Hi there!
a)
When the motor is first turned on, the coils are initially stationary. Thus, there is no change in magnetic flux and, consequently, no induced emf.
Therefore:
[tex]iR = \epsilon - \epsilon_{back}[/tex]
Since there's no back emf:
[tex]iR = \epsilon[/tex]
Solving for i using Ohm's Law:
[tex]i = \frac{\epsilon}{R}\\\\i = \frac{120}{10} = \boxed{12.0 A}[/tex]
b)
We are given that at max speed, the back EMF is 70.0 V.
Using the same equation as above:
[tex]iR = \epsilon - \epsilon_{back}[/tex]
Plugging in the values:
[tex]10i = 120 - 70 \\\\10i = 50 \\\\[/tex]
Solving for current:
[tex]i = \frac{50}{10} = \boxed{ 5.0 A}[/tex]
