解:(1)当闭合开关S
0、S
1,断开开关S
2时,灯L
1两端的电压U
1=I
1R
1,当闭合开关S
2,断开开关S
0、S
1时,灯L
1两端的电压U
2=I
2R
1=
![](http://thumb.1010pic.com/pic5/latex/13.png)
U
1,
所以
![](http://thumb.1010pic.com/pic5/latex/18727.png)
=
![](http://thumb.1010pic.com/pic5/latex/228962.png)
=
![](http://thumb.1010pic.com/pic5/latex/19371.png)
=
![](http://thumb.1010pic.com/pic5/latex/453582.png)
=
![](http://thumb.1010pic.com/pic5/latex/7082.png)
.
答:电流表前后两次电流之比为2:1.
(2)当闭合开关S
0、S
1,断开开关S
2时,灯L
1正常发光,灯L
1与电阻R
3串联,I
1=
![](http://thumb.1010pic.com/pic5/latex/208505.png)
,
当闭合开关S
2,断开开关S
0、S
1时,灯L
1、灯L
2、电阻R
4串联,I
2=
![](http://thumb.1010pic.com/pic5/latex/453583.png)
所以
![](http://thumb.1010pic.com/pic5/latex/19371.png)
=
![](http://thumb.1010pic.com/pic5/latex/453584.png)
=
![](http://thumb.1010pic.com/pic5/latex/453585.png)
=
![](http://thumb.1010pic.com/pic5/latex/453586.png)
=
![](http://thumb.1010pic.com/pic5/latex/7082.png)
,
整理得:R
4=2R
3-R
1,
电阻R
3消耗的电功率P
3=I
12R
3=
![](http://thumb.1010pic.com/pic5/latex/229673.png)
R
3=2W,①
电阻R
4消耗的电功率为P
4=I
22R
4=
![](http://thumb.1010pic.com/pic5/latex/453587.png)
R
4=
![](http://thumb.1010pic.com/pic5/latex/453588.png)
(2R
3-R
1)=0.25W,②
①②联立整理可得:R
3=8Ω,R
1=12Ω,
所以R
2=24Ω,
灯L
1的额定电功率P=I
12R
1=
![](http://thumb.1010pic.com/pic5/latex/229673.png)
R
1=
![](http://thumb.1010pic.com/pic5/latex/453589.png)
×12Ω=3W.
答:灯L
1的额定电功率为3W.
(3)电阻R
4的阻值R
4=2R
3-R
1=2×8Ω-12Ω=4Ω.
答:电阻R
4的阻值为4Ω.
等效电路图:
当闭合开关S
0、S
1,断开开关S
2时,灯L
1与电阻R
3串联,电流表测量总电流,电压表测量灯L
1两端的电压,等效电路图如图:
![](http://thumb.1010pic.com/pic5/upload/201310/5284bbad6a29d.png)
当闭合开关S
2,断开开关S
0、S
1时,灯L
1、灯L
2、电阻R
4串联,电流表测量总电流,电压表测量灯L
1两端的电压,等效电路图如图:
![](http://thumb.1010pic.com/pic5/upload/201310/5284bbad7b363.png)
分析:(1)当闭合开关S
0、S
1,断开开关S
2时,灯L
1正常发光,灯L
1与电阻R
3串联,电流表测量总电流,电压表测量灯L
1两端的电压,当闭合开关S
2,断开开关S
0、S
1时,灯L
1、灯L
2、电阻R
4串联,电流表测量总电流,电压表测量灯L
1两端的电压,根据前后两次电压表的示数列出等式,从而求出电流表前后两次电流之比.
(2)已知电流表前后两次电流之比,根据公式I=
![](http://thumb.1010pic.com/pic5/latex/19029.png)
列出等式,求出各个电阻之间的关系,再根据公式P=I
2R求出各个电阻的阻值和灯L
1的额定电功率.
(3)根据已经求出的各个电阻之间的关系和大小,求出电阻R
4的阻值.
点评:本题考查电流、电阻和额定功率的计算,关键是公式及其变形的灵活运用,难点是分析电路开关断开与闭合时电路的连接情况,重点记住串联电阻的规律.