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The TFTs simply act as switches. The thin-film transistors of rows are sequentially opened by applying row-by-row a positive voltage.
When the source-drain line is opened, the voltage on the column lines is forwarded to the liquid crystal cell.
After a row is addressed, the TFT will close again and shield the pixel from the voltage applied to the next row.
The electric field on the liquid crystal is kept by own capacity, and it (= the electric field) is kept by an additional capacitor in most cases.