A tritium battery with solid dielectric has been built utilizing a tritium beta source, an electron collector, and a separating layer of dielectric much thicker than the range of tritium beta particles. Electric current between the electrodes is due to an electric field that is created by direct charge accumulation of beta particles in the dielectric. A macroscopic model describing the behavior of current and voltage is proposed. Based on this model and experimental results with 37 GBq (1000 mCi) tritium sources, the electrical characteristics of a device with 37 TBq (1000 Ci) tritium are extrapolated. It is predicted that this battery will have open circuit voltage over 6 kV, short circuit current more than 1 A, and 1 mW of electric power on an optimal load with overall efficiency near 9%.