Question

How can three resistors of resistances 2 Ω. 3 Ω. and 6 Ω be connected to give a total resistance of (a) 4 Ω (b) 1 Ω ?

Answer 1

1 ohm
all three in parallel
4 ohm
3 and 6 in parallel and 2 in series

Answer 2

(a) equivalent resistance = 4Ω

let's connect 3Ω and 6Ω in parallel combination.

1/R' = 1/3Ω + 1/6Ω

= 3/6Ω

= 1/2Ω

⇒R' = 2Ω

now connecting R' and 2Ω are joined in series combination.

so, Req = R' + 2Ω = 2Ω + 2Ω = 4Ω

so, equivalent resistance will be 4Ω when 3Ω and 6Ω are joined in parallel and then these are joined in series with 2Ω as shown in figure.

(b) equivalent resistance = 1Ω

joining all resistors are in parallel combination.

1/Req = 1/2Ω + 1/3Ω + 1/6Ω

= 1/2Ω + (1 + 2)/6Ω

= 1/2Ω + 3/6Ω

= 1/2Ω + 1/2Ω = 1/1Ω

so, Req = 1Ω

so, equivalent resistance will be 1Ω only when all resistors are joined in parallel combination.