Q 12-03-119JEE MainJEE Main 2023 (30 Jan, Shift 2)Hard
The equivalent resistance between $A$ and $B$ is ______.
Answer: (A) $\dfrac23\ \Omega$
The left vertical wire is a single node (joined to $A$) and the right vertical wire is a single node (joined to $B$). So every path runs between $A$ and $B$:
- Top arc: $1.5+0.5=2\ \Omega$
- Top straight: $12\ \Omega$
- The X: $8\parallel2=1.6\ \Omega$ to the centre, then $4\parallel6=2.4\ \Omega$ to $B$: $4\ \Omega$
- Bottom straight: $6\ \Omega$
- Bottom arc: $1+1=2\ \Omega$
All in parallel:
$$\frac1{R}=\frac12+\frac1{12}+\frac14+\frac16+\frac12=\frac{18}{12}\ \Rightarrow\ R=\frac23\ \Omega$$
Solution by Sreeraj P, M.Sc Physics