Answer
a) $t=0.75s$
b) $R=0.37\Omega$
Work Step by Step
(a) We can find the required time constant as follows:
$0.95I_{final}=I_{final}[1-e^{-{(2.24s)/t}}]$
This simplifies to:
$t=-\frac{2.24}{\ln 0.05}$
$t=0.75s$
(b) We can find the required resistance as
$R=\frac{L}{t}$
We plug in the known values to obtain:
$R=\frac{0.275}{0.748}$
$R=0.37\Omega$
