Show how you would connect three resistors, each of resistance 6, so that the combination has a resistance of (i) 9, (ii) 4

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.
(a) Two resistors in parallel
Two 6 Ω resistors are connected in parallel. Their equivalent resistance will be
The third 6 Ω resistorsare in series with 3 Ω. Hence, the equivalent resistance of the circuit is 6 Ω+ 3 Ω = 9 Ω. (b) Two resistor 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 the sum of the resistors

Therefore, the total resistance is 4 Ω.

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