Final answer:
The statement is true; a variable resistor wired as a potentiometer indeed has three leads. A potentiometer is used for obtaining a variable potential along a wire, with one terminal acting as a moving contact that goes along the wire changing the resistance and potential obtained.
Step-by-step explanation:
The statement about a variable resistor wired as a potentiometer having three leads is true. A potentiometer, configured as a null measurement device, is typically made up of a long wire resistor to which a constant current is applied from a voltage source. There is a stable drop in potential, known as an IR drop, along the wire. This setup allows for obtaining a variable potential via connecting to different points along the wire.
In practice, a potentiometer has three terminals: two are connected to the ends of the resistor (long wire), and the third terminal is a movable contact that slides along the wire. When the movable contact (often referred to as the wiper) slides along the resistive element, it taps into different points of the resistance, effectively dividing the potentiometer into two resistors of variable resistance. The connection of an unknown EMF (electromotive force) in series with a galvanometer allows the user to adjust the point of contact until the galvanometer reads zero, at which point the EMF can be related to the resistance of the wire segment.