I am under the impression that if you have an inductor and a resistor connected in series with a DC supply, that at the instant the switch is closed, the minimum current that circuit will flow, is flowing at this time? kirchoff's law for the circuit... Vsource - Ldi/dt - Ri = 0 therefore, Vsource (as a function of time) = Ldi/dt + Ri. divide both sides by L, V/L = di/dt + (R/L)i this is a linear differential equation... find integrating factor to be e^(R/L)t using power rule for derivatives once multiplying all terms by the integrating factor gives the well known formula - i(t) = Eo/R + Io*e^-(R/L)t --> where Eo and Io are applied voltage and initial current respectively. This would mean, that the maximum current flows once the switch is closed? and it DROPS to steady state valuer as the transient goes to zero as t-->infinity. Intuitively, I would think instead that the current INCREASES to a steady state value as time approaches infinity? Am I missing something.