Introduction:
Field Effect Transistors (FETs) are three-terminal devices that can be used as voltage-controlled resistors. The resistance of a FET can be controlled by varying the voltage applied to its gate terminal. In order to use a FET as a voltage-controlled resistor, it should operate in the ohmic region.

Explanation:
To understand why the FET should operate in the ohmic region to be used as a voltage-controlled resistor, let's first understand the different regions of operation in a FET:

1. Cut-Off Region:
- In the cut-off region, the FET is essentially turned off.
- The channel between the source and drain terminals is closed, and no current flows through it.
- In this region, the FET behaves as an open circuit, and it cannot be used as a resistor.

2. Saturation Region:
- In the saturation region, the FET is fully turned on.
- The channel between the source and drain terminals is fully open, allowing maximum current flow.
- In this region, the FET behaves as a closed switch, and it cannot be used as a resistor.

3. Ohmic Region:
- In the ohmic region, the FET operates in a region between cut-off and saturation.
- The channel between the source and drain terminals is partially open, allowing controlled current flow.
- In this region, the FET behaves as a resistor with a variable resistance that can be controlled by the voltage applied to its gate terminal.

Using FET as a Voltage-Controlled Resistor:
To use a FET as a voltage-controlled resistor, it needs to operate in the ohmic region. In this region, the resistance of the FET can be controlled by varying the voltage applied to its gate terminal. By changing the gate voltage, the channel between the source and drain terminals can be modulated, thereby changing the resistance of the FET. This allows for precise control of the current flowing through the FET, making it suitable for various applications such as amplifiers, attenuators, and voltage-controlled oscillators.

Conclusion:
The FET should operate in the ohmic region to be used as a voltage-controlled resistor. In this region, the resistance of the FET can be controlled by varying the voltage applied to its gate terminal. By operating in this region, the FET can be utilized effectively as a voltage-controlled resistor in various electronic circuits and applications.