Final answer:
To design a circuit with a variable gain from -10 to -500 using only one operational amplifier (OP AMP), use an inverting amplifier configuration with a potentiometer as the feedback resistor.
Step-by-step explanation:
To design a circuit with a variable gain from -10 to -500 using only one operational amplifier (OP AMP), you can use an inverting amplifier configuration.
An inverting amplifier amplifies the input signal and produces an output that is the inverse of the input signal. The gain of an inverting amplifier is determined by the ratio of the feedback resistor to the input resistor. In this case, the feedback resistor is a potentiometer with a variable resistance.
By adjusting the resistance of the potentiometer, the gain of the amplifier can be changed. To achieve a gain range from -10 to -500, you need to choose a potentiometer with a resistance range that allows for this variation.