Question

What is the relative error in the effective resistance in a parallel combination?`R_effective=frac{R_1xxR_2}(R_1+R_2)`.So what will `Delta(R)//R` be?

Answer 1

For parallel combination of two resistors, we have,

`1/R = 1/(R_1) + 1/(R_2)`

or, `-(delta R)/R^2 = -(delta R_1)/(R_1)^2 - (delta R_1)/(R_2)^2`

or, `(delta R)/R = R((delta R_1)/(R_1)^2 + (delta R_1)/(R_2)^2)`

Now,given, `R=((R_1)(R_2))/(R_1 +R_2)`

So, `(delta R)/R=((R_1)(R_2))/(R_1 +R_2)((delta R_1)/(R_1)^2 + (delta R_1)/(R_2)^2)`