Question

A infinite network of resistance constructed with one ohm​

Answer 1

Answer:

Correct option is

A

1Ω

 

Step 1: Find Smallest Repeating unit [Refer Fig. 1]  

Step 2: Replace with equivalent resistance R. [Refer Fig. 2]

After the first smallest repeating unit, the remaining circuit is also same as the initial circuit.

Therefore, if we assume the equivalent resistance between A & B as R, then the resistance of the remaining circuit will also be R as shown in the figure.

Step 3: Find equivalent resistance between A and B and equate with R. [Refer Fig. 3]

From figure, the equivalent resistance between A & B will be equal to the equivalent resistance of the remaining circuit. So,

                 R  

AB

​

=1+  

2+R

2R

​

 

         ⇒  R=1+  

2+R

2R

​

 

         ⇒  3R+2=R  

2

+2R  

         ⇒  R  

2

−R−2=0  

         ∴      

R=2Ω

​

      (Here, Negative value can is rejected)  

 

Hence Equivalent resistance between points A and B is 2Ω.

solution

Explanation: