题目内容
一只氖管的起辉电压与交流电压U="50sin314t" V的有效值相等,若将此交流电接到上述氖管的两极,求氖管每次发光持续的时间Δt及1 s时间里发光的次数n.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120647516323.gif)
起辉电压与交流电压的有效值相等,意即电压瞬时值u≥
时,氖管发光;而当电压瞬时值u<
时,氖管熄灭,画出u="50sin314t" V的图象,如下图所示,由图象看出在第一个半周期内发光时间Δt=t2-t1,再由电压瞬值表达式可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241206475623695.jpg)
=Umsin314t,即sin314t=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120647594266.gif)
所以314t1=
,314t2=
π
t1=
,t2=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120647640317.gif)
可得Δt=t2-t1=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120647516323.gif)
所以,每次发光持续的时间为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120647516323.gif)
因为1个周期内可发光2次,所以1 s发光次数n=2·
=2×
=100.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120647531405.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120647531405.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241206475623695.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120647531405.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120647594266.gif)
所以314t1=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120647594229.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120647625223.gif)
t1=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120647625324.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120647640317.gif)
可得Δt=t2-t1=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120647516323.gif)
所以,每次发光持续的时间为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120647516323.gif)
因为1个周期内可发光2次,所以1 s发光次数n=2·
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120647687227.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120647703698.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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