The difference between the maximum and minimum values of voltage V across the 3 ohm resistor would be 9V.
To find the minimum and maximum values of V across the 3 ohm resistor, you will need to use Ohm’s Law, V=IR.
You already know the resistance is 3 ohms across the resistor; in order to calculate the maximum/minimum voltage across it, you will need to work out the maximum/minimum current of the series circuit.
Using Ohm’s Law to find the maximum and minimum current:
I = V/R
Where:
V = 12V (this is the emf, no volts are lost to the cell because the cell has a negligible internal resistance therefore all the 12V is transferred to the resistors in the circuit.)
The value for R however, changes due to the resistance in the variable resistor varying from 0 to 9 ohms.
The minimum value of R would be 3 ohms, where the resistance of the variable resistor is 0. Therefore total resistance = 3 + 0 = 3 ohms
Maximum value of R would be 12 ohms, where the resistance of the variable resistor is at a maximum of 9 ohms. Therefore total resistance = 3 + 9 = 12 ohms
The rest of the explanation is in the picture, hope it makes sense
