dielectric loss
An ideal capacitor is a perfect spring for charge: push energy in on one half of an alternating cycle, get all of it back on the other half, with nothing lost. Real dielectrics are slightly sticky springs — a little of the energy is turned into heat on every cycle instead of being returned. Dielectric loss is that wasted fraction, and it is the reason a capacitor or an insulator warms up under an alternating field.
The standard measure is tan delta, the loss tangent (also called the dissipation factor). In an ideal capacitor the alternating current leads the voltage by exactly 90 degrees and no power is dissipated; a real one falls short of 90 degrees by a small angle delta, and tan delta is the tangent of that lag. The power turned to heat is proportional to omega times C times V^2 times tan delta, where omega is the angular frequency, C the capacitance and V the voltage — so loss grows with frequency and with the square of voltage. Physically the loss comes from any process where the polarization cannot keep perfectly in step with the field: leakage from ionic conduction, the frictional relaxation of rotating dipoles, the motion of ferroelectric domain walls, and dissipation in the thin glassy film that often coats grain boundaries. Good low-loss ceramics reach tan delta near 10^-4 (one part in ten thousand); a high-permittivity barium-titanate dielectric is nearer 10^-2.
Loss matters for three reasons. It wastes energy and heats the part, and in a resonator it sets the quality factor Q, which is just 1/tan delta — a microwave filter or antenna wants the highest Q, hence the lowest loss. Worse, the heating is self-reinforcing: a hotter dielectric usually loses more, which heats it further, and this runaway can end in thermal breakdown. An honest caveat: loss is never a fixed material number — it climbs with temperature and frequency, spikes near a ferroelectric phase transition where the polarization is sluggish, and in real polycrystalline ceramics is often dominated by the grain-boundary glass rather than the bulk grains.
A microwave dielectric resonator for a base station is prized for its quality factor: with tan delta near 1 times 10^-4 its Q is about 10000, so it rings sharply and selects one frequency cleanly. Push the same job onto a lossy high-k ceramic with tan delta of 10^-2 and Q collapses to 100 — the filter is useless.
Low loss and high permittivity usually pull against each other: the ceramics with the biggest epsilon_r are often the leakiest, so device design is a trade-off.
tan delta is a ratio, not a resistance, and it changes with the conditions of measurement. A quoted loss figure is meaningless without its frequency and temperature; the same capacitor can look lossless at 1 kilohertz and lossy at 1 gigahertz.