Class Concepts
Kirchhoff’s Laws II & Equivalent Resistance
•  Passive sign convention
•  Open & short circuits
•  Recap Kirchhoff
o Current law, KCL
o Voltage law, KVL
•  Equivalent resistance
EGR 220, Chapter 2
February 2, 2016
2
Recap: Nodes & Branches
Open & Short Circuits
•  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.
4
5
1
Recap: Concepts & Laws
Kirchhoff’s Current Law
•  Find i1, i2 and i3
•  Node, Branch & Loop
•  Series resistors
o  Label nodes
o  Write KCL equation and solve (use Ohm’s law for
actual resistor circuits)
o  Series elements; series branches
o  Shared: nodes? current? voltage?
•  Parallel resistors
o  Parallel elements; parallel branches
o  Shared: nodes? current? voltage?
•  KVL: Kirchhoff’s voltage law
•  KCL: Kirchhoff’s current law
6
Kirchhoff’s Current Law
7
Kirchhoff’s Voltage Law, KVL
•  Find i1, i2, i3 and i4
Ø  Combine Ohm’s law with KVL to solve for ______?
o  Label nodes
o  Write KCL equation and solve (use Ohm’s law for
actual resistor circuits)
4Ω
+
v2
1Ω
–
8
2
Kirchhoff’s Voltage Law
Kirchhoff’s Voltage Law
•  Apply KVL
•  Apply KVL
o Label voltages
o Write KVL equation and solve
o Label voltages
o Write KVL equation and solve
10
11
Resistor Combinations
•  Series elements
New Concept:
Equivalent Resistance
o Exclusively share ONE node
•  Parallel elements or branches
o Share TWO nodes
12
14
3
Series Resistors
Parallel Resistors
•  Find Req (as a function of R1 and R2)
•  Find Req (as a function of R1 and R2)
itotal
+
v
−
R1
R2
15
Equivalent Resistance
16
Equivalent Resistance
•  Physical understanding of equations
for equivalent resistance
•  Equivalent resistance is terminaldependent
•  V = I*R so… R = V/I à The ratio of
voltage to current for specific
terminals in a circuit
•  Concept of resistance: the ratio of V:I
o  Water flowing through two pipes put end to end
= series/parallel?
o  People moving through side-by-side doorways =
series/parallel?
17
18
4
Identify Series and Parallel Elements & Identify Series and Parallel Elements & Branches, and Find Req
Branches, and Find Req
19
Identify Series and Parallel Elements & Branches, and Find Req
20
New Terminology
•  Series elements
•  Parallel elements
•  Equivalent resistance
21
22
5