Suppose the drift velocity $${v_d}$$ in a material varied with the applied electric field $$E$$ as $${v_d} \propto \sqrt E .$$   Then $$V-I$$  graph for a wire made of such a material is best given by :

Solution :
$$\eqalign{ & i = neA{V_d}\,{\text{and}}\,{V_d} \propto \sqrt E \,\left( {{\text{Given}}} \right) \cr & {\text{or,}}\,i \propto \sqrt E \cr & {i^2} \propto E \cr & {i^2} \propto V \cr} $$
Hence graph (C) correctly depicts the $$V-I$$  graph for a wire made of such type of material.