Question

What are the possible values of resistances which one can obtain by using resistors of values 2‎Ω, 3‎Ω and 6‎Ω? Justify your answer.

Answer 1

Solution:

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

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  

 

∴ their equivalent resistance will be given as

R=1Ω

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