A current sense circuit, including a voltage regulator, for detecting current conducted by a device under test (DUT) for a wide range of currents, while still providing fine granularity for detecting low/small currents. Two current branches/paths may be established to the supply terminal of the DUT. A switching device, e.g. a transistor device, may be operated to enable a first current branch of the two current branches, or both current branches to conduct current, responsive to the size of the current flowing in the first current branch. The total current conducted by the DUT may be equivalent to a sum of the respective currents flowing in the two current branches. When the switching device is turned off, very small currents conducted by the DUT may be measured with fine granularity. When the switching device is turned on, substantially larger currents conducted by the DUT may be measured.