BASIC CIRCUIT
ANALYSIS
Presentation by Jon Josten, Colin Brown, Ava Zebzda
and Joseph Hemmingson
Circuit Analysis Topics
■ Circuit Elements & Variables
■ Ohm's Law
■ Kirchhoff's Laws
■ Mesh Current Analysis
Why are we doing this?
■ We have to introduce various basic elements, variables, and laws of circuit analysis
in order to get to a point where we can perform Mesh Current Analysis in order to
find the values of current going through any point of a circuit. Once we have these
building blocks, we can develop a system of equations that describe a circuit which
can be put into matrix form and solved using what we’ve learned about matrices.
■ Being able to find the values for current can tell you a lot about a circuit. It is a few
simple calculations away from finding voltage and power, which at the end of the day
can also be used to calculate how much money operating electronics may cost.
CIRCUIT ELEMENTS &
VARIABLES
Voltage, Ground, Current, Resistance, Wires, Nodes
Voltage
Units:
Volts
(V)
Symbol:
V
Circuit Element:
■ Water analogy – Voltage  Pressure.
■ color convention is blue.
■ For our analysis, each point we measure is
going to have a constant voltage associated
with it.
■ Current is proportional to the difference in
voltage between two points.
■ Water Analogy: Current  Water/Time
Current
Units:
Amperes
(A)
Symbol:
I
Circuit Element:
■ the rate at which charge is transferred
through an element or wire
■ caused by a difference in voltage between
two locations
■ Current flows from high voltage to low
voltage
■ color convention is red
■ Imagine which direction water would flow
in the picture below due to pressure
Resistance
Units:
Ohms
(Ω)
Symbol:
R
Circuit Element:
■
Water Analogy: Resistance  Narrowness of pipe
■
a measure of the degree to which an object
opposes the flow of charges through it.
■
similar to friction in Physics (opposing force).
Wires &
Nodes
■
A path must connect circuit elements so that current can
flow between points on the circuit. This path is the wire in
which current is able to flow.
■
A Node is an intersection of paths on a circuit. There is
typically a voltage represented at each node.
■
There is no voltage difference between two nodes
connected only by wire. They can be thought of as one
node.
Circuit
■ A circuit is elements connected together so
that current is able to flow. (i.e. a loop that
has different voltages throughout it)
https://cdn.sparkfun.com/assets/3/4/6/4/e/511bc192ce39
5f3941000002.gif
Thomas Edison
Invented the lightbulb, has 1,093 patents
and electrocuted an Elephant in the
process of advocating DC current.
OHM'S LAW
Ohm’s Law Definition, Solving Circuit#1 with Ohm’s Law
Ohm's Law: Definition
■ V = IR
■ Where 'V' is voltage, 'I' is current, and 'R' is resistance
■ Voltage across a resistor is equal to the current
through the resistor multiplied by its resistance value
+
-
Arrow denotes current
flow, plus & minus signs
denote voltage drop
Circuit #1: Ohm's Law (V=IR)
■ The way the voltage source is applied here, we can see that there is a difference of
6 volts between the two nodes of the resistor. Looking only at the resistor, we can
use ohm’s law to calculate the current.
Circuit #1: Ohm's Law
Circuit #1: Ohm's Law
I
Georg Ohm
Ohm's law was first founded by Henry
Cavendish, but since he did not publish
his discoveries on electricity during his
lifetime, the credit went to Ohm in 1879
when he had independently made the
discovery, and published it himself.
KIRCHHOFF’S LAWS
KVL, KCL, Series versus Parallel Circuits
Kirchhoff’s Voltage Law
■ The sum of the voltages going around any loop in a circuit is zero
V1 + V2 + V3 = VS
Circuit #2: KVL
Circuit #2: KVL
I
Circuit #3: KVL
V
Series Circuits
I
Parallel Circuits
V
Kirchhoff’s Current Law
■ The total amount of current going into any node is equal to the amount of current
going out.
i2 + i3 = i1 + i4
Circuit #3: KCL
Circuit #3: KCL
I
𝑖1
𝑖2
Gustav Kirchoff
Kirchoff worked with Robert Bunsen to
prove elements heated to specific
temperatures emit colored light, leading to
the discovery of cesium and rubidium.
MESH CURRENT
ANALYSIS
Mesh Current Analysis, Circuit #4, Representing Solutions as a System of
Equations, Equivalent Matrix Equation
Mesh Current Analysis Theory
The Mesh Current method uses Kirchhoff's Voltage Law and Ohm's Law
to solve for the unknown current around a mesh.
This is useful to limit the number of equations and unknowns in the final
result.
Def'n: A Mesh is the loop that doesn't contain any other loops within.
Steps for Mesh Current Analysis
1. Label each mesh of the circuit with a mesh current, going in the
clockwise direction.
2. Write KVL equations for each mesh. Each term is a voltage, but will
write the terms using Ohm's law to put them in terms of the mesh
currents. 𝑉 = 𝐼𝑅
3. Solve for the unknown currents using an augmented matrix
Circuit #4: Mesh Current Analysis
Circuit #4: Mesh Current Analysis
𝐼1
𝐼2
𝐼3
Circuit #4: Matrix Equation
𝐼1
𝐼2
𝐼3
Sources
Node Voltage Analysis Process:
http://www.allaboutcircuits.com/textbook/direct-current/chpt-10/node-voltage-method/
Voltage, Current, Resistance, and Ohm's Law:
https://learn.sparkfun.com/tutorials/voltage-current-resistance-and-ohms-law
http://physics.info/electric-current/
http://physics.info/circuits-v/
Resistors:
https://learn.sparkfun.com/tutorials/resistors