SI Unit of Conductivity: Overview, Questions, Preparation

Conductivity measures the ease when the electric charge travels through a material. Conductors are used to provide resistance to the flow of the electric current passing through a material. The great electrical conductor is copper.

Specific conductance is the sample of the electrolytic solution on which electric current is measured. On the contrary, the sample of electrolytic solution that can resist the electric current flow is known as resistance. The conductance is inversely proportional to the resistance of the electrolytic solution.

S (Siemens) is the SI unit of conductance denoted as S/m.

G = 1 / R

R = p I / A

G = 1 / p x A / I

G = k A / I

Here, the specific resistivity is denoted as P,

Specific conductivity is denoted as k

It is also known as reciprocal of resistivity. Both are inversely proportional to each other.

K 1 / p = C / R

Conductivity is broadly categorised into three types:

• Electrical conductivity: It further has two types –
• • Electrolytic conductivity
  • Ionic conductivity
• Hydraulic conductivity
• Thermal conductivity

Siemens per meter (S / m) is the SI unit of the Conductivity and is represented by Sigma (σ). The formula of conductivity is written below:

Σ = 1 / p

If we talk about the thermal conductivity, the SI unit is watts per meter – kelvin (W / MK). The formula of thermal conductivity is represented as:

K = QLA / ΔT

Here, the thermal conductivity is K,

The area of the body is A,

The amount of heat transfer is Q,

And the difference in the temperature is ΔT.

The electrical resistance of any object is directly proportional to its length, l, and inversely proportional to its area of cross-section, A. The constant of proportionality, ρ (Greek, rho), is called resistivity (specific resistance). Its SI units are ohm meter (Ω m) and quite often its submultiple, ohm centimetre (Ω cm) is also used. The inverse of resistance, R, is called conductance, G. 

• The inverse of resistivity, called conductivity (specific conductance) is represented by the symbol, κ (Greek, kappa). The SI unit of conductance is siemens, represented by the symbol ‘S’ and is equal to ohm–1 (also known as mho) or Ω –1. 
• The conductivity of a material in S m–1 is its conductance when it is 1 m long, and its area of cross-section is 1 m2. It may be noted that 1 S cm–1 = 100 S m–1

• We should know that the magnitude of conductivity varies and depends upon the nature of the material. It also depends on the temperature and pressure at which the measurements are made.
•  Materials are classified on the magnitude of their conductivity. Metals and their alloys have very large conductivity and are known as conductors. Certain non-metals like carbon-black, graphite, and some organic polymers are also electronically conducting.

• The conductivity of solutions of different electrolytes in the same solvent and at a given temperature differs due to the charge and size of the ions in which they dissociate, the concentration of ions, or the ease with which the ions move under a potential gradient. Therefore, it becomes necessary to define a physically more meaningful quantity called molar denoted by the symbol Λm (Greek, lambda).

The conductivity of electrolytic (ionic) solutions

The conductivity of the ionic solutions depends upon:

(i) The nature of the electrolyte added

(ii) Size of the ions produced and their solvation

(iii) The nature of the solvent and its viscosity

(iv) The concentration of the electrolyte

(v) Temperature (it increases with the increase of temperature).

SI units of Conductivity for Class 12

The chapter 'Current Electricity' holds a noteworthy weightage of 11 marks. It includes 4 questions consisting of one objective type question of 1 mark, one very short question of 2 marks, one short question of 3 marks, and one long question of 5 marks.

1. Write the formula of Specific Conductivity.

Answer – The formula of Specific conductivity is:

               G = 1 / R

               R = p I / A

               G = 1 / p x A / I

               G = k A / I

              Here, the specific resistivity is denoted as P,

              Specific conductivity is denoted as k

2. Write the formula to measure the conductivity.

Answer – The formula of conductivity is written below:

               Σ = 1 / p

3. Write the conductivity of distilled and drinking water.

Answer – The conductivity of the distilled water is 0.05 uS/cm, and the conductivity of the drinking water is 200 to 800 uS/cm.

4. What type of material is sodium, and what is the value of its conductivity?

Answer –Sodium is considered to be a conductor. The value of its conductivity expressed in terms of S m-1  is 2.1×103.

5. List down a few aqueous solutions whose value of conductivity is known.

Answer –Few aqueous solutions whose value of conductivity is known are : Pure water, 0.1 M HCL, 0.01M NaCl, 0.1 M HAc,0.01M KCl, 0.001M HAc, etc.

6. The electrical resistance of a column of 0.05 mol L–1 NaOH solution of diameter 1 cm and length 50 cm is 5.55 × 103 ohm. Calculate its conductivity.

Answer –

• A = π r 2 = 3.14 × 0.52 cm2 = 0.785 cm2 = 0.785 × 10–4 m2 l = 50 cm = 0.5 m
• R= ρ l/A =5.55*10*10*10Ω* 0.785*0.875/ 50 cm =87.135 Ω cm