JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Current Electricity

Five equal resistances are connected in a network as shown in figure. The net resistance between the points

A

and

B

is :

Answer: (B)

Solution

The five equal resistances join four nodes: the terminal

A

, the terminal

B

which is the corner

C

, and the two corners

D

and

E

. One resistance runs from

A

D

and one from

A

E

; one runs from

C

D

and one from

C

E

; the fifth joins

D

E

. Interchanging

D

and

E

maps the network onto itself while leaving

A

and

C

untouched, so

D

and

E

are at the same potential, the resistance between them carries no current and may be removed. What remains is the path through

D

, of resistance

2 R

, in parallel with the path through

E

, also of resistance

2 R

R_{A B} = \frac{2 R \times 2 R}{2 R + 2 R} = R

so the net resistance between the two terminals is

R

JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Single correct option