Answer
a. No.
b. Yes.
Work Step by Step
a. The current through an LR circuit is given by the following equation.
$$I=\frac{V_o}{R}(1-e^{-t/(L/R)})= I_{max}(1-e^{-t/(L/R)})$$
This can be rearranged to solve for a given fraction of the maximum possible current.
$$\frac{I}{ I_{max}}=(1-e^{-t/(L/R)}) $$
There is no dependence upon the battery emf, so the time needed to reach a given fraction of the maximum current does not depend on the battery’s emf.
b. The current through an LR circuit is given by the following equation.
$$I=\frac{V_o}{R}(1-e^{-t/(L/R)}) $$
If a given value of the current is to be reached, then a larger battery emf, $V_o$, will make it happen faster.
