3个电阻并联,R1=10,R2=20,R3=30,总电阻等于60/11,但是用R=R1R2R3/R1+R2+R3的式子算的结果是100.

题目

3个电阻并联,R1=10,R2=20,R3=30,总电阻等于60/11,但是用R=R1R2R3/R1+R2+R3的式子算的结果是100.
为什么两个结果不一样?60/11是正确答案,用1/R=1/R1+1/R2+1/R3算的.

答案

1/R =1/R1 + 1/R2 + 1/R3,
计算,
1/R = (R2R3+R1R3+R1R2)/(R1R2R3),
再计算,
R =(R1R2R3)/(R2R3+R1R3+R1R2),
所以,R=R1R2R3/R1+R2+R3 是错误的式子