Question

Question 3.21: Determine the current drawn from a 12 V supply with internal resistance 0.5 Ω by the infinite network shown in Fig. 3.32. Each resistor has 1 Ω resistance.

Class 12 - Physics - Current Electricity Current Electricity Page-130

Answer 1

As shown in daigram 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
so, x = 2 + x/(x + 1)
=> x(x + 1) = 2(x + 1) + x
=> x² + x = 2x + 2 + x
=> x² - 2x - 2 = 0
x = (2 ±2√3)/2 = (1 ±√3)
but resistance ≠ negative so, x = (1 + √3) ohm
so, Current I drawn , I = V/Req
= 12/(1 + √3) = 6(√3 - 1)A

Answer 2

Answer:

I hope you get your answer I am sorry for bad handwriting.