Equation i=ER(1−e−t/τL) (rise of current) applies, and the problem requires
iR=Ldidt=ε−iR
at some time t (where Eq. Ldidt+Ri=E (RL circuit)
has been used in that last step). Thus, we have 2iR=ε or
ε=2iR=2[εR(1−e−t/τL)]R=2ε(1−e−t/τL)
where Eq. τL=LR (time constant) gives the inductive time constant as
τL=L/R. We note that the emf ε cancels out of that
final equation, and we are able to rearrange (and take the natural log) and
solve. We obtain t=0.520ms