A circuit shown in the figure has resistances `20 Omega` and `30 Omega`. At what value of resistance `R_x` will the thermal power generated in it be practically independent of small variations of that resistance? The voltage between points `A` and `B` is supposed to be constant in this case.

Answer

A, B

Explanation

V=constant

`V_1=(((30R_x)/(30+R_x))/((3R_x)/(30+R_x))+20)`
`=((30R_x)/(50R_x+600))V`
`:.` Power generated in `R_x` is
`P=V_1^2/R_x=(900R_xV^2)/((50R_x+600)^(2)`
For P to be constant
`(dP)/(dR_x)=0`
`(50 R_x+600)^2(900V^2)`
or `(-1800xx50xxR_xV^2(50 R_x+600))/((50 R_x+600)) = 0`
`or 50 R_x+600-100R_x=0`
`:. R_x=12 Omega`