EE281-Electric Circuits

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# 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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# Steps for Nodal Analysis

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

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# Nodal Analysis with Voltage Sources

![](https://raw.githubusercontent.com/ozank/ee281/master/images/supernode1.png)

## How many nodes?
## How many node equations?

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# Nodal Analysis with Voltage Sources
## Let's solve for Va and Vb

![](https://raw.githubusercontent.com/ozank/ee281/master/images/supernode2.png)
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# Alternative Approach: Supernodes
![](https://raw.githubusercontent.com/ozank/ee281/master/images/supernode3.png)

##Remember: KCL is valid for any closed surface!

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# Example-1:
### Find node voltages
![](https://raw.githubusercontent.com/ozank/ee281/master/images/supernode_ex1.png)
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# Example-1:

### \\(V_1 = -7.33 V \quad V_2=-5.33 V\\)
![](https://raw.githubusercontent.com/ozank/ee281/master/images/supernode_ex1.png)

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# Example-2:
### Find v and i
![](https://raw.githubusercontent.com/ozank/ee281/master/images/supernode_ex2.png)
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# Example-2:

### \\(v = -0.4 V \quad i=2.8 A\\)
![](https://raw.githubusercontent.com/ozank/ee281/master/images/supernode_ex2.png)

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# Example-3:
### Find node voltages
![](https://raw.githubusercontent.com/ozank/ee281/master/images/supernode_ex3.png)
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# Example-3:
### \\(V_1 = 80/3 V \quad V_3=520/3 V \quad V_4=-140/3 V\\)
![](https://raw.githubusercontent.com/ozank/ee281/master/images/supernode_ex3.png)

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# Any questions?

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