Question

Find the equivalent resistance between points $M$ and $N$ in the circuit shown in figure.

• A. $\frac{2r}{3}$
• B. $3r$
• C. $\frac{r}{6}$
• D. $\frac{r}{2}$

Answer 1

The correct option is A $\frac{2r}{3}$

The network shown in figure may be successively reduced step by step as shown in the figure.

We can observe that the two $r$ resistances are connected in series between $M$ and $Q$ and then the equivalent resistance is again connected in parallel to the $2r$ resistance.

Thus the net resistance between $M$ and $Q$ is

$r_{\text{eq}}=\frac{(r+r)\times 2r}{(r+r)+2r}=r$


From figure $\left(d\right)$ we can infer that the two $r$ resistors between $M$ and $N$ are in series and their combination is in parallel with $r$.

Thus, $R_{\text{eq}}=\frac{2r\times r}{2r+r}=\frac{2r}{3}$

$$\begin{array}{c}\text{Why this question?}\\ \underset{–}{\text{Tip}:}\text{Observe the point of connections for the given resistors}\\ \text{and then segregate them in series and parallel connection.}\\ \text{Thereafter reduce the circuit by successive reduction technique.}\\ \text{This method is very helpful in simplifying the complicated circuits.}\end{array}$$