In COPD (emphysema/chronic bronchitis) you have destruction of the alveoli and/or constant air trapping and lung hyperinflation. Because of that the residual volume (RV) increases permanently. On the contrast in asthma for example the bronchial obstruction is reversible, thus the RV is generally not changed (i.e. normal). However would you perform a spirometry during an asthma attack you would of course see increased RV.
I hope that answers your question.