把滑动变阻器分成Ra与Rb两部分,Rb与定值电阻Ro并联
R总=Ra+RoRb/(Ro+Rb)
滑变在干路减小的电阻为R,干路为Ra-R,支路Rb+R与Ro并联
R总'=Ra-R+Ro(Rb+R)/(Ro+Rb+R)
R总-R总'=R+RoRb/(Ro+Rb)-Ro(Rb+R)/(Ro+Rb+R)把后两项通分
=R-Ro²R/(Ro+Rb)(Ro+Rb+R)
(Ro+Rb)(Ro+Rb+R)>Ro²
Ro²R/(Ro+Rb)(Ro+Rb+R)<R
R-Ro²R/(Ro+Rb)(Ro+Rb+R)>0
R总-R总'>0
R总'<R总
总电阻变小