Download Chapter 3 Voltage and Current Laws

Chapter 3
Voltage and
Current Laws
1
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these two networks are equivalent
there are three nodes and five branches
a path is a sequence of nodes
a loop is a closed (circular) path
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2
KCL: The algebraic sum of the currents entering
any node is zero.
iA + iB + (−iC) + (−iD) = 0
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Current IN is zero:
iA + iB + (−iC) + (−iD) = 0
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Current OUT is zero:
(-iA )+ (-iB ) + iC + iD = 0
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Current IN=OUT:
iA+ iB = iC + iD
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4
Find the current through resistor R3 if it is known that
the voltage source supplies a current of 3 A.
Answer: i =6 A
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5
KVL: The algebraic sum of the voltages around
any closed path is zero.
v1 + (-v2 )+ (−v3) = 0
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Sum of RISES is zero (clockwise from B):
v1 +(- v2 ) + v3 = 0
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Sum of DROPS is zero (clockwise from B):
(-v1 ) + v2 + (-v3 ) = 0
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Two paths, same
voltage (A to B):
v1 = (-v3 ) + v2
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Find vR2 (the voltage across R2) and the voltage vx.
Answer: vR2 = 32 V and vx= 6 V.
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Example: find the current ix and the voltage vx
Answer: vx= 12 V and ix =120 mA
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Solve for the voltage vx and and the current ix
Answer: vx=8 V and ix= 1 A
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10
All of the elements in a circuit that carry the
same current are said to be connected in
series.
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11
Elements in a circuit having a common voltage
across them are said to be connected in
parallel.
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12
Calculate the power absorbed by each circuit element.
Answer:
p120V = −960 W, p30 = 1920 W
pdep = −1920 W, p15 = 960 W
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13
Find the voltage v and the currents i1 and i2.
Answer: v = 2 V, i1 = 60 A, and i2 = 30 A
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14
Determine the value of v and the power supplied by the
independent current source.
Answer: v = 14.4 V, power from current source is 345.6 mW
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15
Voltage sources
connected in series
can be combined
into an equivalent
voltage source:
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16
Current sources connected in parallel can be
combined into an equivalent current source:
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Our circuit models are idealizations that can
lead to apparent physical absurdities:
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Vs in parallel (a) and Is in series (c) can lead to
“impossible circuits”
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18
Using KVL shows:
Req = R1 + R2 + … + RN
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19
Find i and the power supplied by the 80 V source.
Answer: i = 3 A and p = 240 W supplied
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Using KCL shows:
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Two resistors in parallel can be
combined using the
product / sum
shortcut.
Connecting resistors in parallel makes
the result smaller :
0.5 min(R1, R2) < R1||R2 < min(R1,R2)
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22
Resistors in series “share” the voltage applied to
them.
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23
Find vx
Answer:
vx(t) = 4 sin t V
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Resistors in parallel “share” the current through
them.
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25
Find i3(t)
Answer: i3(t) = 1.333 sin t V
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