We propose and demonstrate a cost-effective, microring-based, silicon photonic sensor that uses doped silicon detectors and a broadband source. Shifts in the sensing microring resonances are electrically tracked by a doped second microring, which acts as both a tracking element and a photodetector. By tracking the power supplied to this second ring, as the sensing ring's resonance shifts, the effective refractive index change caused by the analyte is determined. This design reduces the cost of the system by eliminating high-cost, high-resolution tunable lasers, and is fully compatible with high-temperature fabrication processes. We report a bulk sensitivity of 61.8 nm/RIU and a system limit of detection of 9.8x10-4 RIU.