Question

In the circuit given below, if the equivalent resistance between points $a$ and $b$ is $R$, then find the value of $R$ in terms of $r$.

• A. $\frac{r}{3}$
• B. $\frac{r}{\sqrt{3}}$
• C. $\sqrt{3}r$
• D. $\frac{\sqrt{r}}{3}$

Answer 1

The correct option is C $\sqrt{3}r$

We can calculate the equivalent resistance between points $a$ and $b$ as shown below.

Equivalent resistance between points $a$ and $b$ is $R_{eq}=\frac{r(R+r)}{R+2r}+r$
However, according to the question, the equivalent resistance between points $a$ and $b$ is $R$.
$\therefore R=\frac{r(R+r)}{R+2r}+r$
$\Rightarrow R^2=3r^2$
$\Rightarrow R=\sqrt{3}r$
Hence, the correct answer is option (c).