A petroleum well (20) for producing petroleum products that incorporates a system adapted to controllably measure a formation resistivity using induction chokes (91-95) to form electrically isolated piping structure sections that can be used as the formation contact electrodes for time-varying current, and methods of producing petroleum products while measuring formation resistivity, are provided by the present invention. The system comprises a first induction choke (91), a second induction choke (92), and a device (50). The first induction choke (91) is located about a piping structure (30) of the well (20). The second induction choke (92) is also located about the piping structure (30) of the well (20), but the first induction choke (91) is distally spaced from the second induction choke (92). The device (50) is located outside of the piping structure (30) and comprises two terminals (71, 72). A first of the terminals (71) extending from the device (50) is electrically connected to the piping structure (30) on one side (81) of the first induction choke (91). A second of the terminals (72) extending from the device (50) is electrically connected to the piping structure (30) on another side (82) of the first induction choke (91), between the first and second induction chokes (91, 92), such that the downhole device (50) is electrically connected across an outside of the first induction choke (91). The system can further comprise other induction chokes (93-95), other terminals (97-99) extending from the device (50), a current sensor (114), a surface power source (54), a power transformer (104), a communications transformer (106), a surface modem (56), a downhole modem (102), a direct current power supply (101), and/or a power amplifier (110, 112). The piping structure can comprise at least a portion of a well casing (30), such that the well casing (30) acts as an electrode for making formation resistivity measurements due to the induction chokes (91-95).