculate the current at t=0.5 sec.

  16. 1.4 Voltage (1) • Voltage (or electromotive force (emf) potential difference) is the energy required to move a unit charge through an element, measured in volts (V). • Mathematically, • w is energy in Joules (J) and q is charge in coulomb (C). • Electric voltage, vab, is always across the circuit element or between two points in a circuit. • vab > 0 means the potential of a is higher than potential of b. • vab < 0 means the potential of a is lower than potential of b.

  17. i i + + v v – – 1.5 Power and Energy (1) • Power is the time rate of expending or absorbing energy, measured in watts (W). • Mathematical expression: Passive sign convention p = +vip = –vi absorbing powersupplying power

  18. 1.5 Power and Energy (2) Example: Calculate the power supplied or absorbed in each case:

  19. 1.5 Power and Energy (3) • The law of conservation of energy • Energy is the capacity to do work, measured in joules (J). • Mathematical expression • The electric power utility companies measure energy in watts-hour(Wh), where: • 1Wh=3,600 joules

  20. Class Activity • Example 1.5 : Find the power delivered to an element at t=3 ms if the current entering its positive terminal is

  21. Class Activity • Example 1.5 : Solution

  22. Class Activity • Example: How much energy does a 100-W electric bulb consumes in two hours. How much will it cost if the rate is 15 cents per Kwh.

  23. 1.6 Circuit Elements (1) • An Active Element is capable of generating energy while a Passive Element is not; Generators and batteries are examples of active elements while resistors, capacitors and inductors are passive element. • An ideal Independent Voltage Source is an active element that provides a specified voltage or current that completely independent of other circuit elements. • An ideal Dependent ( or Controlled) source is an active element in which the source quantity is controlled by another voltage or current.

  24. 1.6 Circuit Elements (2) • Both symbols (a) and (b) can be used to represent an independent dc voltage source while (a) is used only for time varying independent voltage source. • Typical Independent Constant Current Source is shown in the figure below. Symbol for Independent voltage source

  25. 1.6 Circuit Elements (3) • Dependent sources are useful in modeling elements such as transistors, operational amplifiers and integrated circuits • Example of current controlled Voltage source is shown in the right hand side of the figure. • The Voltage source depends on the current “i” through the element “C”.

  26. 1.6 Circuit Elements (4) Active Elements Passive Elements • A dependent source is an active element in which the source quantity is controlled by another voltage or current. • They have four different types: Voltage Controlled Voltage Source (VCVS), CCVS, VCCS, CCCS. Keep in minds the signs of dependent sources. Independent sources Dependant sources

  27. 1.6 Circuit Elements (5) Example Obtain the voltage v in the branch shown in the figure for i2= 1A.

  28. 1.6 Circuit Elements (6) • Solution • Voltage v is the sum of the current-independent 10-V source and the current-dependent voltage source vx. • Note that the factor 15 multiplying the control current carries the units Ω. • Therefore, v = 10 + vx = 10 + 15(1) = 25 V

  29. Class Activity • Example 1.7: Calculate the power supplied or absorbed by each element = 1

  30. 1.7 Applications (1) 1.7.1 Old TVs Picture Tube The Electron beam in a TV Picture carries 1015 electrons per second

  31. 1.7 Applications (2) 1.7.2 Electricity Bills

  32. 1.7 Applications: Electricity Bill Example Example: A homeowner consumes 400 kWh in January. Determine the electricity bill for the month using the following residential rate schedule:

  33. 1.8 Problem Solving 1. Carefully Define the problem. 2. Present everything you know about the problem. 3. Establish a set of Alternative solutions and determine the one that promises the greatest likelihood of success. 4. Attempt a problem solution. 5. Evaluate the solution and check for accuracy. 6. Has the problem been solved Satisfactorily? If so, present the solution; if not, then return to step 3 and continue through the process again.

  34. Assignment # 1 • From Chapter 1 of the text book (3rd Edition) • Review Questions: All (without looking at the answers). • Problems: 1.3, 1.6, 1.8, 1.11, 1.15, 1.19 and 1.29 • Comprehensive Problems: 1.13 and 1.37 • Note: Write down all the questions and submit your solution in sequence. Use A4 size plain paper is possible.

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