The switching process in a direct current (DC) circuit with inductive-resistive load (RL) produces complex switching conditions due to the nature of energy storage by the inductor. This study analyzes the transient phenomenon that occurs when a switch in a DC circuit is activated or deactivated. Using a first-order differential equation describing the relationship between current, voltage, and circuit parameters, the transient characteristics of current and voltage are obtained. Simulations and mathematical analysis show that the recovery time of stable conditions depends on the time constant of the series, which is determined by the values of inductance (L) and resistance (R). This study provides an in-depth understanding of transient dynamics, which is beneficial for electronic system design and network protection.