JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Current Electricity

The equivalent resistance between

A

and

B

of the network shown in figure:

Answer: (D)

Solution

Read as a bridge, the upper arms from

A

are

R

then

3 R

B

, the lower arms are

2 R

then

6 R

B

, and the

9 R

resistor links the two midpoints. The upper ratio

\frac{R}{3 R}

equals the lower ratio

\frac{2 R}{6 R}

, so the bridge is balanced and no current flows through the

9 R

arm; it may be removed. The upper path is then

R + 3 R = 4 R

and the lower path

2 R + 6 R = 8 R

, and these lie in parallel between

A

and

B

R_{A B} = \frac{( 4 R ) ( 8 R )}{4 R + 8 R} = \frac{32 R}{12} = \frac{8 R}{3} .

JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Single correct option