The primary challenges in the implementation of differential protection techniques are Time Synchronization Error (TSE) due to communication delay and low sensitivity towards High Resistance Faults (HRFs). In this paper, a new technique utilizing the difference in voltage measured across the external reactors connected at opposite ends of the cable is proposed for fault detection and classification of HRFs in islanded and grid connected mode of operation of DC microgrid. Further, to overcome the challenges associated with TSE, which causes differential schemes to mal-operate, the proposed technique determines reactor voltage polarity at opposite ends of the cable to distinguish between internal and external faults. The proposed technique is tested for different types of internal faults and system transients such as external faults, load switching, generation uncertainties etc. to demonstrate sensitivity and accuracy of the proposed technique. Finally, a comparative analysis of the proposed technique is performed with the schemes reported in the literature, which confirms the fast fault detection, high sensitivity for internal HRFs, selectivity and stability of the proposed technique for different operating conditions.