lesson 2 basic circuit laws
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Lesson 2
Basic Laws of Electric Cicuits
Ohms Law
Kirchhoffs Current Law
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Basic Laws of Circuits
Ohms Law:
The voltage across a resistor is directly proportional to the current
moving through the resistor.
+_v(t)i(t)
Rv(t) = Ri(t)
+_ v(t)i(t)
R
v(t) = Ri(t)_
(2.1)
(2.2)
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Basic Laws of Circuits
Ohms Law: About Resistors:
The unit of resistance is ohms( ).
A mathematical expression for resistance is
lR
A
2
: ( )
: ( )
:
l The length of the conductor meters
A The cross sectional area meters
The resistivity m
(2.3)
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Basic Laws of Circuits
Ohms Law: About Resistors:
We remember that resistance has units of ohms. The reciprocal of
resistance is conductance. At one time, conductance commonly had units
of mhos (resistance spelled backwards).
In recent years the units of conductance has been established as seimans (S).
Thus, we express the relationship between conductance and resistance as
1G
R (2.4)
We will see later than when resistors are in parallel, it is convenient
to use Equation (2.4) to calculate the equivalent resistance.
(S)
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Basic Laws of Circuits
Ohms Law: Ohms Law: Example 2.1.
Consider the following circuit.
+
_
115V RMS(ac)
R
(100 Watt light bulb)
V
Determine the resistance of the 100 Watt bulb.
2
22
2 115132.25
100
V
P VI I RR
VR ohms
P
(2.5)
A suggested assignment is to measure the resistance of a 100 watt light
bulb with an ohmmeter. Debate the two answers.5
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Basic Laws of Circuits
Ohms Law: Current
Under the influence of an electromotive force, the one valence
electron of each copper atom is pulled from the outer orbit and
moves through the copper space toward a positive potential.
copperwire
electron flow
resistor
EMF
electron flow
electrons move
toward the positive
terminal of the EMF
Electron Flow
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Basic Laws of Circuits
Ohms Law: Current
copper
wire
positive charge
flow
resistor
EMF
Conventional current flow assumes positive charges move toward the
negative side of the circuit EMF.
Conventional
Flow
9
negative
side
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Basic Laws of Circuits
Kirchhoffs Current Law
As a consequence of the Law of the conservation of charge, we have:
The sum of the current entering anode (junction point) equal to the
sum of the currents leaving.
Ia
Ib
Ic
Id
Ia, Ib, Ic, and Idcan each be either a positive
or negative number.
Ia+ Ib= Ic + Id
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Basic Laws of Circuits
Kirchhoffs Current Law
The algebraic sum of the currents entering a node equal to zero.
Ia
Ib
Ic
IdIa+Ib Ic+ Id= 0
Ia, Ib, Ic, and Idcan each be either a positive
or negative number.
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Basic Laws of Circuits
Kirchhoffs Current Law
The algebraic sum of the currents leaving a node equal to zero.
Ia
Ib
Ic
IdIa- Ib+ Ic+ Id= 0
Ia, Ib, Ic, and Idcan each be either a positive
or negative number.
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Basic Laws of Circuits
Kirchhoffs Current Law: Example 2.2.Find the current I x.
4 A2 A
-1 A 6 A
IX9 A
Ans: IX = 22 A
14
Highlight the box
then use bring to
front to see answer.
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Basic Laws of Circuits
Kirchhoffs Current Law
Kirchhoffs current law can be generalized to include a surface.
We assume the elements within the surface are interconnected.
A closed 3D surface
We can now apply Kirchhoffs current law in the 3 forms we discussed
with a node. The appearance might be as follows:
Currents entering and
leaving a closed surface
that contains interconnected
circuit elements16
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Circuit
Circuit
Circuit
1 1j
j
j N k M
kk
i i
1
0r Q
rr
i
1
0m Q
mm
i
Basic Laws of Circuits
Kirchhoffs Current Law
As a consequence of the Law of the conservation of charge, we have:
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Basic Laws of Circuits
Kirchhoffs Current Law:Example 2.4
surface
1
surface
2
-2A
4A
IB IC
9A
2A IA
Find the currents IA, IB, and ICin the circuit below.
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Basic Laws of Circuits
Kirchhoffs Current Law:Solution for Example 2.4
surface
1
surface
2
-2A
4A
IB IC
9A
2A IA
node 1 node 2
At surface 1: IB = 2A: At node 1, Ic= 0A: At node 2, IA= 9A
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Basic Electric Circuit Concepts
End of Lesson 2
circuits
Ohms Law
Kirchhoffs Current Law
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