Consider an infinite ladder of network shown In fig 5.223. A voltage is applied between points A and B. If the voltage is halved after each section, find the ratio of `R_1//R_2`.
Suggest a method to terminate it after a few sections without introducing much error in its attenuation.

Options

A. `1:2`
B. `2:1`
C. `1:1`
D. `2:3`

Answer

B

Explanation

Let `R` be the equivalent resistance. Since the network is infinite .The addition of one more unit of two resistance `R_(1) and R_(2)` will not alter the total resistance of network i.e. it should be `R`

Now `R = R_(1) = (R_(2)R)/(R_(2) + R)`....(i)
Since the voltage is halved after each section
`:. R_(1) = (R_(2)R)/(R_(2) + R)`
Putting the value of `R_(1)` in (i) we get
`R_(1) = (2R_(2)R)/(R_(2) + R)` or `R_(2) = R = 2R_(2)`
`R_(2)= R`...(iii)
From equation (ii) `R_(1) = (R^(2))/(2R)=(R)/(2)`....(iv)
`2R_(1)= R`
From (iii) and (iv) `(R_(2))/(R_(1)) = 2`