如图所示,设R1=R2=R3=R4=R,求开关S闭合和断开时,A、B两端的电阻之比为_.
问题描述:
如图所示,设R1=R2=R3=R4=R,求开关S闭合和断开时,A、B两端的电阻之比为______.
答
开关闭合时,电路结构为:R4被短路,R1、R2、R3并联,AB端总电阻为RAB=
R1 3
开关断开时,电路结构为:R3、R4串联后再与R1、R2并联,R3、R4串联电阻为R34=2R,R1、R2并联电阻R12=
R,1 2
则AB端总电阻为RAB′=
=2R×
R1 2 2R+
R1 2
R2 5
则
=RAB R′AB
=
R1 3
R2 5
5 6
故答案为:
5 6