Part 1 of 1:
At t=0, a 12.6V battery is connected to a series circuit containing a 9 Ω resistor and a 1.2 H inductor.
What will be the current in the circuit, a long time after the circuit is established?
Part 2 of 2:
How long will it take the current to reach 50 percent of its final value?
oldschool
i(t) = i(∞)*(1-e^-Rt/L) where i(∞) = 12.6V/9Ω = 1.4 and R/L = 9/1.2 = 7.5
i(t) = 1.4 * (1 - e^-7.5t) so i(∞) = 1.4 and i = 1.4/2 = 0.7 when
½ = (1 - e^-7.5t) SO e^-7.5t) = 0.5 Take natural logs of both sides:
-7.5t = LN(0.5)
t = LN(0.5)/(-7.5) = 92.4ms
oubaas
If = V/R = 12/9 = 4/3 of Amps
timeconstant Ƭ = L/R = 1.2/9 = 0.1333 sec
0.5 = 1-e^-k
e^k = 0.5
k*ln e = ln 0.5.....(ln e = 1)
k = -0.693 = -t/Ƭ
t = 0.693*0.1333 = 0.092 sec