To fast evaluate the features of the zero potential circuits (ZPCs) for the 2-D networked resistive sensor arrays, such as the setting non-scanned-electrode ZPC, the setting non-scanned-sampling-electrode ZPC, and the setting non-scanned-driving-electrode ZPC, we first proposed the approximate models of the ZPCs with one op-amp. By analyzing the approximate model, we then gave a mathematical expression of the effective equivalent resistor of the element being tested in the ZPCs with one op-amp. Finally, we evaluated the approximate model of the ZPCs with one op-amp by simulation experiments. The results show that the proposed approximate model of the ZPCs with one op-amp is applicable to fast analyze the performance of the resistive sensor array parameters, including array size and the resistance range of the sensitive elements, and the ZPCs’ parameters, including the multiplexers’ switch resistors, the gain of the zero potential op-amp, and the resistance value of the sampling resistor.