Question

how can three resisters of resistances 2ohm,3ohm,and 6ohm be connected to give a total resistance of (a) 4ohm (b) 1ohm?

Answer 1

There are three resistors of resistances 2 Ω, 3 Ω, and 6 Ω respectively.

(a) If we connect the given three resistors in the following way then we get net resistance as 4Ω

Here, 6 Ω and 3 Ω resistors are connected in parallel.

Therefore, their equivalent resistance will be given by

⇒R=2 Ω

This equivalent resistor of resistance 2Ω is connected to a 2Ω resistor in series.

Therefore, equivalent resistance of the circuit = 2Ω + 2Ω =4Ω

==PICTURE 2nd==

Hence, the total resistance of the circuit is 4Ω.

(b) If we connect the given three resistors in the following way then we get net resistance as 1Ω. Here all the resistors are connected in parallel

== PICTURE 3rd==

∴ their equivalent resistance will be given as
R=1Ω

==PICTURE 1st ==

Therefore, the net equivalent resistance of the circuit is 1Ω.

Answer 2

if we connect one 2 ohm resistor in series with the 3 and 6 in parallel so we will get 4 ohm as net resistance

if we connect all these in parallel we will get 1 ohm as net resistance