JEE Mains · Physics · STD 12 - Current electricity
- JEE Mains 2026
- Easy
- MCQ
A wire of uniform resistance \(\lambda \Omega / m\) is bent into a circle of radius \(r\) and another piece of wire with length 2 r is connected between points A and B \(( AOB )\) as shown in figure. The equivalent resistance between points A and B is ___________\(\Omega\).
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \( \frac{6\pi\lambda r}{3\pi+16} \)
Step-by-step Solution
Detailed explanation
\( \frac{1}{R_{AB}}=\frac{2}{\lambda\pi r}+\frac{1}{\lambda.2r}+\frac{2}{\lambda.3\pi r} \)
\(=\frac{1}{\lambda r}[\frac{2}{\pi}+\frac{1}{2}+\frac{2}{3\pi}] \)
\( =\frac{1}{\lambda r}(\frac{12+3\pi+4}{6\pi})=\frac{1}{\lambda r}.(\frac{16+3\pi}{6\pi}) \)
\( R_{AB}=\lambda r(\frac{6\pi}{16+3\pi}) \)
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