题目内容
如图所示为一输电系统,A地有一台升压变压器,B地有一台匝数比为10:1的降压变压器,降压变压器副线圈上的电流为100A,输出功率是12kW,A、B两地输电线的电阻是20Ω,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241809425337846.jpg)
(1)升压变压器输出端的电压;
(2)若不用变压器,要在B地得到同样大小的电流和电功率,那么在A地要用多大的电压将电能输出?
(3)两情况下输电线上损失功率之比是多少?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241809425337846.jpg)
(1)升压变压器输出端的电压;
(2)若不用变压器,要在B地得到同样大小的电流和电功率,那么在A地要用多大的电压将电能输出?
(3)两情况下输电线上损失功率之比是多少?
(1)1400V(2)2120V(3)1:100
试题分析:(1)降压变压器输出端电压:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241809425641067.png)
所以由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824180942876682.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824180943141676.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241809433911011.png)
输电线上损失的电压为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241809436411008.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824180943921439.png)
所以升压变压器输出端的电压:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241809441711081.png)
(2)若不用变压器,B处电压:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824180944436876.png)
线路压降:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824180944655803.png)
所以A处电压为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824180944873741.png)
(3)有变压器时,线路损耗功率:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824180945138891.png)
无变压器,线路消耗功率:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824180945419930.png)
所以两情况下输电线上损耗功率之比为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824180945747556.png)
点评:熟练掌握理想变压器的电流、电压和匝数之间的关系是解此题的关键
![](http://thumb2018.1010pic.com/images/loading.gif)
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