EE281-Electric Circuits

class: center, middle

# EE-281 ELECTRIC CIRCUITS

## Ozan Keysan

[ozan.keysan.me](http://ozan.keysan.me)

Office: C-113 <span class="meta">•</span> Tel: 210 7586

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# Analysis Methods
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## 1-Nodal Analysis
### Unknown: Node Voltages
### Uses Kirchhoff's Current Law

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## 2-Mesh Analysis
### Unknown: Mesh Currents
### Uses Kirchhoff's Voltage Law

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# Steps for Nodal Analysis

## 1-Choose a reference node (ground).
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## 2-Label node voltages.
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## 3-Write KCL equations for each node.
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## 4-Solve the equations.
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# Steps for Mesh Analysis

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# Steps for Mesh Analysis
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## 1-Label each mesh in the circuit.
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## 2- Write KVL equations for each mesh.
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## 3- Solve equations for the mesh currents.

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# Label each mesh in the circuit
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## Mesh: a loop which does not contain any other loops within it
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## It is conventional to use clockwise current direction

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# Write KVL equations for each mesh
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## Use - sign if you encounter the negative polarity of the voltage source first, use + sign otherwise.
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# Example-1

<img src="https://ozank.gitbooks.io/ee281/content/images/mesh_ex1.png" alt="Drawing" style="width: 600px;"/>
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# Example-1
## Answer: \\(i_1 = 1 A \quad i_2 = 1 A\\)
<img src="https://ozank.gitbooks.io/ee281/content/images/mesh_ex1.png" alt="Drawing" style="width: 500px;"/>
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# Example-2

<img src="https://ozank.gitbooks.io/ee281/content/images/mesh_ex2.png" alt="Drawing" style="width: 700px;"/>
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# Example-2
## Answer: \\(i_1 = 2.5 A \quad i_2 = 0 A\\)
<img src="https://ozank.gitbooks.io/ee281/content/images/mesh_ex2.png" alt="Drawing" style="width: 500px;"/>
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# Example-3
## Find \\(I_o\\)

<img src="https://ozank.gitbooks.io/ee281/content/images/mesh_ex3.png" alt="Drawing" style="width: 600px;"/>
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# Example-3
### Answer: \\(i_1 = 2.25 A \quad i_2 = 0.75 A \quad i_3 = 1.5 A\\)
### \\(I_o = i_1 - i_2 = 1.5 A\\)
<img src="https://ozank.gitbooks.io/ee281/content/images/mesh_ex3.png" alt="Drawing" style="width: 500px;"/>
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# Example-4
## Find \\(I_o\\)

<img src="https://ozank.gitbooks.io/ee281/content/images/mesh_ex4.png" alt="Drawing" style="width: 600px;"/>
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# Example-4
### Answer: \\(i_1 = -2.57 A \quad i_2 = -7.71 A \quad i_3 = -4 A\\)
### \\(I_o = i_3 = -4 A\\)
<img src="https://ozank.gitbooks.io/ee281/content/images/mesh_ex4.png" alt="Drawing" style="width: 500px;"/>
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# Mesh Analysis with Current Sources

## Similar to Node Analysis with Voltage Sources

## Current Sources reduces the number of unknowns.

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# Example
## Let's solve for i1 and i2

![](https://raw.githubusercontent.com/ozank/ee281/master/images/supermesh1.png)

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# Supermesh

<img src="https://raw.githubusercontent.com/ozank/ee281/master/images/supermesh2.png" alt="Drawing" style="width: 700px;"/>
##Remember: KVL is valid for any closed loop!

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# Example:
### Find mesh currents
![](https://raw.githubusercontent.com/ozank/ee281/master/images/supermesh4.png)

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# Example:
### Find mesh currents
![](https://raw.githubusercontent.com/ozank/ee281/master/images/supermesh3.png)

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# Exercise:
### Find mesh currents
![](https://raw.githubusercontent.com/ozank/ee281/master/images/supermesh5.png)

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# Any questions?

## You can download this presentation from: [keysan.me/ee281](http://keysan.me/ee281)