And the inductor is in series with a resistor and the battery was connected for a long time
In theory infinite. In practice there will always be some resistance/reactance in parallel with the inductor that will limit the voltage in accordance to ohms law.
After a long time an inductor acts like a short circuit, meaning all the current flows through the element, and there is no effective resistance. Therefore, the voltage across it would be V 0, as there is no voltage across a short circuit.
