Step 1: Understanding the Question:
The question asks us to identify the primary engineering advantage of a hydraulic system compared to an electrical power system.
Step 2: Detailed Explanation:
• Hydraulic systems use pressurized incompressible fluids to transmit energy and generate high forces.
• One of the most significant metrics of any actuator system is its power-to-weight ratio (or power-to-volume ratio).
• Because hydraulic fluid can operate at extremely high pressures (often exceeding $3000\text{ psi}$), hydraulic motors and cylinders can produce massive forces and torque while remaining physically compact.
• To generate an equivalent amount of torque or force, an electric motor would require heavy copper windings, massive iron cores, and robust structural casings, making its physical footprint substantially larger and heavier.
• Therefore, for a given power output, a hydraulic system is much smaller in size compared to an equivalent electrical system.
Step 3: Final Answer:
The principal advantage of a hydraulic system over an electric system is its smaller size for a given power capacity.