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Two resistances of $$6\,\Omega$$ and $$3\,\Omega$$ are connected in parallel. The ratio of the rate of heat production in the $$6\,\Omega$$ and $$3\,\Omega$$ resistances is
In parallel both have the same voltage $$V$$, so the power is $$P = \frac{V^2}{R}$$, which is inversely proportional to $$R$$. The ratio is $$\frac{1/6}{1/3} = \frac{1}{2}$$, i.e. $$1 \colon 2$$.
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