02 PSC rev F09 -...

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Unformatted text preview: EECS
314
//
Passive
Sign
Conven2on
 9/1/10
 Power
in
Electric
Circuits.
 Passive
Sign
Conven2on
  Defini2ons
and
Units
  Power
can
be
absorbed
(dissipated)
or
 supplied
(delivered)
  Passive
sign
conven2on
for
bookkeeping:
 absorbed
power
is
posi2ve;
supplied
power
is
 nega2ve
  Conserva2on
of
power
in
circuits:
the
total
 power
equals
zero
 ©
2010
A.
Ganago
 PSC
rev
F09
 1
 Defini2ons
and
Units
(1)
 •  Voltage
difference
V
is
work
on
a
 unit
electric
charge
 •  Current
I
is
number
of
charges
 moved
per
unit
2me
 •  Thus
V∙I
=
work
on
all
charges
 moved
per
unit
2me
=
Power
 ©
2010
A.
Ganago
 PSC
rev
F09
 2
 Defini2ons
and
Units
(2)
 •  Power
=
Voltage
∙
Current

 •  1
volt
∙
1
coulomb
=
1
joule

 •  1
amp
=
1
coulomb
/
1
sec
 •  (1
volt)
∙
(1
amp)
=
1
joule/sec
=
1
 waW
1
V
∙
1
A
=
1
W
 ©
2010
A.
Ganago
 PSC
rev
F09
 3
 •  In
simplest
circuits,
we
can
easily
see
which
 element
consumes
power
and
which
one
 supplies
power
 In
a
flashlight,
the
baWery
 supplies
power
and
the
lamp
 absorbs
it
 Power
can
be
either
supplied

or
 dissipated
(1)
 
The
current
enters
the
 posi2ve
terminal
of
the
lamp
 and
the
nega2ve
terminal
of
 the
baWery
 ©
2010
A.
Ganago
 PSC
rev
F09
 4
 Power
can
be
either
supplied
or
 dissipated
(2)
 •  During
a
jump
start
of
a
car,
how
can
we
 determine
which
baWery
supplies
power
 and
which
one
absorbs
it?
 Use
the
guideline
from
the
 flashlight
circuit
(see
above):

 if
the
current
enters
the
 element’s
posi=ve
terminal,
the
 element
absorbs
power

 ©
2010
A.
Ganago
 PSC
rev
F09
 5
 •  If
the
posi2ve
current
[conven2onal
 direc2on]
enters
the
posi2ve
terminal
of
an
 element,
the
power
is
absorbed,
or
 dissipated;
otherwise
it
is
supplied
 Power
can
be
either
supplied
or
 dissipated
(3)
 ©
2010
A.
Ganago
 PSC
rev
F09
 6
 ©
2010
A.
Ganago
 1
 EECS
314
//
Passive
Sign
Conven2on
 9/1/10
 The
Passive
Sign
Conven2on
(PSC)
 •  According
to
the
Passive
Sign
 Conven=on
(PSC),

 
the
absorbed
power
is
posi=ve,
and
 the
supplied
power
is
nega=ve
 •  PSC
is
not
a
law
of
Nature:
merely
 the
bookkeeping
conven2on,
which
 we
apply
to
all
circuits
 ©
2010
A.
Ganago
 PSC
rev
F09
 7
 How
to
Apply
the
Passive
Sign
 Conven2on
to
a
Circuit
 •  For
each
circuit
element,
introduce
the
 reference
marks:
the
sign
of
voltage
 difference
V
and
the
direc2on
of
current
I
 •  For
each
circuit
element,
calculate
the
 voltage
across
it
(from
KVL,
etc.)
and
the
 current
through
it
(from
KCL,

etc.)

 •  You
need
both
V
and
I
to
calculate
the
 power
as
their
product
P=V∙I
 ©
2010
A.
Ganago
 PSC
rev
F09
 8
 How
to
Apply
PSC
to
a
Circuit
 (con2nued)
 •  Calculate
the
product
P=V∙I

 •  Pay
aFen=on
to
the
reference
marks
 you
introduced
 •  According
to
the
Passive
Sign
Conven2on
 (PSC),

 the
absorbed
power
is
posi=ve
P > 0
 and

 the
supplied
power
is
nega=ve
P < 0
 ©
2010
A.
Ganago
 PSC
rev
F09
 9
 Remember:
 As
a
consequence
of
the
Energy
 Conserva2on
Law,
 the
total
electric
power
 absorbed
in
any
circuit

 equals
zero
 In
other
words,
in
any
circuit,
the
sum
of
 nega2ve
(supplied)
powers
must
equal
the
 sum
of
posi2ve
(absorbed)
powers
 PSC
rev
F09
 ©
2010
A.
Ganago
 10
 Conservation of Energy
 leads
to
Zero Total Power
 •  Energy
is
conserved
in
any
part
of
the
 Universe,
over
any
interval
of
2me
 •  Thus
in
any
electric
circuit

the algebraic sum of all powers
 (supplied
and
dissipated)
equals zero
 •  This principle is always valid
 •  It
provides
an
addi2onal
tool
for
solving
 circuit
problems
 ©
2010
A.
Ganago
 PSC
rev
F09
 11
 Zero Total Power applied
to
circuit
problems
 •  Aher
you
found
all
voltages
and
all
currents
 in
the
circuit,
you
can
verify
the
correctness
 of
your
answer
by
calcula2ng
the
power
 balance:
if
the
total
power
is
not
zero,
you
 blundered
 •  On
the
other
hand,
an
unknown
voltage
or
 current
can
be
calculated
from
the
power
 balance
(sum
the
powers
in
all
the
rest
 elements
and
subtract
it
from
0)
 ©
2010
A.
Ganago
 PSC
rev
F09
 12
 ©
2010
A.
Ganago
 2
 EECS
314
//
Passive
Sign
Conven2on
 9/1/10
 KCL, KVL, PSC are valid in all circuits
 •  The
laws
of
conserva2on
of
electric
charges
 (KCL)
and
energy
(KVL)
are
so
general
that
 you
can
rely
on
them
in
solving
any
circuit
 problem
 •  Proper
bookkeeping
of
electric
power
(PSC)
 must
also
work
in
all
circuits
 •  These
are
your
most
general
guidelines
 ©
2010
A.
Ganago
 PSC
rev
F09
 13
 Prac=ce
problem
on
PSC
(1)
 •  The
element
 shaded
black
…
 A.  Absorbs
32
W
 B.  Absorbs
8
W
 C.  Neither
absorbs
 nor
supplies
 D.  Supplies
8
W
 E.  Supplies
32
W
 (From
a
midterm
exam

 75%
correct
answers)
 ©
2010
A.
Ganago
 PSC
rev
F09
 14
 Prac=ce
problem
solu=on
(1)
 •  We
need
to
find
 the
current

 •  From
KCL
at
the
 top
node,
it
 equals
2
A,
 flowing
up
 through
the
 shaded
element
 Prac=ce
problem
solu=on
(2)
 We
need
to
find
 the
voltage
 across
the
 shaded
 element,
 labeled
X
here
 •  From
KVL,
 +
10
V
+
2
V
‐
X
‐
8
V
=
0
 Thus
X
=
4
V
 X 2 A
 ©
2010
A.
Ganago
 PSC
rev
F09
 15
 ©
2010
A.
Ganago
 PSC
rev
F09
 16
 Prac=ce
problem
solu=on
(3)
 Apply
PSC
 Power absorbed = =4V·2A=8W Choice:
B
 4V 2 A
 Summary
 •  KCL
and
KVL
are
consequences
of
this
 Universe’s
conserva2on
laws
(for
electric
 charge
and
energy)
 •  Circuits
are
parts
of
this
Universe,
thus
KCL
 and
KVL
apply
to
any
circuit

 •  In
circuits
with
resistors,
we
use
them

 along
with
Ohm’s
law
(see
next
chapter)
 •  Passive
sign
conven2on
is
a
powerful
and
 convenient
bookkeeping
tool
 17
 ©
2010
A.
Ganago
 PSC
rev
F09
 18
 No2ce
that
we
could
choose
whichever
 posi2on
for
the
posi2ve
terminal.

 For
the
sake
of
convenience,
we
chose
it
at
 the
boWom,
because
we
already
knew
that
 the
current
enters
there.
 ©
2010
A.
Ganago
 PSC
rev
F09
 ©
2010
A.
Ganago
 3
 ...
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This note was uploaded on 12/06/2010 for the course EECS 314 taught by Professor Ganago during the Spring '07 term at University of Michigan.

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