circuit elements,ohm's law,kcl
TRANSCRIPT
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Introduction; Circuit Elements;Ohm's Law; KCL
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Basic Electrical Quantities
• Basic quantities: current, voltae and
!ower
" Current : time rate o# chane o# electric chare
I $ dq%dt
& m! $ & Coulom(%sec
" Voltage: electromotive #orce or !otential, V
& )olt $ & *oule%Coulom( $ & +m%coulom(
" Power : P $ I V
& -att $ & )oltm! $ & *oule%sec
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Current, I
• +ormall. we tal/ a(out the movement o# !ositivechares althouh we /now that, in eneral, inmetallic conductors current results #rom electron
motion 0conventionall. !ositive #low1• 2he sin o# the current indicates the direction o##low
• 2.!es o# current:
" direct current 0dc1: (atteries and some s!ecialenerators
" alternatin current 0ac1: household current whichvaries with time
I(t )
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)oltae, )
)oltae is the di##erence in ener. level o# a
unit chare located at each o# two !oints in
a circuit, and there#ore, re!resents the
ener. required to move the unit chare
#rom one !oint to the other
Circuit Element(s)
+ – V(t)
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3e#ault 4in Convention
• Passive sign convention : current should
enter the !ositive voltae terminal
• Consequence #or P $ I V " 5ositive 061 5ower: element a(sor(s !ower
" +eative 071 5ower: element su!!lies !ower
Circuit Element+ –
I
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ctive vs8 5assive Elements
• Active elements can enerate ener.
" )oltae and current sources
" Batteries
• Passive elements cannot enerate ener.
" 9esistors
" Ca!acitors and Inductors 0(ut C+ store
ener.1
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Inde!endent 4ources
n independent source 0voltae or current1
ma. (e 3C 0constant1 or time7var.in 0C1,
(ut does not de!end on other voltaes or
currents in the circuit
+
–
)oltae
4ource
Current
4ource
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9esistors
• resistor is a circuit element that
dissi!ates electrical ener. 0usuall. as
heat1
• 9eal7world devices that are modeled (.
resistors: incandescent liht (ul(s, heatin
elements 0stoves, heaters, etc81, lon
wires
• 9esistance is measured in Ohms 01
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Ohms Law
v0t1 $ i0t1 9 7 or 7 ) $ I 9
!0t1 $ i
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O!en Circuit
• -hat i# 9 $ ∞ ?
• i0t1 $ v0t1%9 $ @
v(t )
The
Rest ofthe
Circuit
i(t )=0
+
–
i(t )=0
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4hort Circuit
• -hat i# 9 $ @ ?
• v0t1 $ 9 i0t1 $ @
The
Rest ofthe
Circuit
v(t )=0
i(t )
+
–
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4eries
2wo elements are in series i# the current that
#lows throuh one must also #low throuh
the other8
R1 R2
4eries
R1 R2
+ot 4eries
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5arallel
2wo elements are in !arallel i# the. are
connected (etween 0share1 the same two
0distinct1 end nodes8
5arallel +ot 5arallel
R1
R2
R1
R2
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Kirchho##s Laws
• Kirchho##s Current Law 0KCL1
" sum o# all currents enterin a node is Aero
" sum o# currents enterin node is equal to sum
o# currents leavin node
• Kirchho##s )oltae Law 0K)L1
" sum o# voltaes around an. loo! in a circuit is
Aero
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KCL 0Kirchho##s Current Law1
2he sum o# currents enterin the node is Aero:
Analogy : mass #low at !i!e unction
i1(t )
i2(t ) i4(t )
i5(t )
i3(t )
∑==
n
j j
t i1
0)(