Rona is told by her physician that she has become physically dependent upon the tranquilizers prescribed for her by another doctor. in this context, "physically dependent" means that:
In the given context, physically dependent means that Rona's body has become chemically dependent
Tranquilizers are drugs prescribed for the treatment of anxiety, depression, fear, tension and for any condition that leads to the disturbance of mind
Tranquilizers or sedative drugs or we can say chemicals that suppress the central nervous system and slow down normal brain function and for that particular reason, they are often referred to as depressants