Each of the resistance in the network shown in figure is equal to R. Find the equivalent resistance between two terminals A and B.

Question

Each of the resistance in the network shown in figure is equal to R. Find the equivalent resistance between two terminals A and B. (A)  R  (B)  5R  (C)  2R  (D)  (2/3)R

Tardigrade Admin · Accepted Answer

Simplified form of the circuit is shown below.

The simplified circuit is balanced Wheatstone's bridge, so the resistance in arm DC remains unaffected.
Resistance of upper arms

R_{U} = R + R = 2 R

Resistance of lower arms

R_{L} = R + R = 2 R

Net resistance of the circuit,

R^{'} = \frac{R _{U} \times R _{L}}{R _{U} + R _{L}}

= \frac{2 R \times 2 R}{2 R + 2 R} = \frac{4 R ^{2}}{4 R} = R

Q. Each of the resistance in the network shown in figure is equal to $R$ . Find the equivalent resistance between two terminals $A$ and $B$ .

$R$

$5 R$

$2 R$

$\frac{2}{3} R$

Q. Each of the resistance in the network shown in figure is equal to R. Find the equivalent resistance between two terminals A and B.

R

5R

2R

32​R

Q. Each of the resistance in the network shown in figure is equal to $R$ . Find the equivalent resistance between two terminals $A$ and $B$ .

$R$

$5 R$

$2 R$

$\frac{2}{3} R$