**Direction: **It consists of two statements, one labeled as ‘Statement (I)’ and the others as ‘Statement (II)’. You are to examine these two statements carefully and select the answer using the codes given below:

**Statement (I):** The Dielectric constant of a substance, under the influence of alternating electric fields is, in general, a ‘complex’ quantity.

**Statement (II): **The ‘imaginary’ part of the dielectric constant is a measure of the dielectric loss in the substance.

This question was previously asked in

ESE Electrical 2013 Paper 1: Official Paper

Option 1 : Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I)

CT 3: Building Materials

2962

10 Questions
20 Marks
12 Mins

**Concept:**

A complex dielectric constant is used to describe the dielectric constant during a periodic variation of the electric field, where the field variation is described by a sine-shaped waveform.

The complex dielectric constant can be expressed as:

**ϵ _{r}^{*} = ϵ_{r}^{'} - jϵ_{r}^{"}**

Where

ϵ_{r}^{'} = Real part of complex dielectric constant

ϵ_{r}^{"} = Imaginary part of complex dielectric constant

**For lossy dielectric, dielectric constant is complex**

In ideal capacitors,it is well known that the ac current leads the voltage by 90°. But real capacitors have a resistive component that makes them lossy so they dissipate some of the applied ac energy as Joule heat. This slightly reduces the lead angle by δ degrees.

The quantity tan δ, plotted schematically in Fig, is a measure of the ratio of the electrical energy lost per cycle to the maximum energy stored.

Values for tan δ are given :

\(\tan \delta = \frac{{{\varepsilon ^{''}}_r}}{{\varepsilon {'_r}}}\)

__Explanation:__

**So, under the influence of alternating electric fields is, the dielectric constant behaves as a complex quantity and imaginary part measure dielectric loss.**