The Solenoid Powered Engine (SPE) is one of the feasible alternative prime movers to replace the existing electric motors. From the machine's design and operational perspective, this particular prime mover design holds a few advantages over the existing electric motor designs. However, SPE development is still in its infant stages and future studies and improvements are required to further refine the SPE wide potential. Therefore, the authors have developed a few equivalent circuits for the machine and applied mathematical derivation models to identify the machine's terminal characteristic. The equivalent circuits are based on a transformer model, which is later refined into a simple and yet easier to analyse model. As a result, the authors have managed to introduce new equations to define the SPE terminal characteristic, which is similar to a DC series motor. This paper basically describes the SPE equivalent circuit, terminal characteristic and multiple solenoids implication.