The charge collection in a liquid-filled matrix ionization chamber system has been investigated. This system, which is used for megavoltage radiography, is scanned electronically by switching the polarizing voltage. In such a system the charge collection cannot be described by the classical ionization chamber theory since this is only valid for a fixed polarizing voltage. A model is presented for an ideal plane-parallel ionization chamber with switched polarizing voltage that gives a good qualitative description of the physical phenomena in our nonideal system. The new model predicts the amount of charge collected and the signal-to-noise ratio as a function of several parameters such as electrode distance, polarizing voltage, radiation intensity, and some liquid characteristics. An important result is that the quantum noise contribution can be made quite small. This situation occurs in liquids with a low ion mobility and long ion lifetimes by a charge-integrating effect in the liquid. Experiments were performed to test various aspects of the model. A reasonable agreement is found between theoretical and experimental results. The possible use of ultrahigh-mobility liquids is also discussed.