兩線圈反向串聯
![反向串聯](/img/0/ba7/wZwpmL4YzN0YzM4cjN0MTN1UTM1QDN5MjM5ADMwAjMwUzL3YzLwgzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
把兩個線圈的同名端連在一起,接入電路時電流均從異名端流入,從異名端流出,稱這種連線方式為反向串聯,簡稱反接,如右圖一a所示。
根據同名端、電壓、電流的關係標出自感電壓和互感電壓的參考方向如右圖一a所示,則有:
![反向串聯](/img/2/408/wZwpmL3MDNzkTN1EjN0MTN1UTM1QDN5MjM5ADMwAjMwUzLxYzL3gzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
用相量式表示為:
![反向串聯](/img/9/416/wZwpmLyQDO4gDN4YDN0MTN1UTM1QDN5MjM5ADMwAjMwUzL2QzLzUzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![反向串聯](/img/b/eb3/wZwpmLyEjM1MjM0IjN0MTN1UTM1QDN5MjM5ADMwAjMwUzLyYzLxYzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
如果用表示反串時的等效電感,則:
![反向串聯](/img/7/f70/wZwpmLygDM2QDNzIDN0MTN1UTM1QDN5MjM5ADMwAjMwUzLyQzL1QzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
(1-1)
等效電路如右圖一b所示。
反接時等效電感是否會小於零呢?不會的。
![反向串聯](/img/a/51e/wZwpmLzIDO0EzN5cjN0MTN1UTM1QDN5MjM5ADMwAjMwUzL3YzL4IzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
由可知:
![反向串聯](/img/b/7dc/wZwpmL3MjNzgzM1UTN0MTN1UTM1QDN5MjM5ADMwAjMwUzL1UzL0UzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
所以
![反向串聯](/img/2/35a/wZwpmLwEjMzgTO3IjN0MTN1UTM1QDN5MjM5ADMwAjMwUzLyYzLyQzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
由於
![反向串聯](/img/2/3d9/wZwpmLzMDOzETN3ITN0MTN1UTM1QDN5MjM5ADMwAjMwUzLyUzL0IzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
所以
![反向串聯](/img/f/d25/wZwpmLxcTN5MzNzATN0MTN1UTM1QDN5MjM5ADMwAjMwUzLwUzLwQzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
可見,反向串聯時,等效電感不會出現負值。
由上面的式子及推導可知,順接時的等效電感大於反接時的等效電感,且兩者都大於零,根據這個特點,還可以用來判別兩個線圈的同名聯關係,並可測出互感係數M的大小。
順向串聯時的等效電感:
![反向串聯](/img/d/591/wZwpmL4YjN5EDNzIDN0MTN1UTM1QDN5MjM5ADMwAjMwUzLyQzL4gzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
反向串聯時的等效電感:
![反向串聯](/img/7/f70/wZwpmLygDM2QDNzIDN0MTN1UTM1QDN5MjM5ADMwAjMwUzLyQzL1QzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
將兩式相減得:
![反向串聯](/img/7/c75/wZwpmLxEDMxkjM1kTN0MTN1UTM1QDN5MjM5ADMwAjMwUzL5UzL4EzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
故互感係數M為:
![反向串聯](/img/1/640/wZwpmL1YTM3cTMxQDN0MTN1UTM1QDN5MjM5ADMwAjMwUzL0QzL3AzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
實驗室經常用這種方法測量互感係數。
互感線圈的反向串聯
![反向串聯](/img/8/a22/wZwpmLzITNwAjM5kTN0MTN1UTM1QDN5MjM5ADMwAjMwUzL5UzLzQzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
所為反向串聯,就是兩個線圈的同名端相連線,如右圖二所示。
電流從兩個線圈的異名端流入,各電壓的參考方向均按習慣選法,示於圖中。
對於正弦電流來說
![反向串聯](/img/a/2e6/wZwpmLycTOxAzN3ATN0MTN1UTM1QDN5MjM5ADMwAjMwUzLwUzL1UzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![反向串聯](/img/2/8f2/wZwpmLyIDM2MDNyMTN0MTN1UTM1QDN5MjM5ADMwAjMwUzLzUzL2MzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![反向串聯](/img/3/ce3/wZwpmL2AjM3gDMwMDN0MTN1UTM1QDN5MjM5ADMwAjMwUzLzQzLzEzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
![反向串聯](/img/f/b5f/wZwpmLzAzNyYDM1EDN3UzM1UTM1QDN5MjM5ADMwAjMwUzLxQzL1gzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
式中,為線圈反向串聯的等效電感
![反向串聯](/img/d/c1d/wZwpmL3YDOxgDO2IjN0MTN1UTM1QDN5MjM5ADMwAjMwUzLyYzL0AzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![反向串聯](/img/f/b5f/wZwpmLzAzNyYDM1EDN3UzM1UTM1QDN5MjM5ADMwAjMwUzLxQzL1gzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
上式中會不會出現負值呢?
由於
![反向串聯](/img/4/6db/wZwpmL1QzN3cDMzQDN0MTN1UTM1QDN5MjM5ADMwAjMwUzL0QzL3AzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
所以
![反向串聯](/img/8/ed2/wZwpmL0MzN5UTN0cjN0MTN1UTM1QDN5MjM5ADMwAjMwUzL3YzL2AzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
因此
![反向串聯](/img/d/17c/wZwpmL2gTM2gzN4ETN0MTN1UTM1QDN5MjM5ADMwAjMwUzLxUzL4UzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
即
![反向串聯](/img/f/d25/wZwpmLxcTN5MzNzATN0MTN1UTM1QDN5MjM5ADMwAjMwUzLwUzLwQzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![反向串聯](/img/f/b5f/wZwpmLzAzNyYDM1EDN3UzM1UTM1QDN5MjM5ADMwAjMwUzLxQzL1gzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
這表明不會出現負值。
反向串聯電動勢
繞組正向串聯也稱首尾相連,即兩個繞組的異名端相連,總電動勢為兩個電動勢相加,電動勢會越串越大。
繞阻反向串聯也稱尾尾相連和首首相連,即兩個繞組的同名端相連,總電動勢為兩個電動勢之差。
利用繞組正、反向串聯時,總電動勢差別很大的特點,可以用來判別兩個繞組的同名端。