Resistance - Important Concepts with Formula and Its Properties for JEE

Electrical resistance is the property of the material which offers a restriction to the flow of electric charge of a conductor when a potential difference is set up across the ends of the conductor. The cause of resistance is the collision of the charged particles due to the zigzag movement of the particles which results in the disturbance of the current flowing through the conductor. Due to the resistance, the dissipation of electrical energy will occur  and get converted into heat which further affects the electromotive force which results in a drop in the production of electric current.   

The reciprocal of the resistance is called conduction which is expressed in the unit named mho. The resistance of a wire is directly proportional to the length and inversely proportional to its cross-sectional area. Also, resistance depends upon the material of the conductor. 

In this article, an informational study has been carried out about the concept of the resistance definition, resistance formula, dimensional formula of resistance, factors affecting resistance, and the difference between resistance and resistivity.

Ohm's Law

The relationship of current with voltage in an electrical circuit at a certain temperature is governed by Ohm’s Law. Ohm’s law states that current is directly proportional to the potential difference across the conductor in an electrical circuit at a certain temperature.

• $V\propto I$

• V=IR

In the above relationship, the constant of proportionality is called resistance, V is the potential difference across the conductor (in volts) and I is the current flowing in the conductor. 

After rearranging the above relation, the obtained resistance formula is given as,

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

The unit in which resistance is expressed in Ohms. Electrical resistance is the restriction to the flow of electric current through the conductor in an electrical circuit.

Dimensional Formula of Resistance

The dimensional formula of the resistance is evaluated by substituting the dimensional formula of the potential difference and electric current in the relationship obtained from Ohm’s law. It is found as,

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

The dimensional form of potential difference (V)  = [M1L2T-3I-1]

The dimensional form of electric current (I) =[M0L0T0I1]

Therefore, the dimensional form of electric current is given by,

$\begin{align} &R=\dfrac{V}{I} \\ &R=\dfrac{\left[M^{1} L^{2} T^{-3} I^{-1}\right]}{\left[M^{0} L^{0} T^{0} I^{1}\right]} \\ &R=\left[M^{1} L^{2} T^{3} I^{2}\right] \end{align}$

Hence, the dimensional formula of electric resistance is [M1L2T-3I-2].

Factors Affecting Resistance

There are major factors that affect the resistance of the conductor in the electrical circuit. Some of the factors which affect the electrical resistance are given below:

• The Cross-Sectional Area of the Conductor

When the voltage is applied across the ends of the conductor, the movement of electrons offers countless collisions with the other electrons. In this case, the cross-sectional area of the conductor comes into play. 

If the area is larger, then there will be minimum collision occurring between the electrons which results in low resistance of the material. If the area is small, then the collision will be high and the resistance will be more in the conductor.

• Length of the Conductor

The length of the conductor is directly proportional to the resistance of the material. As the length of the conductor increases, the collision of the electron going to take place will be more in a longer length of the conductor. Hence, the resistance will be more. 

• The Temperature of the Conducting Material

The resistance of the material will increase if the temperature of the conducting material rises. As the temperature of the conductor increases, the movement of the electrons inside the conductor will increase due to which the rate of collision increases. Since the rate of collision has increased then the resistance offered to the flow of electric charge will be more.

• The Material of the Conductor

The material of the conductor also hampers the resistance offered by the conducting material. This property of the material is known as the resistivity of the material. Those materials having high resistivity will have higher resistance and those having low resistivity will have low resistance offered to the movement of electrons. 

What is Resistivity?

Electric resistivity is the property of the material which is defined as the “electrical resistance of a material offered per unit length and unit cross-sectional area at a certain temperature. The resistivity of the material is denoted by ρ”. The resistivity of the insulator is very high while the resistivity of the conductor is very low. The SI unit of electrical resistivity is ohms-meter. 

Mathematical Derivation of Resistivity

The electrical resistance of a conductor is directly proportional to the length of the conductor. The resistance is inversely proportional to the cross-sectional area of the conductor. Mathematically, it is written below; 

• $R \propto \dfrac{L}{A}$

• $R=\rho \dfrac{L}{A}$

The resistivity formula which is shown below,

$\rho=\dfrac{RA}{L}$

The constant of proportionality is known as resistivity which is expressed in the unit of Ohm-meter, L is the length of the conductor and A is the cross-section area of the conductor. 

The conducting ability of the material is given by the resistivity of the material. The resistivity of the material also depends upon the temperature as well as the electronic structure of the material. It has been found that the resistivity of the material increases with the increase in temperature. The reciprocal of the resistivity is known as conductivity. 

Difference Between the Resistance and Resistivity

Conclusion

This article concludes with interesting information regarding the concept of resistance and resistivity. The article starts with the introduction, formula, and dimensional formula of the electrical resistance. This article also explained the factors which affect the resistance of the material and the material property termed resistivity. It has also explained the difference between the electrical resistance and resistivity of the material. This article also covers the entire concept of resistance from a diagram point of view for a better understanding of the concept.