已知R1=4Ω,R2=6Ω,若将R1和R2串联在电路中,则R1与R2两端的电压之比U1:U2=________,消耗的功率之比P1:P2=________;若将R1与R2并联在电路中,则通过R1与R2的电流之比I1:I2=________,总电阻R总=________Ω.
2:3 2:3 3:2 2.4
分析:(1)两电阻串联时,通过的电流相等,根据欧姆定律求出两电阻两端的电压之比,根据P=I
2R求出两电阻消耗的电功率之比;
(2)两电阻并联时,两端的电压相等,根据欧姆定律求出通过两电阻的电流之比,根据电阻的并联求出总电阻.
解答:(1)两电阻串联时,通过的电流相等,
根据欧姆定律可得:
![](http://thumb.1010pic.com/pic5/latex/18727.png)
=
![](http://thumb.1010pic.com/pic5/latex/203464.png)
=
![](http://thumb.1010pic.com/pic5/latex/34795.png)
=
![](http://thumb.1010pic.com/pic5/latex/283892.png)
=
![](http://thumb.1010pic.com/pic5/latex/168.png)
,
根据P=I
2R可得:
![](http://thumb.1010pic.com/pic5/latex/19369.png)
=
![](http://thumb.1010pic.com/pic5/latex/250816.png)
=
![](http://thumb.1010pic.com/pic5/latex/34795.png)
=
![](http://thumb.1010pic.com/pic5/latex/168.png)
;
(2)两电阻并联时,两端的电压相等,
根据欧姆定律可得:
![](http://thumb.1010pic.com/pic5/latex/19371.png)
=
![](http://thumb.1010pic.com/pic5/latex/168689.png)
=
![](http://thumb.1010pic.com/pic5/latex/134420.png)
=
![](http://thumb.1010pic.com/pic5/latex/33.png)
,
∵
![](http://thumb.1010pic.com/pic5/latex/58382.png)
=
![](http://thumb.1010pic.com/pic5/latex/134423.png)
+
![](http://thumb.1010pic.com/pic5/latex/134424.png)
,
∴R
总=
![](http://thumb.1010pic.com/pic5/latex/19012.png)
=
![](http://thumb.1010pic.com/pic5/latex/176683.png)
=2.4Ω.
故答案为:2:3;2:3;3:2;2.4.
点评:本题考查了串联电路的电流特点和并联电路的电压特点以及欧姆定律、电功率公式的灵活应用,最好能记住他们之间的关系,为以后解题带来方便.