论证:R1和R2并联的电路中,I1=(R2/R1+R2)*I,I2=(R1/R1+R2)*I

问题描述:

论证:R1和R2并联的电路中,I1=(R2/R1+R2)*I,I2=(R1/R1+R2)*I

并联电路各支路的电压相等,U1=U2=U
并联电路各支路的电流之和等于干路电流,I=I1+I2
I1=U1/R1=U/R1,I2=U2/R2=U/R2
I=U/R1+U/R2=U(1/R1+1/R2)=U(R1+R2)/R1R2
U=IR1R2/(R1+R2)
I1=U/R1=(R2/R1+R2)*I
I2=U/R2=(R1/R1+R2)*I

总电阻是R2*R2/R1+R2!并联分流!

R1和R2并联的等效电阻为:R=R1R2/(R1+R2)
则并联电压两端的电压为:U=IR=I*R1R2/(R1+R2)
可知:
通过R1的电流为:I1=U/R1=[I*R1R2/(R1+R2)]/R1=I*R2/(R1+R2)
通过R2的电流为:I2=U/R2=[I*R1R2/(R1+R2)]/R2=I*R1/(R1+R2)
你的式子少括号

V=I1*R1 + I2* R2=I *RT
RT=R1*R2/(R1+R2)
I1+I2=I
3式联立,就可以了