Question

Each resistance of the circuit shown in figure is $r$. The equivalent resistance between A and B is:

• A. $r$
• B. $\frac{r}{4}$
• C. $\frac{r}{2}$
  
• D. $\frac{5r}{8}$
  

Answer 1

The correct option is C $\frac{r}{2}$

Here, the resistances between CD and BD are in series, but they are short circuited.
So they may be removed from circuit and the equivalent circuit will be as shown in figure.
The rest of two resistances are in parallel.
So the equivalent resistance between A and B is: $R_{AB}=\frac{rr}{r+r}=\frac{r}{2}$