If two wires having resistance $R$ and $2R$. Both joined in series and in parallel then ratio of heat generated in this situation, applying the same voltage,
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(c) Heat $H = \frac{{{V^2}t}}{R}$ $ \Rightarrow $ $H \propto \frac{1}{R}$ (If $V$, $t$ constant)
$ \Rightarrow $ $\frac{{{H_S}}}{{{H_P}}} = \frac{{{R_P}}}{{{R_S}}} = \frac{{\left( {\frac{{R \times 2R}}{{3R}}} \right)}}{{(R + 2R)}} = \frac{2}{9}$
$ \Rightarrow $ $\frac{{{H_S}}}{{{H_P}}} = \frac{{{R_P}}}{{{R_S}}} = \frac{{\left( {\frac{{R \times 2R}}{{3R}}} \right)}}{{(R + 2R)}} = \frac{2}{9}$
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