We investigated the size effect on quench development in $Au/YBa_2Cu_3O_7$ (YBCO) thin film meander lines on sapphire substrates. The meander lines were fabricated by patterning YBCO films coated with gold layers. The lines were subjected to simulated AC fault current, and immersed in liquid nitrogen during the experiment. After the initial rapid rise, the resistance increased moderately and then slowly. In 4 inch-diameter meander lines, the period during which the resistance increased moderately was considerably longer than in 2 inch-diameter line. Moderate increase of resistance was originated from quench propagation. The film temperature was about 180 K at the point when the propagation was completed. The rate of resistance increase after the quench completion was not affected by the film size.