Two resistors R and 2R are connected in series in an electric circuit. The thermal energy developed in R and 2R is in the ratio of _________.

The resistor of resistance R ohm and 2R ohm are given.
Now, the current flowing in a series combination is the same through its components. 

Let the current I flow through R as well as through 2R.
We know.
Thermal energy across the resistor in time t sec = I²Rt
Let H₁ and H₂ be thermal energy across R and 2R respectively
H₁ = I²Rt and H₂ = I²(2R)t
Now, $\frac{{\mathrm{H}}_1}{{\mathrm{H}}_2}$ = $\frac{{\mathrm{I}}^{2\mathrm{ }}\mathrm{Rt}}{{\mathrm{I}}^{2\mathrm{ }}2\mathrm{Rt}}$ = $\frac{1}{2}$.

The thermal energy developed in R and 2R is in the ratio of 1:2.