Resistance – What is it? Definition, Unit, Symbol, Law, Formula

What is Resistance?

Definition: Electrical resistance or Resistance is the property of a material or substance (like a conductor), which offers some obstruction opposite to the flow of electrons through the material or substance. It is denoted by the letter R.

I simple words, It is an opposing force that restricts the flow of the electron through the material or substance.

When the voltage or potential difference is applied across a conductor, then the free electrons start moving. While the electrons moving, they collide with each other. Due to collision, the rate of flow of electrons is restricted, which offers some obstruction opposite to the flow of electrons through the material or substance. Due to collision, the rate of flow of electrons is restricted, which offers some obstruction opposite to the flow of electrons through the material or substance.

We know that the flow of electrons is the cause of the flow of electric current. Due to the restriction of the flow rate of electrons, the flow rate of electric current is also restricted. So, this obstruction offered by material or substance to the flow of electric current is called resistance.

Unit of Resistance

Resistance is measured in ohm. This is the SI unit of resistance. Ohm is represented by a greek symbol Ω (omega).

Definition of 1 Ohm Resistance: If a potential difference (voltage) of one volt (1V) is applied across two ends of a conductor and one ampere (1A) current flows through it, then the resistance of that conductor is said to be one ohm.

So, in the SI system, one ohm is equal to one volt per ampere. It can be expressed as

The unit ohm is basically used for moderate resistance values, but large and small resistances values can be expressed in milli-ohm, kilo-ohm, mega-ohm, Giga Ohm, etc.

The value of large and small resistance units is converted to ohm units, shown in the below table.

Resistance Symbol

Two main types of circuit symbols are used to represent electrical resistance. The most common symbol is a zig-zag line which is widely used in North America. The other circuit symbol is a small rectangle box with two terminals, which is widely used in Europe and Asia, it is termed the international resistor symbol. The circuit symbols are shown below.

Factors Affecting Electrical Resistance (Laws of Resistance)

Laws of resistance give the four factors. These factors are affecting the Electrical resistance of conducting material.

First Law

The First Law states that “the resistance (R) of conductive material is directly proportional to the length (L) of the material”. According to the first law, the resistance of the conducting material increases with the increase in the length of the conducting material and decreases with the decrease in the length of the conducting material. It can be expressed as,

R ∝ L……… (eq. 1)

Second Law

The Second Law states that “the resistance (R) of conductive material is inversely proportional to the cross-sectional area (A) of that material”. According to this law, the resistance of conductive material increases with the decrease in the cross-sectional area of conductive material, and the resistance decreases with an increase in the cross-sectional area of conductive material. It can be expressed as,

R ∝ 1/A……… (eq. 2)

Third Law

This Law states that “the resistance value of the conducting material depends upon the nature of that material”. For example, two wires having the same length and cross-sectional area, but they are made up of different types of materials. That’s why they have different resistance values.

Fourth Law

The Fourth Law states that “the resistance of the conducting material depends upon the temperature of it”. According to this law, the resistance value of a metallic conductor is increased with increases in the temperature of that metallic conductor.

Considering the first, second, and third law and neglecting the fourth law, we get a relation between Electrical resistance, Length cross-sectional area of the conductor. Mathematically, from the equation 1 and 2, the resistance of a conductor can be expressed as,

Resistance Formula and Calculation

There are three different basic formulas that can be used to calculate the Resistance in the circuit. Below the figure is the Voltage Formula Triangle, which shows the relation between Voltage (V), Current (I), Resistance (R), and Power (P).

Formula Type 1 (Ohm’s Law)
Ohm’s Law describes the relationship between resistance (R), voltage (V), and current (I) in an electrical circuit. According to Ohm’s law,

V = I x R

Thus, resistance is the ratio of supply voltage and current in a circuit.

R = V/I

Example

Question: if in the circuit below, the supply voltage is 12 V and the current of 2 A is flowing through the unknown resistance.  Calculate the unknown resistance value.

Solution:

Given Data: V = 12 volt, I = 2 Amp

According to ohm’s law,

R = V/I

Put the value of V and I in the above equation we get,

R = 12/2

    R = 6

Thus, by using the equation we get the unknown resistance value is 6 Ω.

Formula Type 2 (Voltage and Power)

This formula expresses the relationship between resistance (R), voltage (V), and Power (P) in an electrical circuit.

The power transferred is the product of supply voltage and electric current flow in an electrical circuit. Mathematically, it can be expressed as

P = V x I

According to ohm’s law, we know that I = V/R, now put the value of I in the above equation we get,

P = V²/R

From the above equation, we get resistance is the ratio of the square of the supply voltage and power. Mathematically,

R = V²/P

Example

Question: if in the circuit below, the supply voltage of 24 volts is applied across a 48W lamp. Calculate the Resistance offered by the lamp.

Solution:

Given Data: Voltage (V) = 24 V, Power (P) = 48 W 

According to the Formula,

R = V²/P

Put the value of V and I in the above equation we get,

R = (24)²/48

R = 12

Thus, by using the formula we get 12 Ω Resistance offered by the lamp.

Voltage Formula Type 3 (Power and Current)

This formula expresses the relationship between Resistance (R), Power (P), and Current (I) in an electrical circuit.

We know that,

P = V * I

According to ohm’s law, now put V = I * R in the above equation we get,

P = I² * R

So, Resistance is the ratio of power and square of the current. Mathematically, it can be expressed as

R = P / I²

Example

Question: if in the circuit below, the current of 2 A flowing through a 24 W lamp. Calculate the resistance offered by the 24 W lamp.

Solution:

Given Data: Current (I) = 2A, Power (P) = 24 W 

According to the Formula,

R = P / I²

Put the value of P and I in the above equation we get,

R = 24/ (2)²

R = 6

So, the answer is 6 Ω.