"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
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
• Overview of EE
– Communication Systems
– Control Systems
– Digital Electronics
– Electromagnetics
• SI Units
– Circuit analysis relys on a system of units and
variables
– SI system prefixes: 10^3 – kilo, 10^-9 nano, etc
– unit analysis
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?"
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
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)
– 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)
– I = Current: the amount of charge flowing by per unit
time
• I = dq/dt (units: C/sec = Amp)
– 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)
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
• 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)
•
• 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
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)
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?
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.
•
• active or
passive?
• Energy:
absorbing or
delivering?
show pos current
show higher V
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
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)
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)
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.
Problem 2 Which of the following
circuit connections are invalid?
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.
•
Problem 2 Which of the following
circuit connections are invalid?