Determine the value of the resistor r so that a current of 0.5a flows through the load.

What is the value of the voltage? There must be one somewhere.

This might be too simple minded, but I'll give it a voltage of 10 Volts.

R = voltage / Current

R = 10 / 0.5

R = 20 volts.

Perhaps you could post a diagram if this is a Kirchhoff Law Question.