Ratio of thermal energy released in two resistor $$R$$ and $$3R$$ connected in parallel in an electric circuit is:

Two resistors $$R$$ and $$3R$$ are connected in parallel and therefore share the same voltage, which we denote by $$V$$.

The power dissipated (rate of thermal energy release) in each resistor is given by $$P = \frac{V^2}{R_{\text{resistor}}}$$. Hence, for the resistor of resistance $$R$$ we have $$P_1 = \frac{V^2}{R}$$, while for the resistor of resistance $$3R$$ it is $$P_2 = \frac{V^2}{3R}$$.

Since both resistors operate under the same voltage and for the same time, the ratio of the thermal energies they release equals the ratio of their powers. It follows that $$\frac{P_1}{P_2} = \frac{V^2/R}{V^2/(3R)} = \frac{3R}{R} = 3$$, so $$P_1 : P_2 = 3 : 1$$.

Answer: Option A (3 : 1)