题目内容
图为一输电系统,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:
(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耗功率之比是多少?![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241359501424524.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耗功率之比是多少?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241359501424524.jpg)
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135950314543.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241359501741061.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135950252727.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135950314543.png)
(1)降压变压器输出端电压:
所以由
得
由 ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241359505011005.png)
输电线上损失的电压为:
(
)
所以升压变压器输出端的电压:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241359501741061.png)
(2)若不用变压器,B处电压:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135950782860.png)
线路压降:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135950876796.png)
所以A处电压为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135950252727.png)
(3)有变压器时,线路损耗功率:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135951000880.png)
无变压器,线路消耗功率:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135951110925.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/20140824/20140824135950314543.png)
本题考查的是远距离输电问题。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://thumb.1010pic.com/pic2/upload/papers/20140824/201408241359503611052.png)
所以由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135950408662.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135950454659.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241359505011005.png)
输电线上损失的电压为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135950579985.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135950673421.png)
所以升压变压器输出端的电压:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241359501741061.png)
(2)若不用变压器,B处电压:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135950782860.png)
线路压降:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135950876796.png)
所以A处电压为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135950252727.png)
(3)有变压器时,线路损耗功率:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135951000880.png)
无变压器,线路消耗功率:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135951110925.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/20140824/20140824135950314543.png)
本题考查的是远距离输电问题。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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