Question

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

Answer 1

question is -> Determine the current drawn from a 12V supply with internal resistance 0.5Ω by the infinite network shown in Fig. 3.32. Each resistor has 1Ω resistance.

solution : see diagram, it is clear that the loop of resistance shown by arrow is repeated it times. let us assume the equivalent resistance is x, so by adding one more loop the resistance will remain same as x.

$x=2+\frac{x}{1+x}\\\\x=\frac{2(1+x)+x}{1+x}\\\\x(1+x)=2+2x+x\\\\x^2+x-3x-2\\\\x^2-2x-2=0\\\\x=\frac{2\pm\sqrt{4-4\times1(-2)}}{2}=(1+\sqrt{3})\Omega$

so, Req = x + internal resistance

= (1+√3)Ω + 0.5Ω

= 3.23Ω

so, the equivalent circuit can be now , current drawn , I = V/Req [ from ohm's law]

= 12/3.23 = 3.71A