Series v/s Parallel Electric Circuit : Resistance Calculation

Series and parallel electric circuits are very important in electrical engineering. If you are not familiar with series and parallel electric circuits then you are not a good engineer. Electrical series and parallel circuits are very important for every field of engineering. In this article We'll drive equation for equivalent resistance in series and parallel circuits and will solve numerical on series and parallel circuit. Before starting let's see basic terms related to electric circuits.

Basic Terms Related to Electrical Engineering/Circuits

Voltage, Current and Resistance are three main terms related to electric circuits. So lets see what they are ?
What is Voltage or Potential Difference ?
Voltage or potential difference is just like an electric pressure which makes electrons flow in an electric circuit. It is defined as the pressure which force electrons to pass in a circuit.
What is Current ?
The flow of charge (electrons or holes) in a circuit is termed as current. When voltage is applied to a circuit, depending upon the magnitude of the voltage some number of electrons start flowing in the circuit this is called current (Ohm's law). The direction of current is opposite to the flow of electrons.
What is Resistance ?
When electrons starts flowing in the circuit the electrons already available in the material starts opposing these electrons (opposite charges repel each other). This causes opposition to the flow of electric current this is called Resistance. In simple words, Resistance is the opposition offered by the material to the flow of current.

Series Electric Circuit : Resistance Calculation

A circuit is said to be series electric circuit if there is only one current path and second terminal of the first resistance is connected to first terminal of the next resistance.This arrangement is shown below :

We know that from Ohm's law : V=IR and as there is no other path in series circuit shown above so the same current will flow through resistances R₁ and R₂. Say the current is I. Now voltage across each resistance is given by :
V₁=I*R₁ and V₂=I*R₂. The total applied voltage V will be equal to V₁+V₂
Thus, V=V₁+V₂
It gives : V=I*R₁+I*R₂
V=I(R₁+R₂)
V/I=R₁+R₂
From Ohm's Law : V/I=R
R_eq=R₁+R₁
Where R_eq is the total resistance of the circuit. This is the relation of equivalent resistance in series circuit.

Parallel Electric Circuit : Resistance Calculation

From the above figure of parallel electric circuit it is clear that it has many current paths and at two points all current separate and then meet. This total current is called I, current in the circuit.
Now, from figure. I₁=V/R₁ and I₂=V/R₂ but from figure :
I=I₁+I₂
I=V/R₁+V/R₂ I/V=1/R₁+1/R₂
From Ohm's Law I/V=1/R thus :
1/R_eq=1/R₁+1/R₂
hence we have derived equation for equivalent resistance in parallel electric circuit.