Unless Council contracts with another Board of Health there shall be a Board of Health of the City health district composed of five (5) members who shall be citizens who are not employed by the City and hold no other office of the City. The members shall be selected by the Council one (1) each year for overlapping terms of five (5) years, so arranged that one member's term shall expire on July 1st of each year. At least one (1) member shall be a physician admitted to practice in Ohio and in good professional standing. The Board shall adopt its own rules and elect its own officers annually. It shall have all the power and authority conferred upon city boards of health by general law, except as may be modified by ordinance.