The Basics
Voltage or Potential Difference.
A linear circuit is a type of a circuit , whose response (in our case) if plotted on graph gives us a linear function
However a nonlinear circuit is a circuit whose output if sketched on a graph is not linear
No!!!!!
Although in real life most of the elements act as a nonlinear device. HOWEVER their behavior is very close to linear devices. Our main interest is to analyze circuits in linear manner is because, nonlinear calculations are easy. Many Linear circuits can be converted to nonlinear circuits by analyzing their behaviors’
Introduction to Circuits
A simple question may rise in our mind that , when human would have first discovered charged or current or electricity . The very first answer to this question that human may have realized that there is something like charge or electricity when they would have seen electricity light sparks on clouds in thunderstorms.
They would have experienced it when they would have taken of some wool clothes, and have seen sparks. The same phenomena would have been observed when they would have touched some metal in winters,
The force of attraction or repulsion between charges would have come to mind when they would have rubbed different materials
Structure of Matter.
The world around us is created form small elements known as the atoms. Atom helps us to realize the basic theory of charge. If we talk about basic structure of atom we know that it have a nucleus, which consists of protons and neutrons . The nucleus is surrounded by electrons. Different atoms can have different number of electron based on the atomic number
Atom and its Components
Atoms can be divided in general in to four parts .
1. Electrons
2. Nucleus
a. Proton
b. Neutron
Electrons
The electrons have negative charge on them . And movement of the electrons present in valence cell are the general reason of electricity .
Nucleus
Nucleus houses neutron and protons
Protons
Proton is the positive charge. For a long time it was considered by scientist that, the movement of proton caused current flow .
Below is a specific chart that help indicates different values of particles
Remember
Like charges always repel, and Opposites attracts
Types of Materials
Materials can be divided in 3 types. (how ever scientists will be coming up new types and subgroups every new day , but for this text , we are fine with three).
They are Conductors, Semiconductors and Insulators
Charge and Current
We have already discussed the charged particles that are present inside a atom.
So if start gathering lot of positive particles on one plate we will end up with a pool of positive charged particles
If now we apply some force to push this charge ….. the charge will moving forward .
So now the charge becomes “MOVING CHARGE”. Same scenario can be applied on negative charged particles.
Now we have three points to discuss from above discussion .
· Charge
· Moving Charge
· And force that move charge
Charge
In SI system the unit of charge is coulomb ( C ) . One Coulomb has a charge if we collect 6.24×1018 Electrons or
If we gather 624000000000000000000 electrons .
We will have one Coulomb. This is a fairly large amount
Now it can be due to positive and negative charges.
The Quantity of charge is represented by Q or q
Current:
The moving Charge is called “Current”
It have a unit of Ampere
Or
It is the amount of charged that is passed through point A to Point B in a particular time and is represented by I
I=Q/t
A real life example to understand in our power lines. Think how they transfer charge to our houses
We can accumulate charge by transferring electrons. The amount of charge is denoted by the letter Q and its unit is the Coulomb (denoted C).
Normally constants levels of charge , voltage and current and other quantities are represented by capital Alphabets like
Current AC
In above material we talked about current . as amount of charge passed in a wire in particular time. How ever we may have cases , where charge is also varying. Hence we will have a charge changing its value continuously in such cases. In such cases the current may be defined as “RATE OF CHANGE OF CHARGE W.R.T TIME”
Note the values here are represented by small vales. Such current is called AC Current
Some errors while representing current
For a time depending current we may define it as,
i(t) = 
[AMPERE]
Or
q(t)=
[COULOMB]
Example 1
Example 2
Example 3
The Current in a certain conductor is 40mA.
a. Find Total Charge in wire passed in 1.5 Second
b. Find total Number of Electrons
Example 4
Example 5
–
(t=1 and t =3)
=96 C
Voltage or Potential Difference
To push Charges, for creating (flow of Charges) current. We need some force.
How this force is created.
This force is created due to potential difference
The charges or any other quantity always moves from higher potential to lower potential (in case of water , it is called pressure). Similar in our case, charges from higher potential moves to lower potential . In case of electricity this is called voltage
So now we have a reservoir of charges, (Battery). Some force is applied to move these charges (voltage). Now the moving charges (current) flow in some pipe (wire) and reaches destination (load e.g. bulb).
Voltage
The voltage (or potential difference) between two points is defined as one volt if it requires one joule of energy to move one coulomb of charge from one point to another.
v=
[Volts, V]
Can Voltage be positive or negative?
Yes it can be positive or negative (called polarity of voltage).
Battery
Find Potential Difference
Types of Voltage sources
1. A voltage source is a two terminal device which can maintain a fixed voltage. An ideal voltage source can maintain the fixed voltage independent of the load resistance or the output current.
Battery
A battery is a device that converts chemical energy to electrical energy .
A battery has a fixed life time , and depend upon the amount of current it supplies.
Life (hours) = ampere hour rating/Ampere of Current Produced
A battery with 60 A h rating can supply 1 Ampere for 60 Hours and 60 Amperes for 1 hour.
Generator
A generator is a device that converts mechanical energy into electrical energy. How ever the out put is AC .(will be discussed later)
Solar Cell
A solar cell, or photovoltaic cell, is an electrical device that converts the energy of light directly into electricity by the photovoltaic effect
Conventional Current
The nice thing about standards is that there are so many of them to choose from
Initially when researches started developing formulas and started studying behavior of electronic circuits. They assumed that current moved from positive to negative terminal. So the standard was made accordingly.
However later on it was discovered that the current is due to moving of charge from negative terminals to positive terminals .
But however the it was decided that same formulas will be used as they gave results accurately, and all theories were still accurate. The only difference was direction, which was changed. So it was decided to keep the same convention.
Drawing Circuits .
Any physical circuit can easily be represented by using symbols and schematics. Here is a list of symbols that are commonly used for electric circuit .
So lets say we have a battery that is connected to a bulb. And we need to redraw it so .
We may conclude that in the end every loads either a bulb, lamp or motor may be represented by a resistor. How ever many electrical components have their own symbols
Case Study 1
Charging a Car battery
There are several reasons your car battery could die
Leaving your car for long period of times (without starting it)
Extreme temperatures
Leaving lights , ACs or any other load on for long time, when car is not in use
In order to charge a dead car battery, a set of jumper cables and a functional car with a charged battery is required
The positive terminal current leaves the positive terminal of charger or battery (Supplying energy ) and enter the positive terminal of dead battery absorbs it
Power
Power is a product of voltage and current , or amount of energy used to do a work .
P= Vx I [watts]
Where v=
And I (t) =
P = 
P=
[watts]
Using the above equation we can easily derive Work done
w(t)=
[watts]
or
w(t)=
[watts]
Sign conventions for power
We know that a battery is represented some thing like this , where we assume or say that the battery have two terminals , positive and negative, and the power leaves the positive terminal of a battery
We know that power can be absorbed (like absorbed by by a bulb to give us light or by a fan to give us air) and can also be supplied , like by a battery .
So we need to summarize a way that can tell us that if the power is being absorbed or supplied . so a simple rule is stated below
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