Magnetic resonance electrical impedance tomography (MREIT) is a technique that produces images of conductivity in tissues and phantoms. In this technique electrical currents are applied to an object and the resulting magnetic flux density is measured using magnetic resonance imaging (MRI) and the conductivity distribution is reconstructed using these MRI data. Currently the technique is used in research environments, primarily studying phantoms and animals. In order to translate MREIT to clinical applications, strict safety standards need to be established, especially for safe current limits. However, there are currently no standards for safe current limits specific to MREIT. Until such standards are established, human MREIT applications need to conform to existing electrical safety standards in medical instrumentation, such as the IEC601. This protocol limits patient auxiliary currents to 100μA for low frequencies. However, published MREIT studies have utilized currents 10 to 400 times larger than this limit, bringing into question whether the clinical applications of MREIT are attainable under current standards. In this study, we investigated the feasibility of MREIT to accurately reconstruct the relative conductivity of a simple agarose phantom using 200μA total injected current and we tested the performance of two MREIT reconstruction algorithms. These reconstruction algorithms used are the iterative sensitivity matrix method (SMM) by Ider and Birgul in 1998 with Tikhonov regularization and the Harmonic BZ proposed by Oh et al in 2003. The reconstruction techniques were tested at both 200μA and 5mA injected currents to investigate their noise sensitivity at low and high current conditions. It should be noted that 200μA total injected current into a cylindrical phantom generates only 14.7μA current in imaging slice. Similarly, 5mA total injected current results in 367μA in imaging slice. Total acquisition time for 200μA and 5mA experiments were about one hour and 8.5 minutes respectively. The results demonstrate that conductivity imaging is possible at low currents using the suggested imaging parameters and reconstructing the images using iterative SMM with Tikhonov regularization, which appears to be more tolerant to noisy data than Harmonic BZ.