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NCERT Class XII Chapter
Current Electricity
Questions With Solutions

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Question : 21
Total: 24
Determine the current drawn from a 12 V supply with internal resistance 0.5 Ω by the infinite network shown in figure. Each resistor has 1 Ω resistance.
Solution:  

As shown in diagram the loop of resistance shown by arrow is repeated at times, let us assume the equivalent resistance is x, so by adding one more loop the resistance will remain as x.

x = 2 +
x
1+x
(1 + x)x = 2 (1 + x) + x
x + x2 = 2 + 3 x
x2 – 2x – 2 = 0
x =
2±√4−4×1(−2)
2
 = (1+√3) Ω = 2.732 Ω
Now, current drawn
I =
12
3.23
 = 3.71 A
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