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)