## Resistors and Resistance

A resistor is a part of the electrical circuit that is responsible for limiting the flow of current in a circuit. Also, they can be used to supply a specific voltage to transistors. Resistors are manufactured in various ways. For instance, carbon composition-based resistors are the most commonly used ones. Another type called wire wound resistor made of Nichrome is used in circuits handling high current.

Resistance is the magnitude of opposition offered by a resistor, or any material for that matter of fact, to the flow of electrical current. It is denoted by the letter R and is expressed in Ohms $\left( \Omega \right)$.

Resistors are often used in a variety of combinations depending on the purpose and the requirements in the electrical circuit. This section will cover the combination of resistors basics, their importance, limitations, resistance in parallel formula and resistance in series formula i.e., the concept of equivalent resistance in these two combination of resistors basics.

## Ohm’s Law

According to Ohm’s law, given that parameters such as temperature and physical factors remain constant, the potential difference across the circuit will be directly proportional to the current flowing through that circuit. That is,

$V\propto I$

Now, the constant of proportionality R is the resistance in ohms i.e.,

V = IR

The above formula can be rearranged based on the parameter to be found as follows:

$I=\frac{V}{R}$

$R=\frac{V}{I}$

Also, electric power can be calculated using Ohm’s law. Since power is a product of potential difference and current, P = VI

Hence,

$P=\frac{{{V}^{2}}}{R}=\frac{{{I}^{2}}}{R}$

The major applications of Ohm’s law include the determination of resistance in combination of resistors basics, current, or voltage in an electrical circuit, determination and maintenance of adequate voltage drop, and diversion of current. However, Ohm’s law is not applicable for electrical components like the transistor, diode, etc. that are unilateral by nature. Also, for capacitors, the resistance might not be constant with respect to time. Hence, in these two cases, Ohm’s law cannot be used.

## Series and Parallel Connection and Series and Parallel Circuits

Often, it is important to connect two or more resistors in an electric circuit in order to get the desired results. Such a combination of resistors is aimed at either increasing or decreasing the equivalent resistance of the combination of resistors. The resistors are combined in series or in parallel and accordingly, the equivalent resistance will change. In the upcoming paragraphs, let us find out more about resistors in series, resistors in parallel, a combination of series and parallel resistors, and the equivalent resistance of combination of resistance.

## Series Combination

When two or more resistors are connected in series i.e., in sequence next to each other, the flow of electric current will be the same through each of the resistors. The potential difference in the electrical circuit is the sum of voltages across each resistor. The following diagram depicts series circuit examples.

Resistors Connected in Series

## Equation for Equivalent Resistance - Series

Let us consider two resistors R_{1} and R_{2} connected in series in an electrical circuit. Since the current flow across both the resistors is identical, the voltage across the entire circuit can be given as follows:

V = V_{1} + V_{2}

Substituting V = IR from Ohm’s law,

IR = IR_{1} + IR_{2}

IR = I(R_{1} + R_{2})

Hence, the resistance in series formula is given by R = R_{1} + R_{2}

## Advantages of Resistors in Series

The resistors in series offer the following advantages:

Simple design

Less expensive in comparison to parallel

The current flow will break if even one of the resistors stops working

The applications of resistors connected series include low power-based circuits, voltage divider circuits etc.

## Resistance in Parallel

When two resistors are connected in parallel, both the terminals of each of the resistors are connected to the respective terminals of other resistors connected in parallel to them.

The main difference between resistors connected in parallel and in series is that in the former type, multiple paths exist for the current flowing through the circuit. Hence, they are also called current dividers. Although the voltage drop across all the resistors is the same, the current flowing through each resistor might be different.

The diagram below depicts three resistors of resistance R_{1}, R_{2}, and R_{3} connected in parallel and the respective current I_{1}, I_{2}, and I_{3} flowing across them.

Resistors Connected in Parallel

## Equation for Equivalent Resistance - Parallel

Since the voltage drop across all the three resistors is the same, it can be written as

V_{1 }= V_{2 }= V_{3 }= V

Also, I_{T} = I = I_{1} + I_{2} + I_{3}

By Ohm’s law, $I=\frac{V}{R}$. Hence,

$I=\frac{V}{{{R}_{1}}}+\frac{V}{{{R}_{2}}}+\frac{V}{{{R}_{3}}}$

$I=V\left( \frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}}+\frac{1}{{{R}_{3}}} \right)$

Since $R=\frac{I}{V}$ ,

$R=\frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}}+\frac{1}{{{R}_{3}}}$ is the equation of resistance for a number of resistors connected in parallel.

It is to be noted that the total/equivalent resistance of resistors connected in parallel will be lower than the resistance of the smallest resistor present in the considered combination. Unlike resistors connected in series, repair of one resistor will not affect all the resistors connected in parallel.

## Summary

Most often, to achieve the desired results, more than one resistor will be used in an electrical circuit either in series, parallel, or both series and parallel. In such cases, the equivalent resistance is a very important term that gives the value of total resistance offered by a combination of resistors. For instance, the equivalent resistance of resistors connected in parallel is the sum of individual resistances. In contrast, the equivalent resistance formula of the resistance in parallel is the sum of reciprocals of the individual resistances.

## FAQs on Resistors and Resistance for JEE

1. How does the equation of resistors in series and parallel help in solving cases involving complex networks?

For solving complex networks, Kirchoff’s Laws for current and voltage can be used. Apply Ohm’s law to find the equivalent resistance for resistors connected in series and parallel. According to Kirchoff’s Law, the sum of currents leaving a particular node in a network is equal to zero. The first law is based on the electric charge conservation principle. Before equating the currents in a node to zero, the equivalent resistance formula and Ohm’s law will be very helpful in determining the total current coming from a particular circuit direction.

2. How many types of resistor combinations are there?

There are only two ways in which two or more resistors can be connected. One being a series combination and the other a parallel combination. Depending on the need of the electrical circuit, i.e., if a circuit demands high resistance, then the resistors can be combined in series. At the same time if a circuit demands low resistance, then the resistors can be combined in parallel combination.