Question

What is the effective resistance between points P and Q?

• A. $\frac{r}{2}$
• B. $\frac{r}{3}$
• C. $\frac{2r}{3}$
• D. $\frac{4r}{3}$

Answer 1

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

In the given combination, point $B$ is equivalent to point $P$ as they are connected by a conducting wire. Similarly, point $A$ is equivalent to point $Q$ for the same reason.

So, the first resistance ($2r$) is connected between $P$ and $A$, i.e. $P$ and $Q$.

The second resistance ($2r$) is connected between $A$ and $B$, i.e. $P$ and $Q$.

the third resistance ($r$) is connected between $B$ and $Q$, i.e. $P$ and $Q$.

Therefore, $\text{the three resistors are connected in parallel to each other.}$

$\therefore$ Equivalent resistance between P and Q $\frac{1}{R_{eq}}=\frac{1}{2r}+\frac{1}{2r}+\frac{1}{r}$

$⟹$ $R_{eq}=\frac{r}{2}$