Two resistors are connected in series. In series, the current flows through both the resistors is same.

Formula used:

Energy is given by the formula

Energy dissipated,

Where

I is the current

R is the resistance

T is the time period

Energy developed in the resistor R is

Energy developed in the resistor 2R is

The ratio of energy developed in R and 2R is =

When two resistors R and 2R are connected in series then the ratio of thermal energy developed is 1:2.

Conclusion : Two resistors R and 2R are connected in series, the thermal energy developed in R and 2R are in the ratio 1:2 respectively. So option A is correct.