Question

The resistance of all the wires between any two adjacent dots is $R$. The equivalent resistance between $A$ and $B$ as shown in figure is

• A. $\frac{7}{3}R$
• B. $\frac{7}{6}R$
• C. $\frac{14}{8}R$
• D. none of these

Answer 1

The correct option is B $\frac{7}{6}R$

Here the equivalent resistance of each triangle is $R_{eq1}=\frac{(R+R)R}{(R+R)+R}=\left(2/3\right)R$

Now reduce the side by connecting resistance in series as shown in figure.
Here, $R_{eq2}=\left(2/3\right)R+\left(2/3\right)R=\left(4/3\right)R$

Now the circuit is a balanced Wheatstone bridge. So middle resistor R is not working.

Thus, $R_{AB}=\frac{\left[\right(4/3)R+R]\left[\right(4/3)R+R]}{\left[\right(4/3)R+R]+\left[\right(4/3)R+R]}=\frac{7}{6}R$