Question

The unit of specific conductivity is

• A. ohm cm
• B. ohm^-1 cm²
• C. ohm^-1 cm
• D. ohm^-1 cm^-1

Hint:

The conductance of a substance is a property that allows the flow of ions through it to conduct electricity. 

Answer 1

The Correct Option is D

Specific conductivity expresses the ability of a material to conduct electricity. It is reciprocal to the resistivity of a substance. 

The unit of specific conductivity is Ohm^-1 cm^-1.

Answer 2

The conductance of a substance is a property that allows the flow of ions through it to conduct electricity. 

• Resistance is the opposite of conductance and it indicates how much a material can block or resist electricity.
• Mathematically, if the conductance of a material is given by the symbol ‘C’, and the resistance is given by the symbol ‘R’, then, we can write:

\(C=\frac{1}{R}\)  ….….… (1)

Now, we know that the resistance (R) is directly proportional to the length (l) and inversely proportional to the cross-sectional area (A) of the material. \(R∝l\)

And

\(R∝\frac{1}{A}\)

Hence, by combining these two, we will get

\(R∝ρ\frac{l}{A}\)

Here, the constant ‘ρ’ is known as the resistivity of the material.

Now, if we put the value of R in equation (1), then we will have

\(C=\frac{1}{ρ}×\frac{A}{l}\)

Or,

\(C=k\frac{A}{l}\)  …..… (2)

Here, the constant, K, is known as the specific conductance of a substance.

Thus, specific conductance (K) is nothing but the reciprocal of the resistivity of the material.

Unit of Specific Conductivity

The unit of specific conductivity can be determined from equation (2). We can rewrite equation (2) as:

\(K=C\frac{l}{A}\)

Now,

• The unit of conductance (C) is ohm⁻¹ (Since conductance is reciprocal to resistance and the unit of resistance is ohm).
• The unit of the length (l) is centimetres (cm).
• The unit of the cross-sectional area is cm².

Hence,

\(K(unit)=ohm^{−1}\frac{cm}{cm^2}\)

Or,

\(K(unit)=\frac{ohm^{−1}}{cm}\)

Hence, the unit of specific conductivity is ohm⁻¹cm⁻¹.

Therefore, option D is the correct answer to this question.

Note: Students sometimes get confused with conductance and specific conductivity. These are two different properties of a material. Conductance is the ability of a material to conduct electricity, whereas, specific conductance is the conductance per unit length.