Question

Show how you would connect three resistors, each of resistance 6 Ω, so that the combination has a resistance of 4 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 series:

Two 6 Ω resistors are in series. Their equivalent resistance will be the sum 6 + 6 = 12 Ω.

The third 6 Ω resistor is in parallel with 12 Ω. Hence, equivalent resistance will be

`1/(1/12+1/6)=(12xx6)/(12+6)=4Omega.`

Therefore, the total resistance is 4 Ω.