Q 12-03-219JEE MainJEE Main 2021 (27 Aug, Shift 2)Medium
The ratio of the equivalent resistance of the network (shown in figure) between the points $a$ and $b$ when switch is open and switch is closed is $x : 8$. The value of $x$ is
Numerical value type. Enter your answer.
Answer: 9
**Switch open:** two branches of $R + 2R = 3R$ in parallel: $R_{open} = \dfrac{3R}{2}$.
**Switch closed:** the midpoints are joined, giving $(R \parallel 2R)$ in series with $(2R \parallel R)$:
$$R_{closed} = \frac{2R}{3} + \frac{2R}{3} = \frac{4R}{3}$$
$$\frac{R_{open}}{R_{closed}} = \frac{3/2}{4/3} = \frac{9}{8} \Rightarrow x = 9$$
Solution by Sreeraj P, M.Sc Physics