JEE Physics 2023 Question with Solution

Given: Two identical heater filaments are connected first in parallel and then in series at the same applied voltage.

Find: The ratio of heat produced in the same time for parallel to series.

Heat produced in the same time is proportional to power, so we compare powers.

The power dissipated in a resistor is

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

For two identical resistors, in parallel the effective resistance is

$$R_{\text{eff}} = \frac{R}{2}$$

So,

$$P_{\text{parallel}} = \frac{V^2}{R/2} = 2\frac{V^2}{R}$$

For series connection, the effective resistance is

$$R_{\text{eff}} = 2R$$

So,

$$P_{\text{series}} = \frac{V^2}{2R}$$

Now the ratio is

$$\frac{P_{\text{parallel}}}{P_{\text{series}}} = \frac{2 \frac{V^2}{R}}{\frac{V^2}{2R}} = 4$$

Thus, the ratio of heat produced is $4 : 1$.

The correct option is B.