The ratio of heat dissipated per second through the resistors $$5\Omega$$ and $$10\Omega$$ in the circuit given below is

$$P = \frac{V^2}{R}$$

Let $$H_1$$ be the heat dissipated per second in the $$5\Omega$$ resistor and $$H_2$$ be the heat dissipated in the $$10\Omega$$ resistor,

$$\text{Ratio} = \frac{H_1}{H_2} = \frac{V^2 / 5}{V^2 / 10}$$ (Voltage difference is same for both as they are in parallel)

$$\frac{H_1}{H_2} = \frac{10}{5} = \frac{2}{1}$$

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