Introduction to Electric Circuits

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Electric Circuit is an interconnection of Electrical elements. Electric circuit theory and     electromagnetic theory are the two fundamental theories upon which all branches of   electric engineering are built. The basic Electric circuit theory course is the most             important course for an engineering student.


Objectives:

  • To define what is Electric Circuit
  • To be able to know what are the Basic concepts in a Circuit
  • Define Circuit Elements
  • and To solve problems involving charge and current

Electric Circuits

          An electrical circuit is a network consisting of a closed loop, giving a return path for the current. Linear electrical networks, a special type consisting only of sources (voltage or current), linear lumped elements (resistors, capacitors, conductors), and linear distributed elements (transmission lines), have the property that signals are linearly super imposable.

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Here is an example of a Simple Circuit. Composed of three things: the Power source or the battery , the Switch and the Load. A circuit is simply a closed loop through which charges can continuously move.

 

 

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Here is another example of a closed circuit and an open circuit. There is a difference between the two which the electrons flow. Electrons do not flow through an open circuit. Electrons continuously flow through a closed circuit

Basic Concepts:

CHARGE -q(t)

  • Basic quantity in an Electric circuit and defined as electrical property of materials.
  • Each electron carries energy with it.
  • Composed of 2 charges: Negative (electron) and Positive (proton)
  • Measured in coulumbs (c)
  • One electron has a charge of -1.602 * 10 ^-19 c
  • Charge may be constant or varrying.

currentformula

In a circuit, the total Charge Q, is calculated by finding how much charge flows in the circuit: ( derive the formula given)

 

 

 

CURRENT – i(t)

  • Charge flow rate. In electric circuits this charge is often carried by moving electrons in a wire.
  • Measured in Ampere (A)
  • There are two types of current: DC (Direct Current) and AC (Alternating Current)images

VOLTAGE -v(t)

Is the electric potential difference between two points, or the difference in electric potential energy of a unit charge transported between two points.

  • charge rate of doing work
  • Energy required to move a unit charge through an Element
  • Measured in Volts (v)

vcr1

POWER p(t)

  • time rate of doing work
  • measured in watts

Power can be absorbed or supplied by circuit elements.

Positive power- element absorb power

Negative power- element supplies power

  • sign determined by voltage
  • An ideal circuit is ΣPsupplied + ΣPabsorbed = 0

 

Electric_load_animation_2Electric_power_source_animation_2

ENERGY 

       Is energy newly derived from electrical potential energy. When loosely used to describe energy absorbed or delivered by an electrical circuits “electrical energy” refers to energy which has been converted from electrical potential energy. – Measured in joules (J).

battery


CIRCUIT ELEMENTS

an element is the basic building block of a circuit.

Types of Elements:

  1. Active Elements – Capable of generating energy. Examples are batteries & generators. –Negative Power
  2. Passive Elements – Absorbs energy. Examples are capacitors &inductors. – Positive Power

SOURCE 

  • 2 types of source: Independent and dependent Source.

Independent Source- does not depend to other elements to supply voltage or current.

Dependent Source- Depend to other elements to supply Voltage or Current.



EXERCISES

1. Determine the current flowing through an element if the charge flow is given by: q(t) = (9t² +2t-2) C

Solution

2(t) = dq/dt = 18t +2

2. Find the charge q(t) flowing through a device if the current (i(t)) = (2t + 5) mA and                   a(0)=0.

Solution

i=dq/dt                                                 q(t) = t² + 5t +c                             q(0)= (0)²+ 5(0) +c+0

∫dq= ∫i dt                                             q(0) =0                                           c=0

q= ∫dt                                                    q(0)=t² +5t +c=0

3. The change entering a certain element is shown. Determine the current at:
t= 1 ms, 6 ms and 10 ms.

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(a) At t = 1ms,
i= dq/dt = 80/2=  40 A
 (b) At t = 6ms,
 i= dq/dt= 0 A
 
(c) At t = 10ms,
 i= dq/dt = 80/4 = 20 A


LEARNINGS :
This is our first topic in our first Electrical subject.We all know about electricity. It is the flow electrons. Hence the word electricity is derived from the word electrons. A battery itself doesn’t work, if you hold it up in air, there would be no passage of electric current. Hence you need a circuit. In Simple terms an electronic circuit is a closed pathway for electrons to flow.
The Electric Current in a circuit flows from positive to negative while electrons flow from negative to positive. So when the switch is on the path is complete and electricity passes through enabling the bulb to light up, while when the switch is not on, there is a break in the flow of electricity and the bulb does not light up.
You would find circuits in every electrical device you use – from your switch board, television, refrigerator to your laptop.

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