Question

In the given Wheatstone's network, what should be the value of R for the network to be balanced?

Answer 1

Given: R₁ = 50 Ω, R₂ = 50 Ω

R3 = R parallel with 100 Ω, R₄  =50 Ω

To find: R = ?

For a balanced network,

`R_1/R_2 = R_3/R_4`       ...(i)

First, we calculate R₃

`1/R_3 = 1/R + 1/100`

`1/R_3 = (100 + R)/(100R)`

∴ `R_3 = (100R)/(100 + R)`

Putting in equation (i), we get

`50/50 = (100R//100 + R)/50`

∴ `50 = (100 R)/(100 + R)`

∴ 5000 R +50R= 100 R

∴100R- 50R = 5000

∴ 50 R = 5000

∴ R = 100 Ω