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BASIC LAWS
• Ohm’s Law
• Kirchhoff’s Law
• Series resistors & voltage division
• Parallel resistors & current division
• Y - transformation
Ohm’s Law
Property of a material to resist a flow of current known as resistance
Mathematically,
l
R
A
- measured in ohms ()

- Resistivity of the material
l
- length of the material
A
- Cross section area of the material
+
i
V

Ohm’s Law
Ohms’s Law: A voltage across a resistor is directly proportional to
the current flowing through a resistor
+
V

i
vi
Constant of proportionality between v and i is the resistance, R ()
v= iR
Must comply with passive sign convention
Ohm’s Law
Fixed resistors
Wirewound type
carbontype type
Ohm’s Law
Variable resistors
Ohm’s Law
Two extreme values of resistance:
Short circuit
v 0
R  0
i
i
Open circuit
R
v v
 
i o
Ohm’s Law
Conductance: reciprocal of resistance
1 i
G 
R v
- measured in siemens (S)
Conductance: ability of an element to conduct current
Ohm’s Law
Power in a Resistor
+
V

i
p  vi
p  (iR)i  i2R
Always positive
Always absorbs power
v
v2
p  v( ) 
R
R
Kirchhoff’s Law
Network topology
A branch represents a single element such as a
voltage source or a resistor.
Kirchhoff’s Law
Network topology
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.
Kirchhoff’s Law
Network topology
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.
Kirchhoff’s Law
Network topology
Two or more elements are in series if they exclusively
share a single node and consequently share the same
current
Two or more elements are in parallel if they are
connected to the same two nodes and consequently
have the same voltage across them
1 & 2 - parallel
10V & 4 - parallel
5 in series with (1 and 2  in parallel)
Kirchhoff’s Law
Kirchhoff’s Current Law (KCL)
Kirchhoff’s current law (KCL) states that the algebraic sum
of currents entering a node (or a closed boundary) is zero
N
Mathematically,
i
n 1
n
0
Kirchhoff’s Law
Kirchhoff’s Voltage Law (KVL)
Kirchhoff’s voltage law (KVL) states that the algebraic sum
of all voltages around a closed path (or loop) is zero.
Mathematically,
M
v
m 1
n
0