Disclosed herein are tires with a component comprising a cured rubber composition having a high dielectric constant, tire bead fillers comprising a cured rubber composition having a high dielectric constant, and related methods for increasing the dielectric constant of a cured rubber composition for a tire component. According to certain embodiments, the cured rubber composition has a dielectric constant of at least 20 and comprises 100 phr of at least one conjugated diene monomer-containing elastomer, filler comprising at least 25 phr of reinforcing carbon black, a cure package of specified composition, and optionally at least one anti-reversion agent.