Question

An infinite ladder network of resistance is constructed with 1Ω and 2Ω resistances as shown. The 6V battery has negligible resistance. Then the effective resistance between A and B is

(1) 1Ω

(2) 2Ω

(3) 3Ω

(4) Infinite

Answer 1

(2) 2Ω

Let x be the effective resistance between points A and B. Since the chain is an infininte one this may also be taken as the effective resistance of the chain beyond the points C and D. Hence the may replace the given chain by the equivalent diagram as shown

We this have,

Since the equivalent resistance cannot be negative we have,

x = 2Ω