Question

In the network resistors each of value R shown in the fig., calculate the equivalent resistance between the functions A and B :-

• A. $12R$
• B. $7R/12$
• C. $12R/7$
• D. $R/12$

Answer 1

The correct option is B $7R/12$

If we connect a battery across A and B, then E and D will be at the same potential and F and C will be at the same potential. Then the equivalent is as shown in figure.
here, $R_{eq1}=R||2R||R=(1/R+1/2R+1/R{)}^{-1}=(2R/5)$
Thus, equivalent resistance A and B is $R_{AB}=R||(R/2+2R/5+R/2)=R||\left(7R/5\right)=\frac{R\left(7R/5\right)}{R+7R/5}=\frac{7R}{12}$