considering below figure (attachment) plz can any body tell me how to derive equation relating Vo,X (i think it can be done using mesh equations..but im not sure with it..) and derive the relation for linearity error and the maximum linearity error percentage...advance thanks.........

 

plz can any body help me regarding above post.....

 

If X is a distance measurement you can't solve the problem as you have presented it.

Suppose the total resistance along the potentiometer body is Rp - which is the missing information.

The positional resistance is then

\(Rx=\frac{X}{Xm}.Rp\)

So the voltage measured at X would be

\(Vx=\frac{V1.(Rx||Rm)}{Rp-Rx+(Rx||Rm)}\)

where

\(Rx||Rm=\frac{Rx.Rm}{Rx+Rm}\)

If the meter resistance were infinite than you would have an ideal case in which

\(Vx=\frac{V1.X}{Xm}\)

So the non-linearity you seek to quantify is the deviation from the actual value of Vx measured, taking account of the meter loading due to finite meter resistance (Rm), versus the ideal value of Vx measured with infinite meter resistance.

 

thank you very much!
actually earlier i was wondering, what does it mean by linearity error?
and now i understood its ,
simply
"the error caused due to the presence of the measuring instrument in the system and the deviation of its properties from ideal case of the measuring instrument." or (error caused due to presence of non ideal measuring instrument in the cicuit)

ie: in this case the error of the reading "resistance Rx",due to the presence of "voltmeter resistance Rm" in parallel with Rx...