$V-I$ graphs for two wires $A$ and $B$ are shown in the figure. If both the wires are made of the same material and are of equal thickness,which of the two is of more length? Give justification for your answer.

(A) We know that $V = IR$,which implies $R = V/I$. The slope of the $V-I$ graph represents the resistance $R$ of the wire.
From the given graph,the slope of line $A$ is greater than the slope of line $B$,therefore,the resistance of wire $A$ $(R_A)$ is greater than the resistance of wire $B$ $(R_B)$.
We know that the resistance of a wire is given by the formula $R = \rho \frac{l}{A}$,where $\rho$ is the resistivity,$l$ is the length,and $A$ is the cross-sectional area.
Since both wires are made of the same material,their resistivity $\rho$ is the same. Since they are of equal thickness,their cross-sectional area $A$ is also the same.
Thus,$R \propto l$. Since $R_A > R_B$,it follows that the length of wire $A$ is greater than the length of wire $B$.