JEE Physics 2023 Question with Solution

Given: Two resistors $R$ and $3R$ are connected in parallel.

Find: The ratio of thermal energy released in them.

For resistors in parallel, the potential difference across each resistor is the same. The power dissipated is

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

So for $R$,

$$P_1 \propto \frac{1}{R}$$

and for $3R$,

$$P_2 \propto \frac{1}{3R}$$

Therefore,

$$\frac{P_1}{P_2} = \frac{3R}{R} = 3:1$$

Since thermal energy released in the same time is proportional to power, the ratio of thermal energy is $3:1$.

The solution working gives $3:1$, although the solution's marks the correct option as D. Based on the solution, the defensible answer corresponds to option A.