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BASIC LAWS
• Ohm’s Law
• Kirchhoff’s Law
• Series resistors & voltage division
• Parallel resistors & current division
• Y - transformation
• Source Transformation
Series resistors & voltage division
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
N
Req  R1  R2      R N   Rn
n 1
Series resistors & voltage division
Let’s say we want to find v2
v2 = iR2
R2
 v2 
v
R 1 R 2

where,
i
v
R 1 R 2
- Voltage Division Rule

- Principle of Voltage Division
Note that if R2 >> R1, then v2 v
Series resistors & voltage division
i
R1
+ v1 
v
R2
+ v2 
Series resistors & voltage division
i=0
v
R1
R =
+ v1 
+ v2 
If R2 is replaced with open circuit,
the resistance would be 
R2
v2 
v  v2 v
R1  R2
R1
v1 
v  v1  0
R1  R2
Parallel resistors & current division
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:
1
1
1
1


  
Req R1 R2
RN
Parallel resistors & current division
Parallel resistors & current division
+
+
v
v


v
i2 
R2
R1
 i2 
i
R1  R2
Let’s say we want to find i2
where,
v  iR eq
 R1R2 

 i
 R1  R2 
- Current Division Rule
- Principle of Current Division
Parallel resistors & current division
i2 
R1
i  i2  i
R1  R2
i1 
R2
i  i1  0
R1  R2
i2 
R1
i  i2  0
R1  R2
i1 
R2
i  i1  i
R1  R2
Y
Star
 transformation
delta transformation
How can we combine R1 to R7 ?
Y
Star
 transformation
delta transformation
Delta -> Star
Star -> Delta
Rb Rc
R1 
( Ra  Rb  Rc )
Ra 
R1 R2  R2 R3  R3 R1
R1
Rc Ra
R2 
( Ra  Rb  Rc )
Rb 
R1 R2  R2 R3  R3 R1
R2
Ra Rb
R3 
( Ra  Rb  Rc )
Rc 
R1 R2  R2 R3  R3 R1
R3
Y
 transformation
Star
example
delta transformation
Y
 transformation
Star
example
delta transformation
Source transformation
Another circuit simplifying technique
It is the process of replacing a voltage source vS in series
with a resistor R by a current source iS in parallel with a
resistor R, or vice versa
R
a
a
is
vs +
R

b
Terminal a-b sees:
Open circuit voltage: vs
Short circuit current: vs/R
b
For this circuit to be equivalent, it
must have the same terminal
charateristics
Source transformation
Another circuit simplifying technique
It is the process of replacing a voltage source vS in series
with a resistor R by a current source iS in parallel with a
resistor R, or vice versa
a
is
R
b
Terminal a-b sees:
Open circuit voltage: isR
Short circuit current: is
Source transformation
Another circuit simplifying technique
It is the process of replacing a voltage source vS in series
with a resistor R by a current source iS in parallel with a
resistor R, or vice versa
R
a
is
a
R
vs +

b
Terminal a-b sees:
Open circuit voltage: isR
Short circuit current: is
b
Terminal a-b sees:
Open circuit voltage: vs
Short circuit current: vs/R
Source transformation
Another circuit simplifying technique
It is the process of replacing a voltage source vS in series
with a resistor R by a current source iS in parallel with a
resistor R, or vice versa
R
a
is
a
R
vs +

b
For both to be equivalent,
b
isR = vs
or
is = vs/R
Source transformation
Another circuit simplifying technique
It is the process of replacing a voltage source vS in series
with a resistor R by a current source iS in parallel with a
resistor R, or vice versa
R
a
is
a
iy
R
vs +

ix
b
b
Note: current through R (hence power) for both circuits is not the same
i.e.
ix  iy
Example 1
Find vo in the circuit shown below using source transformation
Example 1
Example 2
Find io in the circuit shown below using source transformation