\(Case I : Length (L) ==> Resistance = R , mass = m\)

\(Case II : Length (2L) ==> Resistance = 2R ,mass = 2\,m \)

\(\frac{{{m_1}{S_1}\Delta {T_1}}}{{{m_2}{S_2}\Delta {T_2}}} = \frac{{i_1^2{R_1}{t_1}}}{{i_2^2{r_2}{t_2}}}\)

\(==>\) \(\frac{{mS\Delta T}}{{2mS\Delta T}} = \frac{{i_1^2Rt}}{{i_2^22Rt}}\) \(==>\) \({i_1} = {i_2}\) \(==>\) \(\frac{{{{(3E)}^2}}}{{12}} = \frac{{{{(NE)}^2}}}{{2R}}\)

\(==> N = 6\)