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. $ \frac{2}{3}R $

Answer 1

Answer: (A)

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,
$R'=\frac{R_{U} \times R_{L}}{R_{U}+R_{L}}$
$=\frac{2 R \times 2 R}{2 R+2 R}=\frac{4 R^{2}}{4 R}=R$