# How can three resistors of resistance 2Ω,3Ω and 6Ω be connected to give a total resistance of (i)4Ω, (ii)1Ω?

3.6k views
in Physics

How can three resistors of resistance 2Ω,3Ω and 6Ω be connected to give a total resistance of (i)4Ω, (ii)1Ω?

by (261k points)
selected

(i) As the total resistance (equivalent resistance) is 4Ω, the 6Ω resistor cannot be in series. So, it must be in parallel with some other resistors. In a parallel connection, the equivalent resistance (4Ω) has to be less than all the resistances. So, the resistors of 2Ω and 3Ω cannot be in parallel at one time with 6Ω.

So, the resistors have to be in a mixed combination' Let
us consider the combination shown in the figure. The equivalent resistance between B and C (which are in parallel)  The resistance between A and D = 2Ω + 2Ω = 4 Ω.
So, the combination shown in the figure is true.

(ii) Here, R1=2Ω,R2 =3Ω,R3 = 6Ω, and R =1Ω
Since the equivalent resistance of the combination is of lesser value than any of the resistors of the combination, it is clear that the resistors should be connected in parallel. It can be further confirmed by using the formula  Therefore, resistors should be connected in parallel.