Final answer:
The phase of the current through the inductor is -110°, which can also be represented as 250° since both are equivalent.
Step-by-step explanation:
The phase of the current through a 20-mH inductor when the applied voltage is v(t) = 48 cos(377t - 20°) V is determined by the fact that in an AC circuit, the voltage across an inductor leads the current by 90°. Therefore, if the voltage has a phase of -20° (as given), the current will lag this voltage phase by 90°. To find the phase of the current, subtract 90° from the voltage phase, resulting in a current phase of -20° - 90° = -110°. However, this angle can be usually expressed in a range from 0° to 360°, in which case the phase can also be given as 250°. Both answers are equivalent and the choice between them depends on the specific context of the problem.