In an electric circuit, two resistors of resistance R and 2R are...

In a series circuit, the current $I$ flowing through all the resistors is the same.

The thermal energy developed in a resistor of resistance $R$ over a time $t$ is given by Joule's law of heating:

$H = I^2 R t$

For the first resistor of resistance $R$, the thermal energy developed is:

$H_1 = I^2 R t$

For the second resistor of resistance $2R$, the thermal energy developed is:

$H_2 = I^2 (2R) t$

The ratio of the thermal energy developed in $R$ to that in $2R$ is:

$\dfrac{H_1}{H_2} = \dfrac{I^2 R t}{I^2 (2R) t} = \dfrac{1}{2}$

Thus, the ratio is $1 : 2$.