In the realm of electrical engineering and physics, the concepts of resistance, resistivity, conductance, and conductivity form the fundamental pillars upon which the behaviour of materials and electrical circuits is understood and engineered. These properties govern how materials respond to the flow of electric current and are crucial for designing efficient electronic devices, wiring systems, and communication networks. This article aims to delve into each of these concepts, elucidating their definitions, interrelationships, and practical implications.
Resistance:
Resistance is a fundamental property of any material that impedes the flow of electric current.
It is denoted by the symbol ‘R’ and is measured in Ohms (Ω).
According to Ohm’s law, the resistance of a material is directly proportional to the voltage applied across it and inversely proportional to the current flowing through it, expressed by the formula:
R = V / I
where, V is voltage and I is current.
Materials with high resistance restrict the flow of current, while those with low resistance allow current to flow more easily.
Resistivity:
Resistivity, represented by the Greek letter rho (ρ), is an intrinsic property of a material that quantifies its resistance to the flow of electric current.
It is determined by the material’s composition, structure, and temperature. Resistivity is measured in Ohm-meters (Ω·m) and is related to resistance through the formula:
R = ρ * (L/A)
where,
R is resistance,
ρ is resistivity,
L is the length of the material, and
A is its cross-sectional area.
Resistivity:
Materials with high resistivity, such as insulators, offer significant opposition to the flow of current, while conductors have low resistivity, facilitating the easy flow of electricity.
Conductance:
Conductance is the reciprocal of resistance and quantifies a material’s ability to conduct electric current. It is denoted by the symbol ‘G’ and is measured in Siemens (S).
Conductance is mathematically expressed as,
G = 1/R
where R is resistance.
Thus, materials with high conductance offer less opposition to current flow, while those with low conductance exhibit greater resistance.
Conductivity:
Conductivity is a measure of how well a material conducts electric current and is the reciprocal of resistivity. It is denoted by the symbol sigma (σ) and is measured in Siemens per meter (S/m).
Conductivity is related to resistivity through the equation:
σ = 1/ρ
Materials with high conductivity, such as metals, allow electric current to flow easily, whereas materials with low conductivity, such as rubber or glass, impede current flow.
Interrelationships:
Resistance, resistivity, conductance, and conductivity are interrelated properties governed by the material’s intrinsic characteristics. Conductivity and resistivity are inversely related, as are resistance and conductance. Materials with high conductivity have low resistivity and vice versa. Similarly, materials with high resistance exhibit low conductance, while those with low resistance have high conductance.
Practical Implications:
Understanding these electrical properties is crucial in various practical applications. For instance, in designing electrical circuits, engineers need to select materials with appropriate resistivity and conductivity to ensure optimal performance. High-resistivity materials are used in insulators to prevent leakage of current, while low-resistivity materials are employed in conductors to facilitate efficient current flow. Moreover, knowledge of these properties is vital in fields such as electronics, telecommunications, power distribution, and materials science.
Conclusion:
Resistance, resistivity, conductance, and conductivity are fundamental concepts that underpin the behaviour of materials in the presence of electric current. By comprehending these properties and their interrelationships, engineers and scientists can design efficient electrical systems, develop advanced electronic devices, and innovate in various technological domains. A deeper understanding of these concepts enables the optimisation of materials and circuits, contributing to advancements in diverse fields and enhancing the efficiency and reliability of electrical systems.
Problem :
Question : If cross-sectional area A is 2 x 10-7 m2 , resistance R = 2 Ohm and length L = 10 m. Find out resistivity, conductance and conductivity.
Solution :
