The unit of electrical conductivity is

Question

Examoogle · Accepted Answer

mho/metre

Explanation: Electrical conductivity ($$\sigma$$) is a measure of a material's ability to conduct an electric current. It is the reciprocal of electrical resistivity ($$\rho$$) and is defined as the current density per unit electric field strength.

Working Principle: According to Ohm's Law in point form, $$J = \sigma E$$, where $$J$$ is current density ($$A/m^2$$) and $$E$$ is electric field intensity ($$V/m$$). Since resistance $$R = \rho \frac{l}{A}$$, conductivity is defined as $$\sigma = \frac{1}{\rho} = \frac{l}{RA}$$. Substituting units ($$meters / (ohm \cdot meters^2)$$), we get $$1/(\Omega \cdot m)$$, which is equivalent to $$S/m$$ or mho/meter.

Key Formulas: $$\sigma = \frac{1}{\rho}$$ — Conductivity as reciprocal of resistivity; $$\sigma = \frac{J}{E}$$ — Conductivity in terms of current density and electric field

Key Points: Conductivity is an intrinsic property of a material.; The SI unit of conductivity is Siemens per meter (S/m).; 1 Siemens = 1 mho (the older unit for conductance).; Conductivity varies with temperature, especially in metals and semiconductors.

Advantages: Helps in classifying materials as conductors, insulators, or semiconductors.; Used to determine the power loss in transmission lines.

Applications: Selection of materials for electrical wiring.; Design of grounding systems and lightning protection.; Testing purity of water (conductivity measurement).

Additional Info: The term 'mho' is the backward spelling of 'ohm', representing the reciprocal unit.. Option B (mho/m^2) is dimensionally incorrect as it corresponds to a different physical derivative.. Options C and D represent units of resistance and surface resistance respectively.

Answer: A is correct — The unit of electrical conductivity is mho/metre (or Siemens/metre), representing the reciprocal of resistivity measured in ohm-metres.

Exam Tip: Always remember: Conductivity is the reciprocal of Resistivity ($$\sigma = 1/\rho$$), while Conductance is the reciprocal of Resistance ($$G = 1/R$$). Units follow the same reciprocal logic.

Related Questions

Discussion (0)