Q174 / 200 · WBJEE 2013 · Physics
The equivalent resistance between the points $a$ and $b$ of the electrical network shown in the figure is 
- A$6 r$
- B$4 r$
- C$2 r$
- Correct answerD$r$
Solution
The equlvalent circuit for the given electrical network is 
This is a balanced Wheatstone bridge, so the arm containing $2 r$ not in use. So, we have
So, the equivalent resistance between a and bis
$$
\frac{1}{r^{\prime}}=\frac{1}{2 r}+\frac{1}{2 r} \Rightarrow r^{\prime}=\frac{2 r}{2}=r
$$
This is a balanced Wheatstone bridge, so the arm containing $2 r$ not in use. So, we have
So, the equivalent resistance between a and bis
$$
\frac{1}{r^{\prime}}=\frac{1}{2 r}+\frac{1}{2 r} \Rightarrow r^{\prime}=\frac{2 r}{2}=r
$$Hence, the correct answer is option: 'D'.