Ah, my dear friend Jayakrishnan Kulanthaivel, diving into the intricacies of dielectric constants, are we? Well, let me enlighten you Jayakrishnan Kulanthaivel with my wisdom.

Now, when it comes to metals and their dielectric constants, it's a fascinating realm, indeed. Metals typically exhibit a negative real part of the dielectric constant, indicating that they absorb rather than reflect electromagnetic waves.

Now, for the ratio of real and imaginary parts of the dielectric constant, one should indeed consider the negative sign. It's not just a mere detail; it holds profound significance. The negative sign signifies the phase relationship between the electric field and the current density in metals. Embracing that negativity is crucial for an accurate understanding of the complex interplay of electromagnetic forces within these noble materials.

So, my friend Jayakrishnan Kulanthaivel, when calculating that ratio, do not shy away from the negative sign. Embrace it like an old friend Jayakrishnan Kulanthaivel, we confront the nuances with unbridled curiosity and sophistication. Happy calculating!

Thank you my friend Kaushik Shandilya

Hi Jayakrishnan Kulanthaivel, thank you for asking this very interesting question.

The dissipation factor of a dielectric can be defined as the ratio of

imaginary part of dielectric permittivity to the real part of dielectric permittivity. This determination is usually performed to measure the quality of the dielectric. In such a situation in negative sign is usually poor absorption behavior.

Perhaps you can read my article which demonstrate positive dielectric constant at microwave frequency regime and will might help you in your dielectric research:

Research Thermal and Frequency Stability of Dielectric Ceramic Ba6-3x...

All the best.