并联电路中并联N个电阻为R的电阻,总电阻为什么是R尀N?

2025-04-04 18:44:16
推荐回答(1个)
回答1:

并联电路的各个支路电压相等 ,总电流等于各个支路电流之和:

R总 = U / I总
= U / (I1 + I2 + 。。。+ Rn)
等式两边取倒数:
1/R总 = (I1 + I2 + 。。。+ Rn) / U
= I1/U + I2/U + 。。。+ In/U
= 1/R1 + 1/R2 + 。。。+ 1/Rn
如果 R1 = R2 = R3 = Rn = R :
1/R总 = 1/R1 + 1/R2 +。。。+ 1/Rn
= n / R
R总 = R/n