Figure 38.2: Plots vs. time for an LR circuit. (a) Resistor voltage vs. time; (b) inductor voltage vs. time; (c)
circuit current vs. time; and (d) magnetic flux in the inductor vs. time. The switchSis closed at timetD 0.
has increased to 1 1=eD0:632of the battery voltage; the voltage across the inductor has decreased to
1=eD0:368of the battery voltage; the current has increased to 1 1=eof its maximum value; and the
magnetic flux in the inductor has increased to 1 1=eof its maximum value.
Mathematically, the voltage across the resistorVR, the voltage across the capacitorVC, the current in the
circuitI, and the magnetic fluxˆBin the inductor can be shown to be
VR.t/DV.1et=/ (38.2)
VL.t/DVet= (38.3)
I.t/D.V=R/.1et=/ (38.4)
ˆB.t/D.LV=R/.1et=/ (38.5)As timet!1, current will reach a maximum valueIDV=R, the magnetic flux in the inductor will
have reached its maximum valueLV=R, the voltage across the resistor will equal the battery voltage, and the
voltage across the inductor will be zero.