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Question

An infinite ladder is constructed with 1Ω and 2Ω resistors as shown in figure (a) Find the effective resistance between the points A and B. (b) Find the current that passes through the 2Ω resistor nearest to the battery
1721839_16442f4bc49c47bd8416eac3983da911.PNG

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Solution

a) Let the equation resistance of the combination be R.
(2RR+2)+1=R

2R+R+2R+2=R3R+2=R2+2R

R2R2=0

R=+1±1+4.1.22.1=1±92=1±32=2Ω

b) Total current sent by battery =6Reff=62=3

Total current i=vi=6/2=3A
Potential between A and B=6
3.1+2.i=6

3+2i=62i=3

i=1.5A

1553848_1721839_ans_7a599b8110d84d98abc6496ec200ec35.PNG

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