Question

show how would you join three resistors of 9ohm so that the equivalent resistance of the combination is (i) 13ohm (ii) 6ohm

Answer 1

For 6 Ohm's,

Connect two resistor in series,
then R1 = 9 ohm + 9 ohm
R1 = 18 ohms

Now connect this in parallel,

1/R = 1/R1 + 1/R2
1/R = 1/18 + 1/9
1/R = 1+2 / 18
R = 18/3
R = 6 Ohm's

For 13.5 Ohm's

In parallel,
1/R2 = 1/9 + 1/9
R2 = 9/2

now in series,
R = 9/2 + 9
R = 9 + 18 / 2
R = 27/2
R = 13.5 Ohm's

13 Ohm's is not possible