Electrical Circuits and Engineering Economics

1. Electrical Circuits and Engineering Economics

2. Electrical Circuits • Interconnection of electrical components for the purpose of either generating and distributing electrical power; converting electrical power to some other useful form such as light, heat, or mechanical torque; or processing information contained in an electrical form (electrical signals)

3. Classification • Direct Current circuits • DC • Currents and voltages do not vary with time • Alternating Current circuits • AC • Currents and voltages vary sinusoidally with time • Steady state - when current/voltage time is purely constant • Transient circuit - When a switch is thrown that turns a source on or off

4. Quantities Used in Electrical Circuits

5. Circuit Components • Resistors - Absorb energy and have a resistance value R measured in ohms • I=V/R OR V=IR • AMPERES=VOLTS/OHMS • Inductors - Store energy and have an inductance value L measured in henries • V=L(dl/dt) • VOLT=(AMPERES•HENRIES)/SECONDS • Capacitors - Store energy and have a capacitance value C measured in farads • I=C(dV/dt) • VOLT=(AMPERES•HENRIES)/SECONDS

6. Sources of Electrical Energy • Independent of current and/or voltage values elsewhere in the circuit, or they can be dependent upon them • Page 443 (Figure 18.1) of the text shows both ideal and linear models of current and voltage sources

7. Kirchhoff’s Voltage Law (KVL) Sum of voltage rises or drops around any closed path in an electrical circuit must be zero ∑VDROPS = 0 ∑VRISES = 0 (around closed path) Kirchhoff’s Current Law (KCL) Flow of charges either into (positive) or out of (negative) any node in a circuit must add zero ∑IIN = 0 ∑IOUT = 0 (at node) Kirchhoff’s Laws (Conservation of Energy)

8. Ohm’s Law • Statement of relationship between voltage across an electrical component and the current through the component • DC Circuits - resistors • V = IR OR I = V/R • AC Circuits • Resistors, capacitors, and inductors stated in terms of component impedance Z • V = IZ OR I = V/Z

9. Reference Voltage Polarity and Current Direction • Arrow placed next to circuit component to show current direction • Polarity marks can be defined • Current always flows from positive (+) to negative (-) marks • Positive current value • Current flows in reference direction • Loss of energy or reduction in voltage from + to - • Negative current value • Current flows opposite reference direction • Gain of energy when moving through circuit from + to -

10. Voltage Drops Experienced when moving through the circuit from the plus (+) polarity to the minus (-) polarity mark Voltage Rises Experienced when moving through the circuit from the minus (-) polarity to the plus (+) polarity mark Reference Voltage Polarity and Current Direction

11. Circuit Equations • Current is assumed to have a positive value in reference direction and voltage is assumed to have a positive value as indicated by the polarity marks • For KVL circuit equation (Figure 18.2) • Move around a closed circuit path in the circuit and sum all the voltage rises and drops • For ∑VRISES=0 • VS - IR1 - IR2 - IR3 = 0 • For ∑VDROPS=0 • -Vs + IR1 + IR2 + IR3 = 0

12. Circuit Equations Using Branch Currents • Figure 18.3 • Unknown current with a reference direction is at each branch • Write two KVL equations, one around each mesh • - VS + I1R1 + I3R2 + I1R3 = 0 • - I3R2 + I2R4 +I2R5 + I2R6 = 0 • Write one KCL equation at circuit node a • I1 - I2 - I3 = 0

13. Circuit Equations Using Branch Currents • Use three equations to solve for I1, I2, and I3 • Current I1 is: |VS 0 R2| |0 R4 + R5 + R6 -R2| |0 -1 -1| I1=______________________________________________ |R1 + R3 0 R2| | 0 R4 + R5 + R6 -R2| | 1 -1 -1|

14. Circuit Equations UsingMesh Currents • Simplification in writing the circuit equations occurs using mesh currents • I3 = I1 - I2 • Using Figure 18.3 • Current through R1 and R3 is I1 • Current through R4, R5, and R6 is I2 • Current through R2 is I1 - I2

15. Circuit Equations UsingMesh Currents • Write two KVL equations • - VS + I1(R1 + R2 + R3) - I2R2 = 0 • -I1R2 + I2(R2 + R4 + R5 + R6) = 0 • Two equations can be solved for I1 and I2 • Current I1 is equivalent to that of before |VS -R2 | |0 R2 + R4 + R5 +R6| I=____________________________________________________ |R1 + R2 + R3 -R2 | | -R2 R2 + R4 + R5 + R6|

16. Circuit Simplification • Possible to simplify a circuit by combining components of same kind that are grouped together in the circuit • Formulas for combining R’s, L’s and C’s to singles are found using Kirchhoff’s laws • Figure 18.5 with two inductors

17. Circuit Components in Series and Parallel

18. DC Circuits • Only crucial components are resistors • Inductor • Appears as zero resistance connection • Short circuit • Capacitor • Appears as infinite resistance • Open circuit

19. DC Circuit Components

20. Engineering Economics • Best design requires the engineer to anticipate the good and bad outcomes • Outcomes evaluated in dollars • Good is defined as positive monetary value

21. Value and Interest • Value is not synonymous with amount • Value of an amount depends on when the amount is received and spent • Interest • Difference between anticipated amount and its current value • Frequently expressed as a time rate

22. Interest Example • What amount must be paid in two years to settle a current debt of $1,000 if the interest rate is 6%? • Value after 1 year = • 1000 + 1000 * 0.06 • 1000(1 + 0.06) • $1060 • Value after 2 years = • 1060 + 1060 * 0.06 • 1000(1 + 0.06)2 • $1124 • $1124 must be paid in two years to settle the debt

23. Cash Flow Diagrams • An aid to analysis and communication • Horizontal • Time axis • Vertical • Dollar amounts • Draw a cash flow diagram for every engineering economy problem that involves amounts at different times

24. Cash Flow PatternsFigure 18.7 • P-pattern • Single amount P occurring at the beginning of n years • P frequently represents “present” amounts • F-pattern • Single amount F occurring at the end of n years • F frequently represents “future” amounts • A-pattern • Equal amounts A occurring at the ends of each n years • A frequently used to represent “annual” amounts • G-pattern • End-of-year amounts increasing by an equal annual gradient G

25. Equivalence of Cash Flow Patterns • Two cash flow patterns said to be equivalent if they have the same value • Most computational effort directed at finding cash flow pattern equivalent to a combination of other patterns • i = interest • n = number of periods

26. Formulas for Interest Factors

27. Formulas for Interest Factors

28. Formulas for Interest Factors