JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Current Electricity

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 ____.

Answer: 9

Solution

Label the top path

a - R - C - 2 R - b

and the bottom path

a - 2 R - D - R - b

, with the switch bridging

C

and

D

. With the switch open each path is

R + 2 R = 3 R

and the two run in parallel:

R_{open} = \frac{3 R \cdot 3 R}{3 R + 3 R} = \frac{3 R}{2} .

With the switch closed

C

and

D

merge, so

a

to the junction is

R ∥ 2 R = \frac{2 R}{3}

and the junction to

b

2 R ∥ R = \frac{2 R}{3}

, in series:

R_{closed} = \frac{2 R}{3} + \frac{2 R}{3} = \frac{4 R}{3} .

The ratio is

\frac{R _{open}}{R _{closed}} = \frac{3 R /2}{4 R /3} = \frac{9}{8}

, so

x = 9

JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Integer answer