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Kirchoffs Current Law (KCL)
The sum of the currents entering a node is
equal to the sum of the current leaving the
node.
The algebraic sum of currents entering a
node (or a closed boundary) is zero
!
!N
n
ni
1
0
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Kirchoffs Current Law (KCL)
We know the currentI1 = 2 A. What iscurrent I2?
I1 = I2 = 2A
This confirms for us
that two elements inseries must have thesame current
I1
I2
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Kirchoffs Current Law (KCL)
Find the current I0
in the following circuit.
AIAA
IIoutin
10420!
!
I0
4 A
10 A
2 A
I
I
4
1042
0
0
!
!
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Kirchoffs Current Law (KCL)
There are two ways to
find I:
Find Req and then
calculate I
Find I1 and I2 and
then calculate I
I
I2I1
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Kirchoffs Current Law (KCL)
Find Req and then
calculate I
Req = 10/2 = 5
I = 10/5 = 2A
I
I2I1
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Kirchoffs Current Law (KCL)
Find I1 and I2 and
then calculate I
I1 = 10/10 = 1A
I2 = 10/10 = 1 A
I = I1 + I2 = 2 A
I
I2I1
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Kirchoffs Voltage Law (KVL)
The algebraic sum of all voltages around a
closed path (or loop) is zero
Sum of voltage drops = Sum of voltage
rises
!
!M
m
mv
1
0
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Circuit Definitions
In Series, voltage sources add
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Circuit Definitions
In Parallel, voltage sources provide more
current but have the same voltage
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Review Question 2.9
Which of the circuits below will give you Vab
= 7V?
a) b)
c) d)
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Resistors in Series
The equivalent resistance of any number
of resistors connected in series is the sum
of the individual resistances.
Neq RRRR ! -21
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Resistors in Parallel
The equivalent resistance of any number
of resistors connected in parallel is the
reciprocal of the sum of the reciprocals
Neq RRRR
1111
21
! -
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Resistors in Parallel
The equivalent resistance of any two
resistors in parallel can be expressed
more simply as:
21
21
RRRRReq
!
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Voltage Division
To calculate the voltage drop across each
resistor, use the following equations:
SV
RR
RV
21
1
1
!
SV
RR
RV
21
2
2
!
VS
R1
R2
+ V1_
+
V2_
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Current Division
To calculate the current going through each
resistor, use the following equations:
SI
RR
RI
21
2
1
!
SI
RR
RI
21
1
2
!
IS R1 R2I1 I2