Anhydrous  is a very polar liquid, having a dielectric constant of around 100. It has a high electrical conductivity, a consequence of autoprotolysis, i.e. self-protonation :
The equilibrium constant for autoprotolysis (25 °C) is:
The corresponding equilibrium constant for water, K is 10, a factor of 10 (10 billion) smaller.
In spite of the viscosity of the acid, the effective conductivities of the  and  ions are high due to an intramolecular proton-switch mechanism (analogous to the Grotthuss mechanism in water), making sulfuric acid a good conductor of electricity. It is also an excellent solvent for many reactions.