A uniform metallic wire of resistance \( 4\,\Omega \) is bent to form a circle. What is the effective resistance between the ends of its diameter?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 1\,\Omega \)
The two ends of a diameter divide the circle into two equal semicircular wires. Resistance of a uniform wire is proportional to its length, so each half has half of the total resistance, and the two halves are in parallel between the ends of the diameter.
\( \displaystyle R_{\mathrm{half}} = \frac{4}{2} = 2\,\Omega \)
\( \displaystyle R_{\mathrm{eff}} = \frac{2\times2}{2+2} = 1\,\Omega \)