Series Circuits

What is a Series Circuit ?
As the name indicates, a circuit in which all the circuit components are arranged in series is called a Series Circuit. As you can see in the fig below, there is a voltage source Battery and four Resistors(R) are connected in series.


Why Current (I) is same at all points in a Series Circuit?
This is because, when the voltage is applied to a series circuit, the free electrons start moving from negative terminal to the positive terminal. The free electrons are continuously replaced by free electron flow from an adjacent point. Therefore, at all the points the electron drift is same and at same speed. That is why Current is same in all parts of a Series Circuit.
And also there is just one current path through out the circuit. Therefore current cannot differ at any point.

How to find the Equivalent Resistance in a Series Circuit?
When a series circuit is connected across a voltage source, the free electrons forming the current must drift through all the series resistance. This path is the only way the electrons can return to the battery. So the total opposition to the current will be the combined resistance from all the resistances in the path. That means, the Equivalent Resistance is the sum of all resistances. 
R_Eq= R1 + R2 + R3 +.................etc


A combination of series resistance is often called a String
Let us look at an example :
R1 = 3kΩ
R2 = 10kΩ
R3 = 5kΩ

R_Eq= 3kΩ + 10kΩ + 5kΩ = 18kΩ
Therefore, 
I = V / R = 9 / 18 kΩ = 0.5 mA

Kirchhoff's Current Law( KCL)

Kirchhoff's Current Law( KCL) states that the total current  I_T  in the main line in a parallel circuit equals the sum of individual branch currents.
In the form of equation, KCL can be represented as

I_T = I₁ + I₂ + I₃ + I₄.............+ etc

Schematic Diagram can be shown as below. A parallel circuit with a voltage source of 6V and three resistors  R1, R2, R3 and total current  I_Total


How to find the equivalent resistance? 

Parallel Circuits, Equivalent Resistance

A parallel circuit is formed when two or more components are connected to the same voltage source. A common application of parallel circuits is typical house wiring to the power line, with many lights and appliances connected across the 120V source.

A basic parallel circuit with 2 resistors looks like this. In practical sense, the circuit can be imagined something like this(right fig)


How to find the Equivalent Resistance?
Equivalent resistance R_Eqcan be calculated in two ways. First, find the individual branch currents using Ohm's law. Then find the total current I_T by adding the individual branch currents.
I_T = I₁ + I₂ + I₃ + I₄......
Then R_Eq= V_A /  I_T


When a circuit consists of two resistors, the equivalent Resistance can be calculated as below.
In the fig above lets assume R1=40Ω, R2=60Ω
R_Eq= R1 X R2 / R1 + R2
R_Eq= 40 X 60 / 100 = 2400/100 = 24Ω

When a circuit consists of three resistors, and all three resistors are equal, then the equivalent Resistance can be calculated as below.

R1 = R2 = R3 = 60kΩ, then the equivalent Resistance can be calculated as below.
R_Eq= Value of one Resistance / Number of Resistances = 60kΩ / 3 = 20kΩ

When a circuit consists of many resistors, and all are of unequal values, then the equivalent Resistance can be calculated as below.
1 / R_Eq= 1 / R1 + 1/ R2 + 1/R3 + 1/ R4.........etc

 R_Eq= 1 / (1 / R1 + 1/ R2 + 1/R3 + 1/ R4.........etc)
     

Resistor Color Coding

As the carbon resistors are very small, the resistance values cannot be mentioned on them. Therefore a technique is used to represent the R values for such resistors. It is called Color Coding of Resistors.

The resistors are color coded with stripes of different colors. Be reading those stripes we can calculate the resistance value of the resistor. 

How to read the color stripes on the carbon resistors?

As shown in the fig, a common carbon resistor consists of 4 color bands on it.

1st Color Band - 1digit of Resistance value

2nd Color Band - 2nd digit of Resistance value

3rd Color Band - Value of Multiplier or power of 10

4th Color Band - Tolerance Value - Gold 5%

                                                        Silver 10%
If there is no color band for Tolerance it is 20%

Color bands on Resistors and their values?

Memorize these color bands and their corresponding values. 

[Tip to remember this code

B-0 B-1 R-2 O-3 Y-4 G-5 B-6 V-7 G-8 W-9

I remember this code using this sentence

BBROYGBVGW - B B ROY of Great Britain had a Very Good Wife]

Now let us see some examples :

1st Band - Green (5)

2nd Band - Brown (1)

3rd Band - Red(2) 

4th Band - Gold(5%)

So the resistance value of this resistor is

51X10²+/-5% = 5100+/-5% = 5.1 kohms with 5% Tolerance
With Tolerance the resistance value is 5125-5075ohms

    

1st Band - Brown (1)

2nd Band - Black (0)

3rd Band - Green(5) 

4th Band - Silver(10%)

So the resistance value of this resistor is

10X10⁵+/-10% = 1000 0006 +/-10% = 1M ohms with 10% Tolerance
With Tolerance the resistance value ranges between 1100 000-900 000 ohms

1st Band - Orange (3)

2nd Band - Orange (3)

3rd Band - Red(2) 

4th Band - Silver(10%)

So the resistance value of this resistor is

33X10²+/-5% = 3300+/-10% = 3.3 kohms with 10% Tolerance
With Tolerance the resistance value is 3630-2970ohms

Special Cases : Precision Resistor use FIve bands to represent the Resistance value. Here the first three bands represent the first three digits of the resistance. 4th band is the multiplier and last band is the tolerance value (Brown = +/-1%, Red = +/-2%, Green = +/-0.5%, Blue = +/-0.25%, Violet = +/-0.1%)

So here
1st Band - Orange (3)
2nd Band - Orange(3)
3rd Band - White(9)
4th Band - Black(0)
5th Band - Brown(1%)
The resistance value is 339 ohms with 1% tolerance

Scientific Notation, Engineering Notation, Metric Prefixes

What is the difference between Scientific Notation and Engineering Notation for expressing numbers ?
Both of them are the common forms of powers of 10 notation.


Scientific notation is expressing any number in the form of power of 10.
For eg. 1) 3510 can be written in the scientific notation as 3.5X10³
            2) 0.000000819 can be written in the scientific notation as 8.19X10^-7
Positive powers of 10 are used to indicate the numbers greater than 1 and negative powers are used to indicate the numbers less than 1.


Engineering Notation is similar to scientific notation except that in Engineering notation, the powers of 10 are always multiples of 3 such as 10³, 10⁶, 10⁹, 10^-610^-9, 10^-12 etc. 


Metric Prefixes : Metric Prefix is the name given to the powers of 10 used in Engineering Notation. In Electronics, these metric prefixes are used more commonly to express the values of current, resistance, voltage, power etc.


The SI prefixes are listed below

Prefix Symbol Factor Value yotta Y 1024 1 000 000 000 000 000 000 000 000 zetta Z 1021 1 000 000 000 000 000 000 000 exa E 1018 1 000 000 000 000 000 000 peta P 1015 1 000 000 000 000 000 tera T 1012 1 000 000 000 000 giga G 109 1 000 000 000 mega M 106 1 000 000  kilo k 103 1 000  hecto h 102 100 deka da 101 10 deci d 10-1 0.1 centi c 10-2 0.01 milli m 10-3 0.001 micro µ 10-6   0.000 001 nano n 10-9 0.000 000 001 pico p 10-12 0.000 000 000 001 femto f 10-15 0.000 000 000 000 001 atto a 10-18 0.000 000 000 000 000 001 zepto z 10-21 0.000 000 000 000 000 000 001 yocto y 10-24 0.000 000 000 000 000 000 000 001