Lightning induced voltage is a major factor that causes interruptions on distribution lines. In this paper, analytical expressions are proposed to evaluate a lightning induced voltage on power lines directly in the time domain without the need to apply any extra conversions. The proposed expressions can consider the widely used current functions and models in contrast to the earlier analytical expressions which had a number of limitations related to the simplification of the channel base current and the current along the lightning channel. The results show that the simulated values based on the proposed method are in good agreement with the previous studies and the proposed expressions can be used for optimizing the insulation and protection level of existing and new lines being designed.