题目内容
如图所示为交流发电机示意图,匝数为n=100匝的矩形线圈,边长分别为0.1m和0.2m,内阻为 5Ω,在磁感应强度B="0.5" T的匀强磁场中绕OO′轴以
r/s的转速匀速转动,转动开始时线圈平面与磁场方向平行,线圈通过电刷和外部 20Ω的电阻R相接、求
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241238239021665.gif)
(1)写出线圈内产生的交变电动势瞬时值的表达式
(2)电阻R上所消耗的电功率是多少
(3)如果保持转子匀速转动,外力每分钟需要对转子所做的功;
(4)从计时开始,线圈转过
的过程中,通过外电阻R的电荷量
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123823886430.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241238239021665.gif)
(1)写出线圈内产生的交变电动势瞬时值的表达式
(2)电阻R上所消耗的电功率是多少
(3)如果保持转子匀速转动,外力每分钟需要对转子所做的功;
(4)从计时开始,线圈转过
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123823917334.gif)
解:(1)w=2πn=50
rad/s………………………………………1分
感应电动
势最大值Em=nBSW=100×0.5×0.1×0.2×50
=50
V…1分
交变电动势瞬时值表达式e="Em" coswt=50
cos50
t V…………… 1分
(2)感应电动势有效值E=
=50V………………………………………1分
设流过电阻R电流为I,I=
=
A=2A……………………1分
电阻R上消耗功率P=I2R=2×2×20W=80W…………………………1分
(3)外力对转子所做的功全部转化为热量
即W=Q=I2(R+r)t=2×2×(20+5)×60J=6×103J………………2分
(4)Q=It=
=
………………………………………………1分
线圈转过π/3的过程中,△S=Ssinπ/3
则Q=
=
C=3.5×10-2C…………2分
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123823933225.gif)
感应电动
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412382394965.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123823933225.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123823933225.gif)
交变电动势瞬时值表达式e="Em" coswt=50
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123823933225.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123823933225.gif)
(2)感应电动势有效值E=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123824042424.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412382405872.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123824183404.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123824229348.gif)
电阻R上消耗功率P=I2R=2×2×20W=80W…………………………1分
(3)外力对转子所做的功全部转化为热量
即W=Q=I2(R+r)t=2×2×(20+5)×60J=6×103J………………2分
(4)Q=It=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123824245472.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123824261506.gif)
线圈转过π/3的过程中,△S=Ssinπ/3
则Q=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123824261506.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123824526889.gif)
略
![](http://thumb2018.1010pic.com/images/loading.gif)
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