Question

A circuit ladder is extended to infinity with resistances as 1 ohm & 2 ohm connected perpendicularly . Find its total resistance.......PLZ ANSWER IT ASAP WITH FULL SOLUTION AND THE FORMULA USED......... ^ _ ^

Answer 1

See the diagram for Ladder resistance circuits. The resistances R1 and R2 are connected perpendicularly and in an infinite chain. There are two possibilities.

Let us assume that the equivalent resistance across the battery (junctions A and B) is R.

The diagram also shows the equivalent circuits. 

   We can use the Kirchoff's laws for voltage and current to solve for R.  Or, use the formulas for series and parallel combinations for resistances.

For circuit 1:
  
      R = (R1+ R) * R2 / [ (R1+R) + R2 ]
      R R1 + R² + R R2 = R1 R2 + R R2
      R² + R1 R - R1 R2 = 0

=>  R = [ √{R1² + 4 R1 R2}  -  R1 ] / 2

Substitute for R1 = 1 Ω and R2 = 2Ω , to get:  R = 1 Ω
                      R1 = 2Ω  and R2 = 1Ω  to get:  R = (√3 - 1) Ω

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Ladder circuit 2:
  
     R = R1 + R R2 /(R+R2)
     R² + R R2 = R1 R + R1 R2 + R R2
     R² - R1 R - R1 R2 = 0

=>  R = [ R1 + √{R1² + 4 R1 R2}  ] / 2

   For R1 = 1Ω and R2 = 2Ω, we get:  R = 2 Ω
         R1 = 2Ω  and R2 = 1Ω, we get :  R = (√3 + 1 )Ω

Answer 2

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