Question

Each resistance of the circuit shown in diagram is $r$. The equivalent resistance across the points $\text{A}$ and $\text{B}$ is

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

Answer 1

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

We can redraw the given circuit as shown below.


Since, points $\text{B}$ and $\text{C}$ are connected to a wire, so both have same potential.


So, resistance $\text{AB}$ and $\text{AC}$ are in parallel.

Similarly, $\text{BC}$ and $\text{CD}$ are in parallel.

So,

So, equivalent resistance between points $\text{A}$ and $\text{B}$ is $r/2$.

$\therefore r_{AB}=\frac{r}{2}$

Therefore, option $\left(C\right)$ is the right answer.