Question

Show how would you join three resistors, each of resistance $9$ $\Omega$ so that the equivalent resistance of the combination is $13.5\Omega$?

Answer 1

Resistance of each resistor $R=9\Omega$
Two resistor connected across A and B are connected in parallel.
Equivalent resistance across A and B $R_{AB}=\frac{R\times R}{R+R}=\frac{R}{2}=\frac{9}{2}=4.5\Omega$
This equivalent resistance is connected in series to another resistor $R$.
So equivalent resistance across A and C $R_{AC}=R_{AB}+R=4.5+9=13.5\Omega$