2. 2
Basic Laws - Chapter 2
Basic Laws - Chapter 2
2.1 Ohm’s Law.
2.2 Nodes, Branches, and Loops.
2.3 Kirchhoff’s Laws.
2.4 Series Resistors and Voltage Division.
2.5 Parallel Resistors and Current Division.
2.6 Wye-Delta Transformations.
3. 3
2.1 Ohms Law (1)
2.1 Ohms Law (1)
• Ohm’s law states that the voltage across
a resistor is directly proportional to the
current I flowing through the resistor.
• Mathematical expression for Ohm’s Law
is as follows:
• Two extreme possible values of R:
0 (zero) and (infinite) are related
with two basic circuit concepts: short
circuit and open circuit.
iR
v
4. 4
2.1 Ohms Law (2)
2.1 Ohms Law (2)
• Conductance is the ability of an element to
conduct electric current; it is the reciprocal
of resistance R and is measured in mhos or
siemens.
• The power dissipated by a resistor:
v
i
R
G
1
R
v
R
i
vi
p
2
2
5. 5
2.2 Nodes, Branches and Loops
2.2 Nodes, Branches and Loops
(1)
(1)
• A branch represents a single element such as a
voltage source or a resistor.
• A node is the point of connection between two
or more branches.
• A loop is any closed path in a circuit.
• A network with b branches, n nodes, and l
independent loops will satisfy the fundamental
theorem of network topology:
1
n
l
b
6. 6
2.2 Nodes, Branches and Loops
2.2 Nodes, Branches and Loops
(2)
(2)
Example 1
How many branches, nodes and loops are there?
Original circuit
Equivalent circuit
7. 7
2.2 Nodes, Branches and Loops
2.2 Nodes, Branches and Loops
(3)
(3)
Example 2
How many branches, nodes and loops are there?
Should we consider it as one
branch or two branches?
8. 8
2.3
2.3 Kirchhoff’s Laws (1)
Kirchhoff’s Laws (1)
• Kirchhoff’s current law (KCL) states that the
algebraic sum of currents entering a node
(or a closed boundary) is zero.
0
1
N
n
n
i
Mathematically,
9. 9
2.3
2.3 Kirchhoff’s Laws (2)
Kirchhoff’s Laws (2)
Example 4
• Determine the current I for the circuit shown in
the figure below.
I + 4-(-3)-2 = 0
I = -5A
This indicates that
the actual current
for I is flowing
in the opposite
direction.
We can consider the whole
enclosed area as one “node”.
10. 10
2.3
2.3 Kirchhoff’s Laws (3)
Kirchhoff’s Laws (3)
• Kirchhoff’s voltage law (KVL) states that the
algebraic sum of all voltages around a closed
path (or loop) is zero.
Mathematically, 0
1
M
m
n
v
11. 11
2.3
2.3 Kirchhoff’s Laws (4)
Kirchhoff’s Laws (4)
Example 5
• Applying the KVL equation for the circuit of the
figure below.
va-v1-vb-v2-v3 = 0
V1 = IR1 v2 = IR2 v3 = IR3
va-vb = I(R1 + R2 + R3)
3
2
1 R
R
R
v
v
I b
a
12. 12
2.4 Series Resistors and Voltage
2.4 Series Resistors and Voltage
Division (1)
Division (1)
• Series: Two or more elements are in series if they
are cascaded or connected sequentially
and consequently carry the same current.
• The equivalent resistance of any number of
resistors connected in a series is the sum of the
individual resistances.
• The voltage divider can be expressed as
N
n
n
N
eq R
R
R
R
R
1
2
1
v
R
R
R
R
v
N
n
n
2
1
13. 13
Example 3
10V and 5
are in series
2.4 Series Resistors and Voltage
2.4 Series Resistors and Voltage
Division (1)
Division (1)
14. 14
2.5 Parallel Resistors and Current
2.5 Parallel Resistors and Current
Division (1)
Division (1)
• Parallel: Two or more elements are in parallel if
they are connected to the same two nodes and
consequently have the same voltage across them.
• The equivalent resistance of a circuit with
N resistors in parallel is:
• The total current i is shared by the resistors in
inverse proportion to their resistances. The current
divider can be expressed as:
N
eq R
R
R
R
1
1
1
1
2
1
n
eq
n
n
R
iR
R
v
i
15. 15
Example 4
2, 3 and 2A
are in parallel
2.5 Parallel Resistors and Current
2.5 Parallel Resistors and Current
Division (1)
Division (1)
16. 16
2.6 Wye-Delta Transformations
2.6 Wye-Delta Transformations
)
(
1
c
b
a
c
b
R
R
R
R
R
R
)
(
2
c
b
a
a
c
R
R
R
R
R
R
)
(
3
c
b
a
b
a
R
R
R
R
R
R
1
1
3
3
2
2
1
R
R
R
R
R
R
R
Ra
2
1
3
3
2
2
1
R
R
R
R
R
R
R
Rb
3
1
3
3
2
2
1
R
R
R
R
R
R
R
Rc
Delta -> Star Star -> Delta
