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Question

An infinite ladder is constructed with 1 Ω and 2 Ω resistors as shown in figure. Find the total current provided by the battery of EMF 12 V?


A

2Ω

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B

1Ω

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C

Infinite

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D

None of these

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Solution

The correct option is A

2Ω


Its an infinte circuit. The first thing we need to identify the repeating unit. There has to be a repeating unit or the infinte circuit will become impossible to solve. Let’s see…

So we see the unit encircled is the repeating unit here...it comes again and again I can take out one of those units and the total number of units still remains infinte…Like this.

All I did was take out just one repeating unit and express the rest as Req
The 2 Ω resistor is in parallel with Req so they together become 2Req2+Req
And this would be in series with 1 Ω resistor so the resistance across 12 V battery becomes 1+2Req(2+Req)
But wait!!! Isnt the equivalent resistance across 12 V supposed to be just Req?
Yeah right! So lets equate them
2Req(2+Req)= Req
This will be a quadratic equation...
Req= 2 Ω
We ignore the negative answer!


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