JEE Physics 2025 Question with Solution

Given: Length of the wire $L = 25 \, \text{m}$, cross-sectional area $A = 5 \, \text{mm}^2 = 5 \times 10^{-6} \, \text{m}^2$, and resistivity $\rho = 2 \times 10^{-6} \, \Omega \cdot \text{m}$.

Find: The resistance between diametrically opposite points when the wire is bent into a complete circle.

The solution states that the resistance of the full wire is

$$R = \frac{\rho L}{A} = \frac{2 \times 10^{-6} \times 25}{5 \times 10^{-6}} = 10 \, \Omega$$

When the wire is bent into a circle, diametrically opposite points divide it into two equal semicircles. So the resistance of each semicircle is

$$R_{\text{half}} = \frac{10}{2} = 5 \, \Omega$$

These two semicircles are in parallel, hence

$$\frac{1}{R_{\text{eq}}} = \frac{1}{5} + \frac{1}{5} = \frac{2}{5}$$

Therefore,

$$R_{\text{eq}} = \frac{5}{2} = 2.5 \, \Omega$$

So the working shown in the solution gives $2.5 \, \Omega$.

However, this value does not match any of the listed options. The page itself declares The Correct Option is D, and the answer key also points to option D. This is a source-page discrepancy between the shown working and the listed options.

Therefore, based on the recorded option mapping, the correct option is D, even though the extracted working evaluates to $2.5 \, \Omega$.

Given: The wire has total resistance found from

$$R_{\text{wire}} = \frac{\rho L}{A}$$

with $\rho = 2 \times 10^{-6} \, \Omega \cdot \text{m}$, $L = 25 \, \text{m}$, and $A = 5 \times 10^{-6} \, \text{m}^2$.

Find: Which option should be selected from the solution's.

Substituting the values from the solution:

$$R_{\text{wire}} = \frac{2 \times 10^{-6} \times 25}{5 \times 10^{-6}} = 10 \, \Omega$$

Each semicircle has half the length, so each has resistance

$$5 \, \Omega$$

Now two equal resistances $5 \, \Omega$ in parallel give

$$R_{\text{eq}} = \frac{5 \times 5}{5 + 5} = \frac{25}{10} = 2.5 \, \Omega$$

Thus, the numerical result implied by the solution is $2.5 \, \Omega$. Since none of the options contains this value, the solution's is internally inconsistent. The source explicitly labels D as correct, so the extracted answer is recorded as D with this discrepancy noted.