The current in a direct current resistor inductor circuit is given by:
i(t) = (-ℰ/R)e^{-Rt/L} + ℰ/R
Where i(t) is the current, t is time, ℰ is the battery's terminal voltage, R is the resistor's resistance, and L is the inductor's inductance.
Given values:
ℰ = 5.6V
R = 100Ω
L = 4.1×10⁻²H
Plug in the values to get i(t):
i(t) = -0.056e^{-2440t} + 0.056
We want to calculate when the current is 0.012A, i.e. find a time t when i(t) = 0.012A. So let us set i(t) equal to 0.012 and solve for t:
-0.056e^{-2440t} + 0.056 = 0.012
0.056e^{-2440t} = 0.044
e^{-2440t} = 0.786
-2440t = ㏑(0.786)
t = -㏑(0.786)/2440
t = 9.87×10⁻⁵s
