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<!DOCTYPE html>
<html>
<head>
<title>EE281-Electric Circuits</title>
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class: center, middle
# EE-281
# Capacitors - Inductors
## Ozan Keysan
[ozan.keysan.me](http://ozan.keysan.me)
Office: C-113 <span class="meta">•</span> Tel: 210 7586
---
# Capacitors
---
#Capacitors
### A capacitor is a device that consists of two conducting plates seperated by an insulator layer.
<img src="http://www.kranzle-pressure-washers.co.uk/media/catalog/product/cache/1/image/9df78eab33525d08d6e5fb8d27136e95/i/n/inside-motor-run-kranzle-capacitor.jpg" alt="Drawing" style="width: 400px;"/>
---
# Capacitance
## Capacitance is the ratio of electric charge to voltage.
# \\(C = \dfrac{Q}{V}\\)
---
# Capacitance
## can be defined using the material properties.
# \\(C = \dfrac{\varepsilon A}{d}\\)
--
## \\(\varepsilon\\): permitivity of the dielectric material
## \\(A\\) is the surface area
## \\(d\\) is the distance between layers.
---
# Capacitor Voltage & Current
# \\(i = C\dfrac{dV}{dt}\\)
--
# \\(V = \dfrac{1}{C} \int_0^t i(t) dt\\)
---
# Energy stored in a capacitor is:
# \\(w = \dfrac{1}{2} C V^2\\)
---
# DC Response
# \\(i = C\frac{dV}{dt}\\)
--
- ## Current of capacitor is zero if there's no change in the voltage (i.e. DC voltage)
--
- ## Capacitor voltage cannot be change instantenously as this means infinite current.
---
## Parallel Capacitors
--
## \\(C_{eq} = C_1 + C_2 + C_3 ... + C_N\\)
---
# Series Capacitors
--
## \\(\frac{1}{C\_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} ... \frac{1}{C_N}\\)
---
# Series Capacitors
### For two capacitors
## \\(C_{eq} = \frac{C_1 C_2}{C_1 + C_2}\\)
---
#Exercise
### What is the equivalent capacitance?
---
#Exercise
### Find the energy stored in the capacitors?
---
# Inductors
---
# Inductance
# \\(L = \dfrac{N^2 \mu A}{l}\\)
### \\(N\\) is the number of turns, \\(\mu\\) is the permeability of the core, \\(A\\) is the cross-section area, \\(l\\) is the mean length of the magnetic flux.
---
# Inductors
# \\(V = L \dfrac{di}{dt}\\)
--
## \\(I = \dfrac{1}{L} \int_0^t V(t) dt\\)
---
## Energy stored in an inductor is:
# \\(w = \dfrac{1}{2} L I^2\\)
---
#DC Response
--
## - An inductor behaves like short-circuit under DC
--
## - Inductor current cannot be change instantenously as this means infinite voltage.
---
# Series Connection
Equivalent inductance of series connected inductors are the sum of inductances:
## \\(L_{eq} = L_1 + L_2 + L_3 ... + L_N\\)
---
# Parallel Connection
## \\(\frac{1}{L\_{eq}} = \frac{1}{L_1} + \frac{1}{L_2} + \frac{1}{L_3} ... \frac{1}{L_N}\\)
---
# Exercise:
##Find the energy stored in capacitor and inductor under DC conditions.
---
# Any questions?
## You can download this presentation from: [keysan.me/ee281](http://keysan.me/ee281)
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