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______.

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=

1
3
R
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=
1
2
R,
则AB端总电阻为RAB′=
2R×
1
2
R
2R+
1
2
R
2
5
R

RAB
R′AB
1
3
R
2
5
R
5
6

故答案为:
5
6