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Examples: Units Units
& Prefixes
& Scales
Dr. Robert Barsanti
Fall 2016
numbers & units: used to express some measurable quantity
• numbers: we typically use base-10 (numerals 0 through 9)
• units: we typically use either English or Metric (SI)
ELEC 201 – Electric Circuit Analysis I
Lecture 1
Units & Scales,
Charge & Current,
Voltage / Power / Energy
SI units:
THE CITADEL, THE MILITARY COLLEGE OF SOUTH CAROLINA
8/21/2016
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171 Moultrie Street,
Charleston, SC 29409
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Units Units
& Scales
Examples:
& Prefixes
• decimal system relates larger/smaller units to the basic units
• prefixes signify the various powers of 10
• adopted by the National Bureau of Standards in 1964
• used by all modern engineering textbooks
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Examples: Units & Prefixes
The clock speed of your computer is 2.6 GHz.
This clock speed is equal to…
MHz
kHz
Hz
A typical refridgerator/freezer runs at 600 W.
If the unit runs 20 hr/day, every day, for 30 days…
(a) How much energy (in kWh) does the unit consume?
(b) What is the cost if energy is charged at 10 cents/kWh?
(a)
(b)
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Charge
Examples: Units & Prefixes
The clock speed of your computer is 2.6 GHz.
This clock speed is equal to…
2600 MHz
2.6·106 kHz
2.6·109 Hz
• charge, q is the basic unit of electricity
property of electrons & protons: attract each other (opposite “charge”)
or repel each other (same “charge”)
• we will focus on the behavior of electrons
A typical refridgerator/freezer runs at 600 W.
If the unit runs 20 hr/day, every day, for 30 days…
(a) How much energy (in kWh) does the unit consume?
(b) What is the cost if energy is charged at 10 cents/kWh?
(a)
 1 kW 
 20 hr 
energy = ( 600 W ) 
 ( 30 days ) 
 = 360 kWh
 1000 W 
 1 day 
(b)
 10 cents  1 dollar 
cost = ( 360 kWh ) 

 = $36.00
 1 kWh  100 cents 
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• fundamental unit of charge (SI system) = coulomb
1 electron holds a charge of q = –1.602 x 10-19 C
1 proton holds a charge of q = +1.602 x 10-19 C
• unit of current = ampere
1 ampere or 1 “amp” = 1 C / s
flowing past a given point
(usually within a wire)
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Current
•
•
6
Current
current, i is the flow of charge / “charge in motion”
• the mechanism by which electrical energy is transferred
• send power from generation point consumption point
• send signals from transmission point reception point
has direction and value
dq
i =
dt
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•
defined as the flow of positive charge in a conductor
(i.e. in reality, a positive forward current
means the electrons are flowing backwards)
•
when written, current must be labeled with direction & value:
positive or negative,
depending upon
reference direction
amount of charge that has passed
a given point:
t
q =
∫
−∞
(a)
(b)
(c)
(d)
(e)
i dτ
• direct current (DC) is constant over time
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Current
Example: Charge & Current
•
defined as the flow of positive charge in a conductor
(i.e. in reality, a positive forward current
means the electrons are flowing backwards)
•
when written, current must be labeled with direction & value:
(a)
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(b)
(c)
(d)
The figure (left) represents the
amount of charge accumulated on a
capacitor plate versus time.
Plot the current into the plate
versus time.
(e)
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Example: Charge & Current
The figure (left) represents the
amount of charge accumulated on a
capacitor plate versus time.
Plot the current into the plate
versus time.
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Elements & Circuits
element: the smallest building block
of an electric circuit
A
B
(representations of a generic
element with 2 terminals)
(examples of standard 2-terminal elements)
i=
dq
dt
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current = “slope”
of charge vs. time
circuit: a collection of elements containing
at least 1 closed path
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Voltage
Passive vs. Active
•
current may pass a point (enter/leave an element)
in 2 directions
•
energy must be expended to move charge
• voltage, v is the work required to move current
through an element, per charge (e.g. from A to B)
• unit of voltage = volt = 1 J/C
v =
•
voltage can exist even when no current is flowing “potential”
• higher voltage + terminal higher potential
• lower voltage – terminal lower potential
•
charge tends to flow from higher voltage to lower voltage
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(a,b) If a positive current flows
into A (higher voltage) and
out of B (lower voltage),
the element is consuming /
absorbing electrical energy:
“passive”
dw
dq
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(c,d) If a positive current flows
into A (lower voltage) and
out of B (higher voltage),
the element is generating /
supplying electrical energy:
“active”
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Examples Electrical Energy
iC
+
iB ≈ 0
Let vCE = 5 V and iC = 1 mA .
Is the element supplying or
absorbing electrical energy?
Examples: Electrical Energy
iC
Let vCE = 5 V and iC = 1 mA .
Is the element supplying or
absorbing electrical energy?
+
iB ≈ 0
vCE
–
–
Let vC = 1 V (constant).
When is the capacitor
supplying energy & when
is it absorbing energy?
+
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vCE
iC
–
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vC
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• positive current is flowing
from a higher to a lower voltage
absorbing electrical energy
iC
supplying
+
–
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vC
absorbing
Let vC = 1 V (constant).
When is the capacitor
supplying energy & when
is it absorbing energy?
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Examples Power Absorbed
Energy is the work required to move charge through a voltage difference.
Power is an amount of energy absorbed/supplied per time .
dw
p = v ⋅i =
dt
∫
w =
t
−∞
p dτ
Determine the
power absorbed by
each element (a,b,c).
20 mA
3V
Power & Energy
4 mV
8 mA
1 Joule = 1 kg·m2/s2
•
1 Watt = 1 J / s
•
proportional to the # of coulombs transferred / time
& to the work required to transfer 1 coulomb through the element
passive sign convention (in the figure)
w.r.t. positive current into higher-voltage terminal
positive for power/energy absorbed ;
negative for power/energy supplied
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2e −10t V
3e −10 t mA
(a)
(b)
(c)
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Examples: Power Absorbed
20 mA
3V
Determine the
power absorbed by
each element (a,b,c).
4 mV
8 mA
(a)
P = ( 3 V )( 20 mA ) = 60 mW
(b)
P = ( 4 mV )( −8 mA ) = − 32 µW
(c)
P = ( 2e −10t V )( 3e−10t mA ) = 6e −20t mW
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2e −10t V
3e −10 t mA
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