Determine the current drawn from a 12V supply with internal resistance 0.5Ω by the infinite network shown in Fig. Each resistor has 1Ω resistance.
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Let X be the equivalent resistance of the infinite network
This network consists of infinite sets of three resistors of 1Ω,1Ω and adding one more set across AB to he infinite network will not affect the equivalent resistance.
We know that
Resistance between A and B
Rp=xx+1(∴1R=1x+11)
Rs=1+xx+1+1=2+xx+1
This must be equal to the initial resistance x
∴x=2+xx+1
⇒x+x2=2+2x+x
⇒x2−2x−2=0
⇒x=2±√4+82=1±√3
But x≠1−√3
∴x=(1+√3)Ω
=2.732Ω
Current I=e.m.fTotalresistance=122.732+0.5
I=3.7A
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