(a) The defendant shall not be held in confinement under an execution for a fine for a longer period than at the rate of one (1) day for each two dollars ($2.00) of the fine. However, the confinement shall not discharge the fine, which thereafter can only be collected by proceeding against the defendant's property.
(b) The provisions of this section shall not apply to judgments in city or police courts, which may be discharged by confinement in the city workhouse, according to the provisions of the special statutes regulating them.