ENGR 12 Chapter 1 Circuit Variables

1. "There are, it seems, two muses: the Muse of Inspiration, who gives us inarticulate visions and desires, and the Muse of Realization, who returns again and again to say "It is yet more difficult than you thought." This is the muse of form. It may be then that form serves us best when it works as an obstruction, to baffle us and deflect our intended course. "It may be that when we no longer know what to do, we have come to our real work and when we no longer know which way to go, we have begun our real journey. The mind that is not baffled is not employed. The impeded stream is the one that sings." — Wendell Berry

2. ENGR 12 Chapter 1 Circuit Variables • This Week: • Overview of EE • SI Units • What is Circuit Analysis? • Circuit Variables (Q,V, I, P, W) • Basic Circuit Element • Voltage and Current Sources

3. Overview of EE • Communication Systems • Control Systems • Digital Electronics • Electromagnetics

4. SI Units • Circuit analysis relys on a system of units and variables • SI system prefixes: 10^3 – kilo, 10^-9 nano, etc • unit analysis

5. CLEO Example Problem 4 • Beginning in Beijing, China, you need to travel about 11,000 kilometers to reach New York City. Fiber optic signals traveling between these two cities move at close to the speed of light (3x108 meters per second). The eye blink duration of a human is approximately 300 milliseconds. So, is it possible for a communication signal to jump from Beijing to New York in the "blink of an eye?"

7. What is Circuit Analysis? • Solution of circuit unknowns • given a circuit and sources applied to it • Problem solving method – how to navigate unfamiliar territory • draw circuit • label unknowns • apply known laws • simplify • if you get stuck, backtrack, try a different approach • TIP #1: keep a positive attitude • TIP #2: after arriving at an answer, • assume you made a mistake

8. Charge, Voltage and Current variables • Q = Charge: fundamental unit related to attraction of subatomic particles • 1 electron has 1.6x10^-19 Coulombs of charge • 1 Coulomb is 6.25x10^18 charges (electrons or protons)

9. V = Voltage: “energy created by separation of charge” • OR energy each charge gets from passing thru a voltage source • OR energy each charge loses when passing thru a resistor • V = dw/dq (units: Joules/Coulomb = Volt)

10. I = Current: the amount of charge flowing by per unit time • I = dq/dt (units: C/sec = Amp)

11. the SIGNS of these variables are EVERYTHING!!! (and will need constant questioning) • by convention, I represents the flow of POSITIVE charge • the + for V indicates the higher energy end for positive charges • (more later)

14. Ideal Basic Circuit Element • (Passive Sign Convention) • solves the sign confusion problem – MEMORIZE • Ideal – we are ignoring physical limits, nonlinearities • Basic – cannot be subdivided • Element – component (like voltage source, resistor, capacitor) • notice, current arrow flows into positive terminal : PSC • every element imposes some function i = f(v), • an ideal mathematical relation between current and voltage

15. Power (P) and Energy (W) • Power is defined as the change of energy over time: • P = Power = dw/dt which can be expanded into • P = dw/dt = ( dw/dq) * (dq/dt) = V * I • ( units: Volt*Amp = Watt) • W = Energy = integral ( p dt) • (units: Watt*second = Joule = Newton-meter)

16. Energy is conserved! • In every circuit, some components will absorb, others release, power • total power = 0 in every circuit we analyze • (otherwise the circuit would explode or freeze) • How to determine which components absorb/release power? • PASSIVE SIGN CONVENTION

17. Passive Sign Convention • is when circuit element has i drawn flowing into + side of v, • then we use P = I V for power • if P > 0 the device ABSORBS power • if P < 0 the device RELEASES or DELIVERS power into the circuit • BUT, if the circuit element has i flowing OUT of + side of v, • this is called ACTIVE SIGN CONVENTION • and we use P = - I V instead • same rule applies for ABSORB ( P>0) or DELIVER ( P < 0)

18. CLEO Example Problem 1 • (a) Suppose that a 12-volt automobile battery with 100 amp-hour capacity is fully charged. How much energy (in joules) is stored in the battery?

19. CLEO Problem 2 • For each device, state whether Passive Sign Convention (PSC) or Active Sign Convention (ASC) is used for the defined current and voltage. Then determine whether the device is absorbing or delivering power. Then For labeled currents, draw an arrow to show the direction of positive current. For labeled voltages, circle the node that is at the highest potential.

20. active or passive? • Energy: absorbing or delivering? show pos current show higher V

21. Chapter 2.1 Voltage and Current Sources • Circuit elements are either: • passive – dissipate energy (resistors, light bulbs, rail guns...) • active – provide energy (voltage and current sources) • SOMETIMES a V or I source will dissipate energy! • depending on circuit

22. Voltage source: • a constant pressure pump • maintains steady voltage no matter what the current flow through it • Symbol: • V-I characteristic: (for example, a 9V source)

23. Current source: • a constant flow pump • maintains current flow no matter what the voltage change across it • Symbol (dual or complement of voltage source): • V-I characteristic (for example, a 2A source)

24. VOLTAGE Source Examples • Problem 1 For each voltage source, draw a voltage label (polarity indicators and value) with the positive indicator at the top or to the right that is equivalent to the indicated voltage.

25. Problem 2 Which of the following circuit connections are invalid?

26. CURRENT Source Examples • Problem 1 For each current source, draw a current label (arrow and value) pointing up or to the right that is equivalent to the indicated current.

27. Problem 2 Which of the following circuit connections are invalid?