First Order Circuits

FUNDAMENTAL OF ELECTRIC CIRCUITS

WHAT I HAVE LEARN IN CIRCUITS 1 

INTRODUCTION :

THIS BLOG IS ALL ABOUT WHAT I HAVE LEARN IN CIRCUITS 1 THIS CONTAINS THE TOPIC THAT OUR TEACHER TEACH US FROM CHAPTER 1 TO CHAPTER 7. IT IS ALL ABOUT THE THING OF WHAT I HAVE LEARN, BUT NOT ALL OF THEM I UNDERSTAND BECAUSE SOME OF  THE TOPICS ARE QUITE HARD TO UNDERSTAND BUT AT LEAST THE THINGS THAT I HAVE LEARNED ARE THE MOST IMPORTANT THING. THIS BLOG SEEKS TO REVIEW THE TOPICS THAT OUR TEACHER THOUGHT US AND ALSO TO GAIN MORE KNOWLEDGE AND EDUCATION IN ORDER TO PROCEED TO THE NEXT LEVEL OF THE WORLD OF COMPUTER ENGINEERING.

 THIS ARE THE TOPICS THAT OUR TEACHER THOUGHT US 

CHAPTER 1: BASIC LAWS

This topic focus on the basic theory in electric circuit and on how do the circuits work and the terms that are use. 

these are the terms and definition that used in circuits.

Charge- A form of charge, designated positive, negative, or zero found on the elementary particles that make up all known matter. Particles with electric charge interact with each other through the electromagnetic force creating electric fields, and when they are in motion, magnetic fields

Current - An electric current is a flow of electric charge. Electric charge flows when there is voltage present across a conductor.

Voltage - is a representation of the electric potential energy per unit charge. Voltage is a scalar quantity. The SI unit of voltage is the volt, such that 1 volt = 1 joule/coulomb.

Power - electric power is the rate at which electric energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second.

Circuit element - an element is the basic building block of a circuit. 
Types of Elements:

Active elements - capable of generating energy (i.e. batteries generators).
Passive Elements - absorbs energy (i.e. resistor,capacitors, and inductors).
Voltage and current sources - the most important active elements.

Energy - The capacity for work or vigorous activity; vigor;power and is measured in joules. 

A source is divided in to two sources:

independent source -Does not depend to other elements to supply voltage or current

dependent source -  depends on the element to supply voltage.

Constant voltage source - Voltage same for all elements.

 Constant current source -Current same throughout the circuits.

CHAPTER 2  : OHM'S LAW KCL AND KVL 

Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points. introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship.

V=I X R (Voltage = Current multiplied by Resistance)
R= V / I (Resistance = voltage divided by current )
I = V / R (Current = Voltage divided by resistance)

Elements of electric circuits can be interconnected in several way.

Branch: Represents a single element   (i.e. voltage, resistor & etc)

Node:   The meeting point between two   or more branches.

Loop:  Any closed path in a circuit.

Kirchhoff's Current Law (KCL)

can be use to determine an unknown circuit value. KCL can be used to check your arithetic calculation as they relate to a parallel branch.

KCL states that the sum of the current entering a node is equal to the sum of the current leaving the node.

example ;

It = Ir1 + Ir2 + Ir3

use  I = V/R to substitute for the currents

= 4mA + 3mA + 2mA

= 9mA

KIRCHHOFF'S CURRENT LAW (KVL)

Kirchhoff's voltage law can be determine an unknown circuit value. KVL can also be used to check your arithmetic calculations as they relate to a series circuit. 

KVL states that the sum of the voltage "drops" around a closed loop will equal the applied voltage.

Vt = Vr1 + Vr2 + Vr3

= 3V + 4V + 5V

=12V

the voltage around 3k is 3v, at 4k is 4v and 5k is 5v because the current is 1mA you can still apply the ohm's in using kvl.

SERIES AND PARALLEL RESISTORS 

Series circuits

A series circuit is a circuit in which resistors are arranged in a chain, so the current has only one path to take. The current is the same through each resistor. The total resistance of the circuit is found by simply adding up the resistance values of the individual resistors:

equivalent resistance of resistors in series : R = R₁ + R₂ + R₃ + ...

Example:
A series circuit is shown in the diagram above. The current flows through each resistor in turn. If the values of the three resistors are:

With a 10 V battery, by V = I R the total current in the circuit is:

I = V / R =
10 / 20 = 0.5 A.
The current through each resistor would be 0.5 A.

Parallel circuits

A parallel circuit is a circuit in which the resistors are arranged with their heads connected together, and their tails connected together. The current in a parallel circuit breaks up, with some flowing along each parallel branch and re-combining when the branches meet again. The voltage across each resistor in parallel is the same. The total resistance of a set of resistors in parallel is found by adding up the reciprocals of the resistance values, and then taking the reciprocal of the total:

equivalent resistance of resistors in parallel: 1 / R = 1 / R₁ + 1 / R₂ + 1 / R₃ +...

A parallel circuit is shown in the diagram above. In this case the current supplied by the battery splits up, and the amount going through each resistor depends on the resistance. If the values of the three resistors are:

With a 10 V battery, by V = I R the total current in the circuit is: I = V / R = 10 / 2 = 5 A.

The individual currents can also be found using I = V / R. The voltage across each resistor is 10 V, so:

I₁ = 10 / 8 = 1.25 A
I₂ = 10 / 8 = 1.25 A
I₃=10 / 4 = 2.5 A

Note that the currents add together to 5A, the total current.

A parallel resistor short-cut

If the resistors in parallel are identical, it can be very easy to work out the equivalent resistance. In this case the equivalent resistance of N identical resistors is the resistance of one resistor divided by N, the number of resistors. So, two 40-ohm resistors in parallel are equivalent to one 20-ohm resistor; five 50-ohm resistors in parallel are equivalent to one 10-ohm resistor, etc.

When calculating the equivalent resistance of a set of parallel resistors, people often forget to flip the 1/R upside down, putting 1/5 of an ohm instead of 5 ohms, for instance. Here's a way to check your answer. If you have two or more resistors in parallel, look for the one with the smallest resistance. The equivalent resistance will always be between the smallest resistance divided by the number of resistors, and the smallest resistance. Here's an example.

You have three resistors in parallel, with values 6 ohms, 9 ohms, and 18 ohms. The smallest resistance is 6 ohms, so the equivalent resistance must be between 2 ohms and 6 ohms (2 = 6 /3, where 3 is the number of resistors).

Doing the calculation gives 1/6 + 1/12 + 1/18 = 6/18. Flipping this upside down gives 18/6 = 3 ohms, which is certainly between 2 and 6.

Circuits with series and parallel components

Many circuits have a combination of series and parallel resistors. Generally, the total resistance in a circuit like this is found by reducing the different series and parallel combinations step-by-step to end up with a single equivalent resistance for the circuit. This allows the current to be determined easily. The current flowing through each resistor can then be found by undoing the reduction process.

General rules for doing the reduction process include:

1. Two (or more) resistors with their heads directly connected together and their tails directly connected together are in parallel, and they can be reduced to one resistor using the equivalent resistance equation for resistors in parallel.
2. Two resistors connected together so that the tail of one is connected to the head of the next, with no other path for the current to take along the line connecting them, are in series and can be reduced to one equivalent resistor.

Finally, remember that for resistors in series, the current is the same for each resistor, and for resistors in parallel, the voltage is the same for each one.

CHAPTER 4

WYE TO DELATA TRANSFORMATION 

We don’t have to memorize this also. The easy way to remember is, each resistor in the Delta Network is the sum of all possible product formation of Wye network’s resistors taken two at a time, divided by the opposite Wye resistor.

CHAPTER 5 : NODAL AND MESH ANALYSIS 

       In this chapter we will develop two very powerful methods for analyzing any circuit: The node analysis and the mesh analysis. These methods are based on the systematic application of Kirchhoff’s laws. In nodal analysis, the unknowns are the node voltages. In mesh analysis, the unknowns are the mesh currents. Nodal analysis and mesh analysis provide approaches for defining a reduced number of unknowns and solving for these unknowns.

Mesh Analysis

          The mesh method uses the mesh currents as the circuit variables. The procedure for obtaining the solution is similar to that followed in the Node method and the various steps are given below.

1.  label all circuit parameters and distinguish the unknown parameters from the known.
2. Identify all meshes of the circuit.
3. Assign mesh currents and label polarities.
4. Apply KVL at each mesh and express the voltages in terms of the mesh currents.
5. Solve the resulting simultaneous equations for the mesh currents.
6. Now that the mesh currents are known, the voltages may be obtained from Ohm’s law.

Nodal Analysis

          It is a very powerful approach for circuit analysis and it is based on the application of KCL, KVL and Ohm’s law. The procedure for analyzing a circuit with the node method is based on the following steps.

1. label all circuit parameters and distinguish the unknown parameters from the known.
2. Identify all nodes of the circuit.
3. Select a node as the reference node also called the ground and assign to it a potential of 0 Volts. All other voltages in the circuit are measured with respect to the reference node.
4. Label the voltages at all other nodes.
5. Assign and label polarities.
6. Apply KCL at each node and express the branch currents in terms of the node voltages.
7. Solve the resulting simultaneous equations for the node voltages.
8. Now that the node voltages are known, the branch currents may be obtained from Ohm’s law.

CHAPTER 6 SUPER POSITION,TRANSFORMATION, THEVENIN AND NORTON THEOREM

The basic concept of the superposition method is to analyze a circuit, one source at a time. Using the superposition method we remove all the independent sources, except one, and analyze the circuit for that one. Then we repeat the procedure for another source, and so on. after the results by each, we sum up the single source results. 

in removing source, we should know that if you remove a voltage source replace it with short circuit. And if it is a current source replace it with a current source.

Thevenin's Theorem

          Thevenin’s theorem states that at a linear two-terminal circuit can be replaced by any equivalent circuit consisting of a resistor (RTH) where (VTH) is the open circuit voltage the terminals (RTH) is the input or equivalent resistance at the terminals when the independent sources are turned off . Thevenin's Theorem states that we can replace entire network by an equivalent circuit that contains only an independent voltage source in series with an impedance (resistor) such that the current-voltage relationship at the load is unchanged. 

How to find Thevenin's Equivalent Circuit? 

If the circuit contains Resistors and Independent sources:

1) Connect an open circuit between a and b. 

2) Find the voltage across the open circuit which is Voc. 

 Voc = Vth. 

3) Deactivate the independent sources. 

Voltage source - open circuit 

Current source - short circuit

4) Find Rth by circuit resistance reduction 

If the circuit contains Resistors and dependent sources or independent shorces
 1) Connect an open circuit between a and b.
2) Find the voltage across the open circuit which is Voc.  (Voc = Vth. )

If there are both dependent and independent sources.
3) Connect a short circuit between a and b.
4) Determine the current between a and b.
5) Rth = Voc / Iab

If there are only dependent sources.
3) Connect 1 Ampere current source flowing from
terminal b to a. It = 1 [A]
4) Then Rth = Voc / It = Voc / 1 

Norton's Theorem

          Norton’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a current source IN in parallel with a resistor RN where IN is the short-circuit current through the terminals and RN is the input or equivalent resistance at the terminals when the independent sources are turned off. Norton's Thereom is identical to Thevenin's Theorem except that the equivalent circuit is an independent current source in parallel with an impedance resistor. Therefore, the Norton equivalent circuit is a source transformation of the Thevenin equivalent circuit. 

How to find Norton's Equivalent Circuit?

If the circuit contains You should do Resistors and independent sources:
1) Deactivate the independent sources.
Voltage source  -  open circuit
Current source  -  short circuit
2) Find Rt by circuit resistance reduction
3) Connect an short circuit between a and b.
4) Find the current across the short circuit which is Isc. 

If the circuit contains Resistors and Dependent sources or Independent sources

1) Connect a short circuit between a and b.
2) Find the current across the short circuit which is Isc.
 Isc = In.

If there are both dependent and independent sources.
3) Connect a open circuit between a and b.
4) Determine the voltage between a and b. Voc = Vab
5) Rn = Voc / Isc

If there are only dependent sources.
3) Connect 1 Ampere current source flowing from
terminal b to a. It = 1 [A]
4) Then Rn = Voc / It = Voc / 1 

here are some of the examples in youtube to better understand in solving thevenin and nortons theorem

THEVENINS THEOREM

NORTONS THEOREM 

CHAPTER 7 : CAPACITORS AND INDUCTORS

CAPACITORS

• Capacitance is a measure of a component's ability to store charge.
• A capacitor is a device specially designed to have a certain amount of capacitance.
• This ability to store charge means that capacitors can be dangerous. Some common electronic devices, such as televisions, contain large capacitors that can hold a deadly charge long after the device has been turned off and unplugged. Just as you should always assume that a firearm is loaded, you should always assume that a capacitor is charged.

The amount of charge (q) stored is directly proportional to the applied voltage (v).

q = Cv

C = known as the capacitance of the capacitor, 

measured in Farad.

Capacitors in Parallel 

Suppose you have two or more capacitors connected in parallel, as in the picture above. To find their total capacitance, simply add the individual capacitances:

CT = C1 + C2 +  ... + Cn

Capacitors in Series

Suppose you have two or more capacitors connected in series, as in the picture above. To find their total capacitance, use the reciprocal formula:

 CT = 1 ÷ (1÷C1 + 1÷C2 +  ... + 1÷Cn)

INDUCTOR

• An inductor is a device designed to have a certain amount of inductance.
• Here's the schematic symbol for an inductor: Inductor symbol.    
• Most of the inductors in our labs look similar to this: Inductor photograph 
• Typical inductors found in electronic equipment are in the microhenry (μH) or millihenry (mH) range. Recall that micro- means 10-6 and milli- means 10-3.

Inductors in Series

Suppose you have two or more inductors connected in series, as in the picture above. The total inductance is equal to the sum of the individual inductances:

LT = L1 + L2 +  ... + Ln

Inductor in Parallel

Suppose you have two or more inductors connected in parallel, as in the picture above. To find the total inductance, use the reciprocal formula:

First Order Circuits

A first-order circuit can only contain one energy storage element (a capacitor or an inductor). The circuit will also contain resistance. So there are two types of first-order circuits

• RC Circuit
• RL Circuit

Source-Free Circuit

• A source-free circuit is one where all independent sources have been disconnected from the circuit aftersome switch action. 
• The voltages and currents in the circuit typically will have some transient response due to initial conditions (initial capacitor voltages and initial inductor currents).

• A source-free RC circuit occurs when its dc source is suddenly disconnected. 
• The energy already stored in the capacitor is released to the resistors.

CONCLUSION FOR THIS BLOG 

So far this are the things that i have learn a little bit in circuits 1 I apologize that some of the sources came from the internet and and some of it still i don't understand a little but at least i know the basics on how to solve it and what is the purpose of the circuits theories. But I hope that i can pass the subject in order to proceed and i can learn more about circuits. THANKS FOR VIEWING !! :D