We find the max potential difference first.

To find pd across the 12 ohm resistor, we take 12/12+6 x 6V, and we get 4V.

Hence, the maximum voltage we get is 4V


Now, we try and the min potential difference

If the wire is connected to the front most end of the resistor, the resistance is 0 ohm. Since V=IR, when R=0, V=0.

Hence, max is 4V and min is 0V

Why when connected as such then r=0?

Basically, we assume the wires themselves to have zero resistance, so if we connect the arrow to a point next to A (where there are no resistors in between), then the resistance between the two points is zero, so there is no potential difference.

Hmmmm what do they mean by move from a to b tho? How does the contact change? In what way?

The slider’s fixed contact point is at A while the slider’s variable point is allowed to move freely. Let’s call this variable point P.

Though Arnold mentioned that the slider can move between A and B, I am more of the view that the variable point P moves “from one end of the resistor to the other”. But since the question has mentioned it, then we accept it as such. This is what makes the slider variable. We are able to control the voltage output by adjusting the position of P.

When P is close to A, there will be technically no resistance between A and P. As such, no voltage reading will be registered.

When P is close to B, the voltage reading measured will be that across the full resistor, so the reading is at its maximum.

When P is located, say, in the middle, the voltage reading measured will be somewhere in between the two values as we are only taking a portion of the resistance of the resistor.

Ok understand alr ty