The student first measures the potential difference $V_1$ across a single resistor ${\mathbf{R}}_{\mathbf{A}}$ and the current $I_1$ in the circuit:

Calculate the resistance $R_1$ of the resistor ${\mathbf{R}}_{\mathbf{A}}$ using the equation:

The student then connects a second resistor ${\mathbf{R}}_{\mathbf{B}}$ in series with ${\mathbf{R}}_{\mathbf{A}}$. She measures the potential difference $V_2$ across the combination and the current $I_2$ in the circuit:

Calculate the combined resistance $R_2$ of the two resistors in series, using the equation:

The student then connects a third resistor ${\mathbf{R}}_{\mathbf{C}}$ in series with both ${\mathbf{R}}_{\mathbf{A}}$ and ${\mathbf{R}}_{\mathbf{B}}$. She measures the potential difference $V_3$ across all three resistors and the current $I_3$ in the circuit:

Calculate the combined resistance $R_3$ of the three resistors in series, using the equation:

Another student suggests that $R_3=3\times R_1$. State whether the results support this suggestion. Justify your answer by comparing the values.

Explain how the student could use the single-resistor circuit to check if the three resistors ${\mathbf{R}}_{\mathbf{A}}$, ${\mathbf{R}}_{\mathbf{B}}$, and ${\mathbf{R}}_{\mathbf{C}}$ each have the same individual resistance.

In a separate part of the experiment, three resistors are connected in parallel with a variable resistor in the main branch. Suggest a reason for including a variable resistor in this circuit.