灯L1的额定电压是灯L2额定电压的2倍.将L1和L2并联在电压为U的电路中时,灯L2消耗的电功率为9W;若将灯L1和L2串联接入电压仍为U的电路中时,灯L2消耗的电功率为4W.不考虑灯丝电阻的变化,则下列说法中正确的是( )
A.在并联和串联两种方式中,灯L2两端的电压之比为3:2
B.在串联和并联两种方式中,通过灯L1的电流之比为3:1
C.灯L2的电阻是灯L1的电阻的2倍
D.灯L1和L2的额定功率之比为2:1
【答案】
分析:本题考查灯泡电功率相关知识以及电路串联和并联电流电压关系.属于常规考点,考试必然出现.属于中等题目.
A选项利用功率
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/0.png)
,得出并联和串联电压是3:2.
B选项有很强的干扰性,需要考试清楚审题,计算出串联和并联电流之比是1:3,也可以直接排除,串联电流必然小于并联电流,不可能是3:1,此法作为检查的一种方法,不失为一种选择.
C选项通过串联是电压比为2:1得出.
D额定电压之比为2:1,电阻之比为1:2.利用
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/1.png)
求比例得出功率比为8:1.
解答:解:A、在并联和串联两种方式中,灯L
2的功率之比
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/2.png)
=
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/3.png)
=
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/4.png)
=
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/5.png)
,所以
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/6.png)
=
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/7.png)
,故A正确.
B、两灯串联的总电压是U,L
1的分压小于U,两灯并联时L
1的电压为U,L
1的电阻不变,由I=
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/8.png)
知灯L
1的串联电流应小于并联电流,故B错误.
C、由A知
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/9.png)
=
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/10.png)
,由题意知U
2=U,所以U'
2=
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/11.png)
U,L
1和L
2串联电路总电压为U,则U'
1=U-U'
2=U-
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/12.png)
U=
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/13.png)
U,
两灯串联时,电流相等,
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/14.png)
=
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/15.png)
=
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/16.png)
=
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/17.png)
=
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/18.png)
,即灯L
2的电阻是灯L
1的电阻的2倍,故C正确.
D、灯L
1的额定电压是灯L
2额定电压的2倍,设灯L
1的额定电压是2U,则灯L
2额定电压是U,由C知
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/19.png)
=
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/20.png)
,
灯L
1和L
2的额定功率之比
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/21.png)
=
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/22.png)
=
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/23.png)
=
![](http://thumb.zyjl.cn/pic6/res/czwl/web/STSource/2013102409250204706605/SYS201310240925020470660014_DA/24.png)
,故D错误.
故选AC.
点评:知道串并联电路的特点、掌握并灵活应用欧姆定律、电功率的公式是解本题的前提与基础,比值法的应用是本题的解题关键.