The $V-I$ graphs for two resistors of the same material and the same radii with lengths $L_{1}$ and $L_{2}$ are shown below. If $L_{1} > L_{2}$, state with reason, which of these graphs represents voltage-current change for $L_{1}$?

(B) The resistance $R$ of a conductor is given by $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity, $L$ is the length, and $A$ is the cross-sectional area.
Since both resistors are made of the same material ($\rho$ is constant) and have the same radii ($A$ is constant), the resistance $R$ is directly proportional to the length $L$ $(R \propto L)$.
Given $L_{1} > L_{2}$, it follows that $R_{1} > R_{2}$.
In a $V-I$ graph, the slope represents the resistance $(R = \frac{V}{I} = \text{slope})$. A steeper slope indicates a higher resistance.
Comparing the two graphs, graph $B$ has a greater slope than graph $A$, meaning the resistance of graph $B$ is greater than that of graph $A$.
Since $R_{1} > R_{2}$, graph $B$ corresponds to the longer length $L_{1}$.