Answer
See explanation.
Work Step by Step
Note that at all times, $\epsilon=v_{ab}+v_{bc}$ by the loop rule.
Use the relation $i=\frac{\epsilon}{R}(1-e^{-(R/L)t})$.
a. At t=0, the current $i=0$. $v_{ab}=0V$ and $v_{bc}=60V$.
b. As t approaches infinity, the current $i$ approaches $ \frac{\epsilon}{R}$ and $di/dt$ approaches zero. $v_{ab}=60V$ and $v_{bc}=0V$.
c. When the current $i=0.150A$, $v_{ab}=iR=36.0V$ and $v_{bc}=60.0V-36.0V=24.0V$.
