题目内容
(16分)交流发电机的端电压是220伏,输出功率为4400瓦,输电导线总电阻为2欧。试求:①用户得到的电压和功率各多大?输电损失功率多大?②若发电机输出端用1:10的升压变压器升压后,经同样输电导线输送,再用10:1的降压变压器降压后供给用户,则用户得到的电压和功率又多大?
①180V 3600W ②219.6V 4392W
试题分析:①如图,由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824221656537453.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824221657348985.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242216591731973.png)
由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824221700515592.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242217017321070.png)
由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824221703151606.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242217043841292.png)
输电损失功率为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242217060061116.png)
②输电电路如图所示
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082422170719211777.png)
根据理想变压器原副线圈两端的电压与匝数成正比可得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824221708533640.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242217095471229.png)
因理想变压器不改变功率,即
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824221710780420.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824221711996749.png)
由图可知:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242217132761154.png)
由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824221714570643.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242217158961371.png)
用户得到的功率等于发电机的输出功率减去输电线上损失的功率,即
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242217171291127.png)
故用户得到的电压和功率分别为219.6V和4392W。
![](http://thumb2018.1010pic.com/images/loading.gif)
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