• Lecture 2: VIP
ECEN 1400 Introduction to Analog and Digital Electronics
Lecture 2
Voltage, current and power
•  Units
•  The hydraulics analogy
–  Voltage (work/charge)
–  Current (charge/time)
–  Common (hydro) circuit devices
•  Current vs. voltage curves
–  Short (wire)
–  Open (air)
–  Switch
–  Voltage source
–  Current source
Robert R. McLeod, University of Colorado
15
• Lecture 2: VIP
ECEN 1400 Introduction to Analog and Digital Electronics
Units – quantification of stuff
•  Stuff: Charge in coulombs [C]
•  Flow of stuff: Current in amps [I]
–  Amp = charge through point per time [C/s]
–  In direction of positive charge flow
•  Work stuff can do: Potential in volts [V]
–  Volt = potential energy per unit charge [J/C]
–  Potential = between two points, just like
gravitational potential energy
•  How quickly can stuff do work?: Power in
watts [W]
– 
– 
– 
– 
We measure these, calculate the others
–  Electron (and proton) charge = 1.6 10-19 C
–  The world is charge neutral to a very high
degree, otherwise would explode
Energy expended per time
Watt = J/s = (J/C)(C/s) = V A
So power = V I
By convention
•  positive power = dissipation (e.g. resistor)
•  negative power = generation (e.g. battery)
Robert R. McLeod, University of Colorado
16
• Lecture 2: VIP
ECEN 1400 Introduction to Analog and Digital Electronics
Application:
Cooking a hotdog – dangerously!
“Suicide cable”
LEDs stuck in hot dog
P [W] = V [V] I [A]
If we draw 25 A of current from a 120 V wall
socket, how much power is this? There is a
small simplification in this equation because
the current is alternating. It’s close enough
for now to consider the current as constant.
= 120[V] 25[A]
= 3[kW]
m[g] = 3[oz]28[g/oz]
What’s the mass of the hotdog?
= 84[g]
t[s] =
=
=
E [J]
P [W]
HOW LONG ‘TIL DINNER?
C p [ g J! K ]m [g]ΔT [! K]
P [W = sJ ]
(4)(84)(75) = 8.4[s]
3000
Robert R. McLeod, University of Colorado
Specific heat of a substance tells you energy
per gram to raise it 1 degree in temperature.
Pretty darn quick.
DON’T do this at home. See name of cable.
http://www.evilmadscientist.com/2007/cooking-hot-dogs-via-electrocution/
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• Lecture 2: VIP
ECEN 1400 Introduction to Analog and Digital Electronics
Voltage:
the
potential
dobetween
worktwo points
potential energy
of some
charge whento
moved
Voltage ≡
quantity
of that charge
unit
of stuff
Hydraulics
Measured by
Electronics
Pressure
N/m2=J/m3
Voltage
V = J/C
pipes
wires
Moves in
Capacity for work
given by
Potential energy is
relative so we often
define a universal
reference.
P1
P2
?
V1
Pressure difference =
ΔP = P1 – P2
Voltage difference =
ΔV = V1 – V2
Sea level
“Ground”
+
ΔP1
“If you walk in a
circle, you’d better
get back to where
you started.”
V2
?
+
ΔP2
ΔV1
ΔV2
-
-
0 = ΔV1 + ΔV2
Finite source
Robert R. McLeod, University of Colorado
18
• Lecture 2: VIP
ECEN 1400 Introduction to Analog and Digital Electronics
Quantity of charge moving through a point
Current ≡
measurement time
Current
Hydraulics
Measured by
Volume flow rate
m3/s
Quantum of
“stuff”
One molecule.
Always + mass
Electronics
Current
C/s
Electron or proton.
Can be – or +.
e = -1.602 10-19 C
Ben Franklin assigned sign to charges and made the more mobile one (electron)
negative. Oops. Don’t worry about it in this class – just think about + charge
carriers going in direction of current. Two wrongs do make a right in this case.
Iout2
Conservation of
“stuff”
Iout2
Iin
Iin
Iout1
Iout1
0= Iin - Iout1 – Iout2
Robert R. McLeod, University of Colorado
19
• Lecture 2: VIP
ECEN 1400 Introduction to Analog and Digital Electronics
Hydraulic circuit components
Electronics
Component
Hydraulics
Analogy
Wire
Pipe.
Resistor
Paddle wheel.
Idealities &
Assumptions
No friction (lossless).
No leak at end or along pipe.
Incompressible fluid.
Perfectly stiff.
Mass = 0.
Friction = dissipation.
Completely elastic.
Mass = 0.
Friction = 0.
Capacitor
Membrane
Inductor
Paddle wheel.
Voltage
source
Current
source
Robert R. McLeod, University of Colorado
Pump
Pump
Perfectly stiff.
Mass = Inertia.
Friction = 0.
Maintain fixed pressure
difference for any flow rate.
Maintain fixed flow rate for
any pressure difference.
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• Lecture 2: VIP
ECEN 1400 Introduction to Analog and Digital Electronics
I/V characteristics of ideal sources
I
V
V
I
By convention:
current enters +
voltage terminal.
I
V
Breakdown
Open circuit
e.g. air
“0 amp source”
Breakdown
Short circuit
e.g. wire
“0 volt source”
+
Provides zero
voltage
independent
of current.
Provides zero
current
independent
of voltage.
I
Switch
Short to open
V
Operates as
either short or
open.
I
Voltage source
e.g. battery
or
+
-
V
Provides
fixed voltage
independent
of current.
V
Provides
fixed current
independent
of voltage.
V
I
Current source
Robert R. McLeod, University of Colorado
I
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• Lecture 2: VIP
ECEN 1400 Introduction to Analog and Digital Electronics
Quiz 2.1 – Unit relations
Q: Which two quantities are related by an
integral?
A: Current is the time integral of charge.
B: Charge is the time integral of current.
C: Power is the time integral of current.
D: Current is the time integral of voltage.
E: Charge is the time integral of power.
That is, the sum over time of the current in units of coulombs per
second is the total charge that has passed by in units of coulombs.
Robert R. McLeod, University of Colorado
22
• Lecture 2: VIP
ECEN 1400 Introduction to Analog and Digital Electronics
Quiz 2.2 – Language
Q: Given a component in the lab (a black
box with some wires), which phrase is an
accurate use of electrical terminology?
A: “Current across the component”
B: “Voltage through the component”
C: “Voltage across the component”
D: “Power across the component”
E: “Charge across the component”
Voltage is a measure of the potential energy that can be extracted
from a quantity of charge if the charge were allowed to flow from
point A to point B. Thus voltage is always a relative (A to B)
measure.
Current, on the other hand, goes through components and is not
relative. It is just the amount of charge per unit second that is passing
by.
Robert R. McLeod, University of Colorado
23
• Lecture 2: VIP
ECEN 1400 Introduction to Analog and Digital Electronics
Quiz 2.3 – IV curves
I
a
b
V
Q: Given the two current (I) vs. voltage
(V) curves above (a and b), you are told
one of them corresponds to a copper wire
(a good conductor) and one to a piece of
plastic (a poor conductor). Which is
which?
A: (a) is the copper, (b) is the plastic
B: (a) is the plastic, (b) is the copper
C: Not enough information
Line (a) results in lots of current for low voltage and is thus a good
conductor. The slope of the line is conductance = 1 / resistance.
Robert R. McLeod, University of Colorado
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