Show how you would connect three resistors, each of resistance 6 Ω, so that the combination has a resistance of (i) 9 Ω, (ii) 4 Ω.
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 resistor in parallel
Two 6 Ω resistors are connected in parallel. Their equivalent resistance will be
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.
(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
