Question

Show how you would connect three resistors, each of resistance 6 Ω, so that the combination has a resistance of 9 Ω.

Answer 1

If we connect the resistors in series, then the equivalent resistance will be the sum of the resistors, i.e., 6 Ω + 6 Ω + 6 Ω = 18 Ω, which is not desired. If we connect the resistors in parallel, then the equivalent resistance will be 6/2 = 3 Ω is also not desired. Hence, we should either connect the two resistors in series or parallel.
Two resistors in parallel:

Two 6 Ω resistors are connected in parallel. Their equivalent resistance will be

`1/(1/6+1/6)=(6xx6)/(6+6)=3Omega`

The third 6 Ω resistor is in series with 3 Ω. Hence, the equivalent resistance of the circuit is 6 Ω+ 3 Ω = 9 Ω.