Final answer:
To determine the value of the variable rheostat needed in series with the shunt field winding resistance for the specified shunt-connected DC motor, additional information on the motor's operating point or required field current is essential, as the question provided lacks these details.
Step-by-step explanation:
The student is asking for the value of a variable rheostat needed in series with the shunt field winding resistance of a shunt-connected DC motor that is rated at 15 kW power, has an armature resistance of 0.25 Ω, a shunt field winding resistance of 30 Ω, and is connected to a 120 V DC voltage supply. Unfortunately, the question does not provide enough information to directly calculate this value, as it requires knowledge of the desired current through the shunt field winding or other operational parameters. Additional details like the motor's operating point or required field current are necessary to determine the value of the variable rheostat.